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HENDERSON, AMD - ■ MISS R. CHURCH, MISS A. HARDING. 'Vteofy TMt**n in Okurtk Sfn*i Mmlti Sckool, Tof9iU». t^mCB QO CENTS. *i ^ THE EPUCATWIAL tUiS^MTNG CtS, Ik ■A% I i|^Mp^>PfHI^7 Entered according to Act of the Parliament of Canada, in the year one thousand eight hundred and ninety-»even. by iJ. E. Hkndbrson, Miss R. Church and Miss A. HARniNo. at the Department ot Ag^riculture. fSi-' PREFACE. The following ezercues « -e intended to farniih prim- ary teacher, with a .impl«, practical and intelligible method of preMnting number to litUe children. A« Arithmetic is taught not only for its practical u-ility, but also as a means of mental discipline, it foUows that in order t., develop thought and awaken interest, the teach- er must present the subject with an orderUness of ar- rangement and a unity of purpose in order to secure clear, definite conceptions on the part of the pupil, and enable him to make rapid and thorough progress. The plan laid down in the following pages has been tested and found to work satisfactorily. It should be the practice of the teacher to make first the process clear, then to secure skill and quickness in its working. If the procest be not dear the working will not be inteUi- gent. The methods of teaching number presented are not mere theories ; all of them have been tested by actual ex- perience in the Bchool-room» and it is therefore to be hoped that this Uttle book may be of value and benefit to many young teachers entering the profession. THE AUTHORS. Arithmetic for First Boole Classes NOTATION. The tMchmg of notation to very young children rt- quirw mueh care »...d skiU. In it U inTolved the diffloalt tranution from the concrete to the abstrMt. The tint leMons m number ahould be given by means of Mncible objocta. When a child enten the primaiy room from the kudei;garten, he hui a ^ured (by experience in atiok- laying, peaa-work, mat-weaving, the leparating and unit- ing of cube, etc ) a degree of mental power by the uae of hia inventive and constructive faculties : he has obU aed Ideas not onlv of form, but of number. His flrtl format lesson m arithmetic should be an interesting one. ChU- drens numerical ideas are often vague and indefinite Use objects, then, and these number exerdses wiU oive the pupils distuicc ideas of arithmetical quantities. Arithmetical language is the method by which we ex- S^iL"""***"- i^'»^^^,o»'UndwrUUH. The former IS called num»raH»n, the latter »4o«a«on. The oral v ^f?tu *"**l°»etic (numeration) is taught in oonnec i with the development of the idta of number. The v ^a and the word are so intimately related that the former l«»d8 immediately to the latter. As soon ss »be name of the number u learned the child is t. . rht to ex .. sss that number in a written character. Wt..\ n langusRe of the numbers is notation. -"Hju-b" «« »ne Lesfoa I. pretend to go asleep). At the call " Awake " aU at once are interested. * (5) - ^'*: " ARITHMETIC. T. Who came to see you when sleeping ? P. A slat, a stick. T. Hold slat in right hand. T. How many slats have you in the right hand ? P. One slat. T. Place on the table otus bean, one pebble, one slate, om book, &c. bhow me one finger, one cube, one marble, (object bemg to accumulate instances). Teacher then pkces figure (1) on the blackboard, the written character representing the idea. ChUdren make It on their slates. Tell them that it represents on^ stick, one slat, one flag, one top, one marble, &c. Impress upon them the fact that " 1 " always means one somethingfso that they will recognize the written symbol for one. ^■ii'—^orm. of figures might be made interesting bv comparing them to different objects. 1 stands stmcht like a good soldier. «* As before, give another slat to each child. Holders* slat in right hand. How many in right hand ? One. Hold sectMtd slat in left hand. How many in left ? One. Transfer left hand slat to right hand. How many ones in right hand. Two ones. torn " A (like a little duck in the water). Let the children make the figure, on their sktes. Make them understand that figure « « " stands for two ZmaX, la'""' ''' '"^ '" ^^^'''^ °"* '«« ^--. How many ones in two ? Take away one, how many left ? How many arms has a man ? How many ears has a boy ? How many eyes has a girl 1 Numbers three to Jive. Proceed in a similar way. NOTATION. Testing ExercisM. 1. Place groups on the table. 0. 00. 000. 0000. 00000. a. Let the teacher name them in order. Pupils give the number of the group b. Let the teacher point to them irregularly, each group to be named by class individuaUy or collectively. ./ .V. ^i^''^\^ ^""^ g'°"P« on the desk as direct- ed-other children decide whether right or not. d. Distribute objects, such as beans, peas, Ac. Teacher places figure-e.g. (6). Children make group correspond- ® • J^**'®/.*?mF''"? ^?) ^°^ *» ™any smaUer groups as possible. ChUcfren led to think of Jive as five ^s,thrTe and two, four and one, &c. f. Arrange your^.>e group in ones. (1) How many ones ? Five. (2) Take away middle one. How many left ? Four. TuH) twos. ' (3) Make three groups, using the five peas, beans, &c. TI,io K '^^' ^' ^' ^' &c. ihis can be made a very interesting exercise. in this wav teach the numbers up to vine (9) „nMwiP"P m reading and writing numbers to "9." until they are entirely familiar with them. BUSY WORK. tr«iniV?P'''"^J'^ ^^''^ ^""T *^« fi"*^ Children Should be trained to make correct forms of the figures. Perfect mSn T'-"" " ju-t as necessary as perfect letJetfor- S the ficn, ""^"^ f '^°"'*= ^""^ ^'^^'' «»«» to make some of the figures properly, as many children have a tenden^ to reverse the forms of some-2, 3. 4 5 6 7 8 S obviate this a little story connecting tj^ fom of the fi.uT^ Zn Sr-tt-^'"''^" '-'"' ^^'" ^^" '^ '^'^^^- 1:^3 8 ARITHMETIC. 6— An umbrella handle. Curve roust be to the right, because we want to hold the umbrella in the right hand. 3 — Have children make two apples — ** Tom takes a big bite out of his — i Nell takes a big bite out of hers — D This is how the apple looks — 3. 4— L i» a chair with perforated seat. Boy put a darning needle through one of the holes. This is the chair L- This is the knitting needle I. The chair with the knitting needle looks like this 4, figure 4- 8- Snake, the head, of course at the top, but to the right, thus — S. 8, e.g., 8, twisted, coiling shape of lK)dy shown— 8. These illustrations are only suggestive. Every teacher will have certain devices of her own See that every child learns the correct formation of the figures at this stage. This will save a great deal of trouble afterwards. 1. Make a row of I's standing like soldiers. Let them stand in the school yard : 111111 1111111 2. Make a row of 2*8 climbing a ladder : 2 For variety, let them be little ducks in the water, must be perfect ducks if they want to swim well. They NOTATION. 9 l,i5"f^^fi *!."''' u^f> ^'''"S: up the hUl. They look /W .'fi' »'^^- ^'^^ ^""' "^'"" «**^« «f the hill, and t/iree " 5 s " running down. ° '^ . ' 4. Place groups irregularly, e.g., people looking at the Jubilee procession: o «« 111 11111 iiiii]i 11 mill 1 iiuiiuiuiiiiiuii, «> 5 7 2 6 I 4 y 8 Let the children place number in group underneath. Teaching of Ten. Review the numbers one to niue. Distribute ten slats ^ rewhed children pick up slats till the tenth T. Hold nwie slats in the left hand. T. Hold new slat in the right hand ,,,^tf ^^®' t^« T'SJ^J h*nd slat to the left one. How many altogether? Give the new name ten. Let them show the ten slats and name them. Pick out ten beans, ten marbles, &c. f},« „ ''*'•' "^X^l*" ?°'"« ^ P^*y * g*'"^' and the rule of the game is that when we get ten slats we must tie them up in a bundle ; if not, we are out. and cannot pky. Jfeth^bTnlTes'r '"' '''' '' "'^^^ ^' ^'^ ^" T. Hold bundle in left haua. T. How many bundles have you ? One. T. How many slats in • bundle ? Ten T. We call it a ten bundle. «illf *. TJ"^ ^^^^ *°' *®" ^'^ bhick-board. Children see that It means ten- something? as before. Test as be- Sli. Tu <*«•}??»<« the ten and its position use colored chalk-.thu«, 10; or make the o»*« indicating the f Z^}X)M 20. As before, on reaching 19, another slat is given Game NOTATION. 11 Draw the two roomed house, designating the frans* room and also units' room. How many bundles now ? Two. How many in each bundle ? Ten. How many tens have we ? Two. Give name and symbol for the two bundles. Twen*^y. Twenty means how many tens ? Two. Copy symbol. Plac^ in the nouse : 20-30. Process practically the same. Teach to 20, using ob- jects. After thit stage there is no further necessity for them, except perhaps for one or two individual pupils. Teacher may exemplify or ebe have two children come up : one holds three bundles. That means three tens- new name— thirty. T. Who will come up and find Let them arrange the numbers in the house in order from one to 39. &c. * ^32 34 36 31 33 .15 37 38 39 When children are lamUiar with t.ie new names for symboUi, 30, 40, 60, &c., up to 90, the connection be- tween them and the numbers from 12 to 20 might be con- trasted and explamed thus : .3— three. 13 — thirteen. 30— thirty. ^A S®.*'!'?^!®'* *?* *>** "*««»^" »^^ay«» means on? ^en, and that the termination " ty " means or may mean two tens ^^20), four tens, as in 40, six tens as iu sixty— m short. ty signifies many i "2" «.g» 6 4 2 C. Nines. 1 + 8 or 8 + 1 3+6 6+3 4+5 5+4 2+7 7+2 Those whose sum ia "9" or whose sum ending niiie. IS 4+"4 tenets °'ai .^"•V""-" -»■ i. 9+9 i taught. 2+0 l+l j,8,°^,»l'o.. sum ending £)• jSeve^M. 1+6 or 6+1 4+3 3+4 2+6 5+2 9+8 8+9 ,,^<»e whose sum is , 7 OP whose sum end- mg is "7." F. Sixea. .3+3|Webeenltl°'*2ti """' «+8( taught. 9+7 7+9 o or whose sum end mg is "6." O. Fives. 1+4 or 4+1 3+2 2+3 8+7 7+8 ^+6 6+9 „J|j^® whose sum is . o or whose sum end- ing is "6.' H. Fours. 2 + 2^havebeen9+6'"'6+9 -JS^"^ 'f^''^ """» " 7 + 7 f taught. 8+6 6+8 i„^ i."' /.^^^ ""'» ««^- ADDITION. 21 I. Threes. 1+2 or 2+1 4+9 9+4 6+7 7+6 8+6 5+8 J. Twos. 7+5 or 5+7 1 + 1 /h8vebeen3+9 9-J.3 6 + 6 f taught. 4+8 8+4 K. Ones. 2+9 or 9+2 4+7 7+4 3+8 8+3 5+6 6+5 Those whose sum is three, or whose sum end> ing is three. Those whose sum end- ing is •• 2." Those whose sum end- ing is one. Of^course, the subtraction table will be the converse of 10-2=8 10-5=5 18-9=9, &c. obfeJte"°?Mf ♦S"^^"^^^^" 't^"J^ ^ ^"8ht by mean, of oDjects. It IS the way m which the pupils reallv must ?h?^" '^A ""T ^l^^^^rB if they TrJ to SSSS ^h^}^^ V!5 ?^®*"" ^*''" * ^'^^ ^«"8*J» of fcinie. Children i,T?J^ ^^ ^'^'" concrete to abstract ; from i^ng sumi and differences to thinkitig them. ^ Addition.— Lesson I. -w;?~^^ ®*5^ ^t^^i^** *° ^""K » J»"I« cotton bag. into which are placed eighteen (18) pegs (18=9+9 SaK ^.^n^Tr S'^^*^- T^« P««*«^ eksily handl^^and Sd^loS^ *^ '^" "^^^ advantageous object, in t^^il^ To teach 5 + 6 = 10. ort? nr&^ place their pegs in a little pile at centre or at tho bottom ot their slates. ^""ire T. Place 5 pegs side by side at the top of your slates. ^•8" 1 1 1 1 1— 6 ^^ HiiM 22 ABITHilBTIC. Oppo«te With dtte-pendl place the no. of the gtouv neatn the first group of pegs, e.g. : 1 1 1 1 1 1 1 1 1- 5 1— 5 'I I I I I I I I I —10 B. B. picture. As Wore write symbol of second group opposite. T. How many pegs in 1st group ? Pupili^Five. T. •. .. ..altogether? .. Ten!' How many are ^«e negs and five pegs ? Tm pegs. Ws " " boys? TenCs. &c. ^M — ^"^'wction can be taught simultaneously with i^??^tn.? -'^tK**"^ *^ muftiplication and Kn K in J^^t: "? *5® ?**°^« combination, when the sum of fhrdiffern'c?"^"*' *'* chUdreneasay^id readily Xi' T. Take aw^ five, how many left ? Five. 1. len leaafive, how many ? Five. ^^ How many^iw, do we have to take to make feti/ tw^^nwl'® ^' */« "e'die"; let fchem march in twos. How many twos ? Five. rOBUATION or TABLE. 6 6 6 6 6 6 5 16 26 36 45 66 &o. 10 20 90 40 60 60 H J^ 7? ^■"**"* ^""^« °^ ■'»'■• »nd five more, oren readily answer. —w™. How many slate altogether ? Fifteen. Fifteen = *?»» ,„ m., - , 1 and 6=16 lake 6 more slats = 5=6 How mmj are fiv© and fiv© = Ten, Ohil. ADDITION. 23 We already have one ten and this ten make how many tens ? Two tens. Two tena = twenty. .-.15+6 = 20. So on with 26+5, and the other parts of the table. DRILL. When table is completed, drill in many ways till chil- dren know it perfectly. 1. Let the children repeat the table : (1) Without answer ; (2) " constant figure ; (3) " inconstant figure. 5 5 5. 6 6 E.g.: (1) 5 15 25 35 45 &c. (2) 5 15 25 35 45 le 20 30 40 60 (3) Let them repeat the table rapidly now without guide of any kind. NEXT STEP. To show that any digit added to a number ending in " " will have for its sum ending the digit added. This is merely put in the form of a sum, thus : 6 9 3 8 7 4 10 20 40 10 60 30 16 29 43 18 67 34 Take a ten bundle and six slats. How many ? 16. Take two (ten) bundles and nine. How many ? 29. This lesson is easily taught and readily understood ; the children give the answers rapidly and accurately. We are now ready to apply our knowledge. Little sums may now be given both mentally and fur slate work. mmm^mmmm^Um 24 ABITHMETIC. For mental work, examples given quickly, as i ')11owb Five, five. Five, five, five. Five, five, five, five, six. &c. Slate work, easy at first : 8 9 6 6 6 6 6 6 6 6 5 6 6 6 6 6 6 Have these little sums added rapidly. Insure asainst counting right from the beginning ^^ NEXT STEP. Combinations 1 + 9, 9 + 1. Teach as before^Jbrm table-drill. Give examples- for mental and date work. »"'p*w» Table 9 9 9 9 9 9 1 11 21 31 . I 61 &c. f ,vi!?° t^^'^l ^ **^* '^® numbers n order in the forma- tion of the table, eg.. 9 9 9 9 1 21 11 31 ^c. This means, of course, when Uaching the table when KSIS ^ r«P«».ti^ the table, the nTmbers. of cou^^ should be given m order, e.g., ' 9 9 9 9 1 H 21 31 &c. ADDITION. 26 CARKTINO, Carrying may now be introduced. Take sum 85 95 Draw a little two-roomed house, making the tens' room and the units' room. 85 = eight (tens) and fi /e. 95 = nine (tens) and five. Five and five are how many ? Ten. Ten means one bundle and no single ones. Let the children show the tens' room. We have now one more ten to bring in, five, five are how many 1 Ten. Carry our one ten to its own room, then we have one ten, nine tens, and eight tens. Altogether how many ? Eighteen tens, eighteen tens or one hundred and eighty = 180. Tables should be committed to memory. Teacher simply says : Table, five, five. Pupils repeat it rapidly. METHODS OF niPRESSIKG TABLE. (1) Oral repetition, as above, individually and in class. (2) Place numbers down irregularly, as 5 26 15 45 35. «fec. Every time teacher points add Jive. Children give answers rapidly (3) Number wheel Teacher points to number on cir- cumference of wheel. Pupils add to tliis the number in centre and give answers rapidly. N.B.— Draw a circle on board, place " 6 " in centre, at distances on circumference place numbers 15, 35, 26, 46, etc. (4) Let the i)upils write out the table neatly on slates. (5) Care should be taken that there is no guess work, but that each child understands the process clearly, tA«H and only then will the working be intelligent. Introduce next combinations, 2-f 8, 8-t-2. So on with the others that make ten. The teacher should have a book in which ar« placed J^^^^^ ■aiiuBird £L 26 ARITHMBTIC. 8UIIU involving combinations taught. To make these sums, begin from the bottoi, upwards. For the guidance of the teacher, many sums wiU be found at the end of this littie book which apply the new combination as soon as It 18 taught, and also review the old ones. Rapidity bnd accuracy are easily secured, and very young children learn to add without the habit of counting. In all the combinations impress the sum ending. Thus, 5+6 ends in " " - 9_j.9 « *« 8 " • The signs + and — may be introduced at this stase and readily understood. '^ ' To fix the combinations, to awaken interest and give variety, sometimes have a littie game. Make a houM— some of the httle numbers live here. Mrs. Ten is the mother. Who are her children/ The twitu, 5 and 5 play always together. 1 and 9 walk to school togetiier j and 6 stay home help motiier, « and « pky under the tree when they come from school. ;? and 7 play always together. ' N.B.— Draw a littie house, caU it Mrs. Ten's house: place the numbers as designated. Points to be Remembered. 1. In the new combinations taught bring in always what hM already been learned. For example, when the eights are taught, in the mental and written work con- stantly review the* nines, doubles and tetu. 2. IndividHol adding should be conducted at least onee a day. Every chUd should be asked to add orally. If this practice is continued and no new combination taught till the o/d ones are thoroughly mastered the result will be intelligent, rapid and accurate addition. *•!?; J®*f mI**® combinations in onUr. Do not leave one till the children have obtained perfect mastery over it and can use it readily and intelligently. ' The combinations are given in the order taught, and a sample table is also given; one from each set of combin- ations. ii ADDITION. S7 SAMPLE TABLE FROM KACH SIT Or COMBXITATIOKS. Tens— 8 2 8 12 8 22 8 3^ 8 42 8 6i 8 62 Ac 2 2 2 2 2 8 18 28 3d 48 2 58 2 68 Ao. Impress endings, 2 + 8 ends in " 0." 8 + 2 " "0." Doubles— 7 7 7 7 7 7 7 17 27 37 47 67 7 67 *o. Nines- Impress ending 7+7 ends in 5 5 6 5 5 4 14 24 34 44 "4." 5 54 6 64 Ac 4 4 4 4 4 6 15 26 36 45 4 56 4 66 Ac. Eights — Impress ending 4+6 ends in 5+4 « 2 2 2 2 2 6 16 26 86 46 "9." "9." 2 66 3 66 Ac. ; 6 6 6 6 6 2 12 22 32 42 6 62 6 63 Ac ■^ Sevens — Impress ending 2+6 ends in 6+2 « 8 8 8 8 8 9 19 29 39 49 ♦•a" 8 59 8 69 dUtfiUidte^iittiiii&i iiii 88 ARITHMBTIC. 9 9 9 9 9 9 9 18 28 38 48 58 68 Sixes- Impress ending 9-f 8 ends in 8+9 " 9 9 9 9 9 7 17 27 37 47 "7." 9 57 9 67 &e. 7 9 7 19 7 29 7 7 39 49 7 69 7 69 i^fi. Fives— Impress ending 9+7 ends in 7+9 7 7 7 7 7 8 18 28 38 48 " 6." '•6." 7 68 7 68 S 4 8 17 8 27 8 8 37 47 8 57 8 67 Impress ending 8+7 ends in 7+8 " "5." "6." Fours— 5 9 6 19 6 29 6 5 39 49 6 59 6 69 &0. 9 6 9 16 9 25 9 9 35 46 9 65 9 65 &c Impress ending 9+5 ends in 6+9 ♦• "4." i< 4;.. Threes- 7 6 7 16 7 26 7 7 • 36 46 7 56 7 66 &e. 6 7 6 17 6 27 6 6 37 47 6 67 67 Aa mmuM AODITIOK. 39 Two«— Onea — Iiupreu ending 6+7 ends in " S." 7+6 " «»3." 8 8 8 8 8 8 4 14 24 34 44 64 2 9 2 19 2 29 2 39 2 49 2 59 8 64 &c. 4 4 4 4 4 8 18 28 38 48 4 68 4 68 &c. ImpreM ending 4+8 ends in 8+4 •• 9 9 9 9 9 2 12 22 32 42 "2." "2." 9 62 9 62 &o. 2 69 &o. Impress ending 2+9 ends in " 1." 9+2 " "1." SuggMtlons for Attaining Rapidity. 1. Teacher holds cards on which are two digits, 7 8 and says : " I shall show you a card just a second ; when I hide it write on slates (1) the turn of the two digits, 15, (2) the two numbers that made the sum (7 and 8). (3) also the difference of the two numbers (1). N.B. — ^The boys may give the sum, the girls the differ- ence, and vice veraa. 2. Place a number of strokes (soldiers) in groups. Ask how many altogether first, (2) how many croups, (3) what the groups were to make up the total. For in- stance : « , v^ ^ ^' 1111, IL 9 altogether. 3 groups. Three, four, two made up the nine. iiiiii ds^^MmmMMMMmm ^ism ^M. 30 AtttTRMBTIC. 3. Let the children count by twos, threes, in concert ; at a certain signal all stop— then tell how many twot, as 2, 4. 6, 8, 30, 12, 14—7 _.,l^ . ^4 It JO ARITHMETIC. 1 2 3 4 5 987 6 7 8 82] 374 893 681 124 879 731 754 459 946 467 199 466 661 699 (i96 652 161 664 914 662 452 412 419 »48 429 926 266 698 428 868 241 J«6 685 189 868 419 684 254 868 845 585 681 982 481 480 486 882 266 625 421 126 629 624 624 225 664 666 669 664 661 666 666 666 4,820 4,370 4,890 4,680 6,007 4,870 4,730 4 750 40,005 2 47,670 7671 9785 3975 5274 6946 4489 4815 4646 9446 4162 6624 6294 6462 1662 9448 2946 6446 9468 4648 1668 8166 6668 1644 6461 5862 8964 8682 8646 8689 6241 2162 2421 2464 2621 6679 6668 6669 6666 6669 49,780 43,970 45,270 58753 27529 75174 27371 73765 11997 46491 49496 46949 45415 99114 66614 61612 66164 65699 94246 19256 98948 19266 22491 16866 91864 12169 91852 88616 84984 89286 86861 89288 98984 26121 21824 24261 21824 12126 66669 66666 66669 66666 66664 458,750 427,520 475,170 427,370 473,760 „^JL, ADDITION. 37 6+5, 1+9. 9+1, 2+8, 8+2, 4+6, 6+4, 3+7, 7+3. 2 8 3 7 !^.. 7 5 5 7 3 ';. 7 6 3 4 3 4 6 4 9 8 6 3 5 7 6 7 6 4 5 5 7 8 8 1 8 7 6 1 8 5 5 3 2 2 9 2 3 4 9 2 ^ 5 6 6 8 9 6 9 2 2 1 2 5 4 4 2 1 4 I 8 8 9 8 5 6 7 8 9 7 6 7 6 5 1 5 4 3 2 1 3 5 3 4 6 9 'f 39 38 36 40 40 40 47 45 46 62 68 i 59 67 69 98 72 17 42 32 11 1 . 1 65 65 61 19 18 43 58 78 97 «> 66 65 68 71 61 62 59 35 23 45 46 62 39 69 68 71 85 84 85 84 47 81 41 48 39 25 66 ■^i — — 73 — 79 72 71 75 66 309 307 — 308 — — 74 360 370 310 340 330 401 978 946 472 633 436 916 672 189 166 468 479 894 224 248 Ml 874 666 861 216 889 867 548 231 174 246 685 651 688 786 789 938 785 426 468 644 772 776 772 776 3008 3005 3470 3003 3430 3910 3570 ■.^iiaaBatj^...;..k^^,^ ^m ■ikiii^aiiliiLiiMlia i^ttitutii^iimiimdaMt ^J' ;i^.r 38 ARITHMBTIC. 6672 4672 6461 6761 6868 6298 9139 9629 4269 6816 1978 1681 9861 9696 6262 9699 1241 1416 6846 1411 7779 7774 7775 7779 36670 34670 36460 36760 4694 6317 7763 3962 6148 4062 7678 6261 6843 7317 3792 6968 4164 6676 40604 40001 62434 34366 54739 14317 96249 48672 76769 56375 96791 16866 99418 29841 39966 39229 69146 11699 812to 71142 71886 61969 76691 86862 68248 86866 98371 34612 26243 62862 26246 12732 66678 66677 66678 66676 66678 400004 400006 400009 400007 400009 Review ExerclAes. TENS. 6 1 9 8 2 6 4 7 3 6 9 1 2 8 4 6 3 7 5 6 9 1 8 6 4 15 46 31 19 42 36 26 6 9 1 8 2 3 7 35 11 39 32 68 17 63 6 9 7 8 8 S 4 e 65 61 13 67 12 68 46 34 •^ — — — — — - -" — ^ ^"--^■'-''' aimmm ^ib ■ T^^>, ... j-.^. ,..s^a./.^^a^.^,^jiajia».aiat«a3 ADDITION. 39 5672 4672 6461 6761 6858 6298 9139 9529 9445 4259 6815 1978 1581 1663 9861 9695 5262 9699 8747 12a 1416 5845 1411 2362 7779 7774 7776 7779 7898 3337 3338 3336 3337 3216 6663 987*? 3846 8943 7864 4446 1239 7266 2163 3248 5655 6661 5655 6667 6662 65670 54670 56460 56760 60005 6 7 8 9 82686 68282 72784 39767 47376 77748 24196 71364 63737 33365 86917 71366 77243 97745 77273 39761 33869 13366 33837 99769 72261 96975 43423 11352 38849 14136 67689 84768 79861 94874 19281 26362 31241 16231 91825 66668 65659 66559 66656 6(10007 682680 668280 572780 h^irffiftlitiiir -liiiffi- "**--— -^"-'•^ ''^- ..%-;t,%»^. -.,»■».■».■. ^ . ijig f^gg^ ., 40 ARITHMETIC. 9 9 9 + 9-18. Oral Exercises. 9 29 9 49 9 39 9 19 9 69 9 79 ^^ -""■ "~~ ~~ "~~ ■ ~ ^^ 1 2 3 4 6 6 7 8 9 10 11 12 6 2 2 9 9 9 2 1 9 6 9 9 9 9 9 9 9 2 2 9 2 9 9 9 2 2 2 9 ? 9 9 2 9 9 2 7 9 9 9 9 9 9 9 9 9 I 9 3 9 9 9 1 9 7 6 9 8 3 9 6 8 7 8 9 2 3 5 2 2 7 2 4 • 2 3 2 1 9 6 6 9 7 3 9 6 4 3 2 9 9 6 4 9 3 7 9 4 6 7 8 1 40 40 41 68 46 48 60 60 68 58 68 66 N.^B.-1 Jse one column sums for Oral addition. 1 2 3 4 5 6 7 8 9 298 69 99 272 999 879 72 69 76 29 99 267 929 959 429 29 29 22 99 26 922 999 762 694 99 92 99 91 95 999 492 379 696 96 99 99 29 96 299 629 239 627 74 79 82 91 65 952 499 922 993 36 37 29 97 45 959 692 989 194 64 63 69 63 65 660 658 649 566 470 468 476 568 588 5067 t>J70 6080 4878 i£k MMMaWifekk itmimi ttttm i^iiiii ADDITION. 41 8 8 8 28 8+8 = 16. Oral Exercises. 8 48 8 18 8 58 8 38 8 68 8 88 5 6 8 10 II 12 4 8 8 8 4 8 8 9 9 8 8 8 8 7 8 8 8 1 4 8 9 2 4 8 7 4 7 9 9 4 8 9 4 9 8 4 3 8 3 9 9 8 8 9 8 9 9 8 8 8 7 8 4 8 8 4 8 9 9 8 2 2 3 2 8 4 2 6 4 1 2 8 3 9 7 5 9 8 8 4 8 7 9 2 7 9 3 5 9 8 2 6 8 3 9 dO 50 47 46 46 66 50 40 46 66 56 66 1 2 3 4 5 6 7 8 s^ 10 11 68 48 88 84 2^ 74 74 43 52 42 88 578 244 547 88 48 28 28 84 29 89 24 428 488 982 78 89 98 98 88 99 99 98 894 888 189 37 89 98 99 28 98 99 98 398 844 249 63 72 62 61 92 52 51 94 968 488 984 48 39 47 59 99 67 57 18 147 689 988 52 59 63 61 69 63 63 58 663 559 568 556 420 470 470 503 460 500 666 4576 4200 4607 Jiiiililiii mmtim mm <■.' .. 42 ARITHMETIC. 7 7 7 47 7+7 = x4. Oral ExerciMS. 7 27 7 17 7 67 7 37 7 67 8 9 10 11 12 6 7 7 2 6 8 7 7 6 6 7 6 7 7 7 4 7 8 7 7 6 7 7 7 4 7 4 » 7 6 6 2 7 7 2 7 8 6 8 9 6 7 7 9 7 8 9 9 8 7 9 9 6 7 7 9 t 6 2 9 1 2 7 9 6 6 2 2 4 7 8 7 9 9 7 1 7 7 9 9 8 7 2 3 1 9 3 9 7 7 9 9 8 \ 46 5 40 44 46 64 44 60 62 60 60 64 60 6 8 87 763 726 427 727 97 97 66 77 87 776 766 867 247 60 67 74 77 64 277 472 874 986 76 76 78 94 78 927 878 278 987 77 77 68 16 78 982 869 448 247 87 77 72 86 92 971 782 986 28 37 79 27 19 127 179 789 987 72 C3 69 67 69 667 661 669 667 497 494 605 444 664 5403 6420 6024 6724 - ->.A--.-A.-.*.i^-'.„,A»a£^: Mte».ii«Jiiiiiikiiil^ .ii^iitui^mmim ADDITION. 4S 6 6 6 26 6-1-6=12. Oral Exercises. 6 46 6 16 « 6 36 6 66 6 76 5 6 8 9 10 11 12 8 6 8 6 8 8 6 8 6 7 6 6 6 6 6 6 6 4 6 8 8 6 6 6 6 8 6 6 8 8 6 8 6 8 7 2 6 6 2 8 8 6 6 6 8 6 3 9 7 6 9 6 8 6 4 7 8 6 6 9 7 8 9 6 6 8 6 7 2 8 4 2 6 6 6 8 8 6 7 6 9 6 8 9 7 8 7 6 9 6 3 4 9 6 2 9 7 8 7 6 9 60 46 52 57 62 42 62 60 62 60 60 60 3 6 8 66 68 786 785 686 86 86 68 866 988 868 766 678 68 66 66 688 986 666 768 679 66 66 26 686 886 888 486 86ft 76 74 98 948 668 964 868 672 36 36 96 169 666 967 869 679 64 64 66 659 666 567 669 669 452 450 420 4702 4860 5705 6000 4246 ^^ nmm hi^m f . 44 ARITHMETIC. 1 a 3 4 6 6 26080 47667 68626 88887 67897 68662 67266 87678 86698 68698 27698 26629 87066 82876 46698 62696 84886 46849 88828 99668 79786 99878 98966 76672 96692 19669 71727 19239 18964 76679 16696 66669 66667 66669 66676 66769 67676 404207 420202 406067 364087 360260 440202 4 + 4= = 8. Oral Exerci4e4. 4 4 4 4 4 4 4 14 64 34 64 24 44 4 — — — — — ~ ■■^~ ~ 6 6 8 9 10 11 12 4 8 4 4 8 9 4 1 4 8 4 4 4 6 6 8 2 4 2 8 2 4 8 4 8 6 2 2 4 8 4 6 4 4 6 2 6 a 4 4 4 6 7 8 4 8 6 9 8 4 4 4 2 6 7 8 2 6 2 9 8 4 2 2 4 8 6 2 4 8 4 8 4 2 4 9 7 6 7 9 7 9 7 6 8 9 7 9 7 6 7 9 7 9 7 6 8 9 7 46 39 48 41 58 46 48 48 48 58 42 36 ^--'-- ■ -' -,-T-if>^--. ■•■.-■ •■■. ■- -. — -.^.1-. m„^.^.»j. ADDITION. 40 1 2 3 4 6 6 7 8 9 u 84 29 66 964 484 668 6869 47 48 49 86 27 224 464 826 2629 77 78 42 48 92 442 268 948 4842 72 72 84 46 94 449 42U 949 4844 89 29 64 26 24 829 446 229 2224 69 49 82 48 44 642 978 442 4942 66 47 84 46 48 649 176 449 4944 64 63 74 56 78 769 666 749 4n4 608 460 608 422 407 4968 3808 6260 36068 3+3«6. Oral Exercitet. 3 3 3 43 3 23 3 63 3 13 3 63 3 33 1 2 3 4 5 6 7 8 9 10 11 4 3 3 3 3 4 3 3 8 3 3 3 3 3 3 3 4 ;> 8 4 3 3 3 2 4 4 3 3 4 4 3 4 8 8 4 3 3 8 3 3 3 3 3 6 6 4 3 3 6 8 3 3 2 3 6 6 2 4 2 6 6 4 2 4 4 8 8 4 8 4 8 8 3 9 7 8 6 6 7 9 7 6 9 3 9 7 8 6 6 7 9 7 8 9 26 46 30 36 46 46 36 46 40 60 66 ./ ,,i.g»j;aa«r»«i,-.A.i->.--A«^^: ^.....■^. ..tf-^..^.. -ffirftiiilntrifir - 46 ARITHMETIC 1 1 2 3 4 6 6 7 6423 473 36 646 37 437 3988 2443 343 33 338 37 334 3966 4842 388 43 339 24 323 2883 4684 846 88 249 48 443 4643 4364 448 90 438 44 872 7342 3332 429 93 436 27 879 7329 3234 749 73 766 47 779 6649 7484 3076 462 3202 264 4067 36800 35806 • 2 + 2-4, 1 + 1 -2. Oral Exercises. 2 2 2 2 2 2 1 1 1 2 42 12 32 62 62 41 11 81 8 9 10 11 5 2 6 1 2 3 5 4 '2 2 2 6 3 1 2 3 8 3 8 6 2 4 3 3 2 2 2 6 3 4 8 2 2 3 2 4 4 4 3 2 2 4 4 2 2 4 2 7 2 3 4 6 4 4 8 4 4 2 7 6 2 4 6 6 2 6 2 2 4 6 8 4 4 8 2 4 3 1 9 8 7 9 7 8 6 1 4 3 1 9 8 7 9 7 8 6 1 24 36 24 42 32 46 46 40 46 34 ^f. ■Aita ADDITION. ♦7 1 t 3 4 6 26 6 12 19 7 8 SI 63 44 43 92 •9 81 83 26 68 32 73 44 36 99 42 43 24 36 72 22 33 44 34 23 44 26 84 62 93 89 12 82 72 48 62 36 49 19 11 64 79 46 61 32 49 17 91 84 79 76 81 82 79 83 396 302 366 808 609 324 324 262 9 10 1 r 12 13 14 743 642 631 749 658 466 783 826 836 994 829 788 289 4fi 428 <4«9 449 748 424 938 944 886 272 829 792 132 629 138 274 624 791 199 696 199 774 374 691 849 876 848 3266 3822 4406 3284 4264 2780 16 16 17 18 19 2986 8848 8728 7262 4948 4424 4214 9399 2632 9994 2262 2912 6349 9834 6969 6166 2986 8979 9489 8481 8126 9968 4479 4946 8941 4892 1484 9969 8148 9698 9194 6939 1679 8129 1861 6127 5226 1679 7749 5431 3647 6746 7568 57422 50062 46686 46746 84608 . --':<>--^ife^-i|f|i|B|i>iiiii|| ittHii^Kilui 48 8 1 1 9 1 8 31 ARITHMJETIC. New Combinations. Nines. 1+8. 8+1, 2+7. -2. Oral Exercises. i 8 8 7 7 7 n 21 12 42 32 7 I 62 12 3 4 6 I 8 9 JO 11 12 13 8 1 8 9 9 6 8 16 1 4 4 2 4 9 8 8 2 8 9 6 1 19 6 1 1 8 8 8 8 1 9 1 8 6 8 8 6 2 1 6 3 2 8 8 3 8 2 4 2 6 7 7 9 3 3 7 9 3 1 8 4 8 4 7 7 6 4 7 7 2 9 8 1 9 9 2 4 4 1 9 8 1 1 1 8 8 4 1 2 8 6 6 6 6 2 8 4 6 7 6 7 46 48 38 39 46 49 49 39 49 li i ^ 46 18 19 48 21 62 89 49 87 84 93 17 82 17 18 82 8S 14 62 47 86 37 44 11 28 U 14 42 14 76 41 76 79 88 74 66 28 36 48 68 44 14 88 16 43 33 29 27 41 97 89 82 49 19 42 13 29 18 49 48 298 560 409 it*-. ADDITION. 49 7 22 42 2+7, 7+2. Oral Exercises. 2 37 7 12 52 2 67 7 32 2 17 8 9 JO 11 12 1 I 9 7 2 1 7 2 9 2 7 4 8 9 8 1 1 7 2 4 8 4 2 7 1 7 2 4 8 9 9 8 9 7 6 6 8 6 6 8 4 4 7 2 4 7 7 2 1 2 2 9 9 7 2 1 7 2 8 2 5 8 9 7 6 8 4 2 6 6 8 9 7 6 6 2 4 2 1 1 9 7 2 7 3 7 3 6 4 1 1 9 8 1 9 1 M 48 40 49 56 46 39 39 56 46 48 89 62 81 91 29 77 82 71 27 96 96 48 86 46 92 27 72 19 21 74 47 37 94 59 88 47 19 82 17 42 76 24 28 67 68 37 499 470 389 380 6 82 97 71 68 61 82 69 39" 61 89 47 46 88 64 34 8 77 22 41 87 46 48 29 49 47 84 98 74 22 46 36 358 569 429 39Q 40? 1 • V 50 ARITHMETIC. 4 5 6 14 4+6, 6+4. Oral Exercises. 4 35 6 24 4 46 6 64 6 34 6 9 6 4 1 1 9 6 4 9 4 6 2 9 7 6 6 88 48 4 6 2 9 7 2 4 8 8 9 4 6 1 4 6 6 6 8 9 6 7 7 8 6 6 1 4 9 9 5 4 1 1 6 9 7 4 7 6 8 6 8 4 8 9 7 4 9 7 4 7 1 5 4 1 4 5 5 6 10 9 ] 9 5 7 7 4 8 8 ^9 38 66 50 48 48 37 58 6 14 95 74 28 89 65 34 94 46 61 14 46 65 85 82 97 41 67 12 61 48 81 64 45 41 84 45 26 67 37 98 79 65 64 81 67 32 99 44 66 11 64 46 88 61 31 69 76 34 11 68 21 62 38 9 44 89 65 97 11 42 47 51 66 18 86 61 68 21 86 68 46 3J 399 389 469 399 486 488 368 499 "IS • ADDITION. 3+6, 6+3. Oral Exercises. 3 6 6 33 3 6 46 13 3 26 6 63 51 8 9 10 8 9 6 3 2 9 6 3 9 3 8 9 1 9 6 4 46 48 6 3 1 7 2 1 6 7 7 3 3 3 2 9 3 3 3 6 1 3 8 9 3 8 4 4 8 9 4 5 1 3 8 9 9 S 6 1 6 2 6 6 8 6 6 6 7 7 1 3 8 9 3 6 39 29 46 66 8 8 9 4 6 1 3 8 9 8 1 3 8 9 6 7 7 2 9 9 49 49 69 69 6 8 9 17 3v 84 98 62 37 3 a 73 28 19 36 33 49 88 61 99 19 73 68 64 27 47 47 66 99 61 39 23 16 98 78 34 26 66 87 47 56 41 17 62 32 19 69 27 91 68 17 66 31 38 21 14 47 22 37 37 31 88 41 32 69 39 10 19 92 99 86 13 16 74 409 399 39 8 466 488 296 307 209 290 399 ^ gj- ^./'^. ^>^., M^aritjHSa.B.a.;iaii 52 AKiril.WliTJC. 8983 9398 5849 4967 1716 7678 2829 6469 46869 Review of Nines. 2 3 9147 9893 6234 4928 77] 6 6679 7837 1327 1683 6192 3648 7134 8842 7988 8625 6548 5345 48689 58097 16-7 1391 4068 6831 4121 6147 7622 3425 7676 41907 97882 369^ 88656 99347 47117 52376 22827 44467 489660 74692 15179 31S27 86826 93496 48254 56248 73658 479580 19893 33938 88789 99293 24128 75374 22827 44447 4086bd 8 81898 45934 27282 17796 11136 83788 282iH> 64556 360686 7 11 6 22 1 + 7, 2+6, 6 + 2,3 + 5,5 + 3. Oral Exercises. 2 66 7 31 6 42 5 13 3 45 2 33 76 •yff ADUITION. 53 1 2 3 4 5 G 8 9 10 7 4 6 5 9 6 3 7 8 7 1 2 5 7 ] 2 1 2 6 8 7 4 2 9 2 2 6 4 2 6 3 2 4 6 2 4 1 2 6 2 8 ^ 7 1 1 4 8 8 y 2 9 9 2 2 6 2 2 2 7 1 4 2 5 3 4 4 8 8 6 8 9 9 3 2 6 2 5 2 5 3 29 42 48 28 29 38 38 48 36 38 11 18 68 32 22 47 21 12 89 26 64 21 46 23 13 29 87 B2 31 25 64 U 29 95 64 31 17 72 15 27 81 32 55 23 42 42 86 16 83 25 62 27 71 12 29 59 17 92 18 27 81 52 37 81 18 82 78 15 23 78 16 76 19 57 21 72 15 2i>. 42 49 79 198 268 288 308 388 368 388 368 358. 20 969 185 964 331 887 668 3828 M I 225 893 652 249 216 573 2808 22 596 392 226 743 142 227 5C1 2886 23 189 156 933 121 947 722 3063 24 216 893 552 344 117 777 2899 2868 .at^^-^tLat.:-^:. ' v^^ifc* -i^-.^.^lr. \ I 54 26 1127 2682 8266 6233 2426 9264 27 8228 8967 6621 2412 6153 3725 ARITHMETIC. 28 6922 2176 4613 4222 2194 6674 29 7522 1386 6173 4612 1319 7869 30 6268 8986 6743 2242 2114 6674 *^eview of Eights. 2 2862 8788 2135 8263 4722 2164 6267 3437 38628 9£93 7395 2622 1246 6376 4678 1229 6449 8683 3236 5762 2124 9227 9787 1188 3226 3446 7213 1846 7622 2364 1187 6797 4296 1127 6647 81882 35678 63317 12121 72522 28486 17193 61794 42228 74648 29583 81398 64264 37242 17816 42376 64522 24229 47449 83263 26635 61222 26626 94386 71276 21418 19426 66746 88137 32961 68422 23626 25186 82136 74752 14124 21297 46467 ADDITION. 55 1+6, 6+1, 2+5, 5+2. Oral Exercises. ( S 6 2 6 2 5 2 11 31 5 22 15 42 55 2 6 1 7 8 5 8 7 3 2 2 6 1 2 2 1 2 4 5 2 6 5 1 1 J 5 6 6 7 6 5 1 3 3 2 8 3 7 7 6 6 3 3 1 6 6 6 5 2 5 6 2 5 8 8 1 I 3 2 5 6 8 4 2 4 8 3 4 2 2 3 8 4 2 6 2 2 6 8 4 9 o 9 7 1 7 6 4 1 8 4 9 2 9 7 1 7 6 4 29 37 30 44 39 57 66 34 40 37 44 74 27 64 84 37 28 53 75 27 78 27 63 67 51 26 66 65 36 76 18 22 11 12 26 26 74 86 74 42 67 58 22 27 28 64 16 29 16 82 24 17 62 49 66 56 64 67 348 358 368 378 349 347 3 + 4 , 4 + 3, . 9 + 8, 8 + J. Oral Exercises. 3 2 8 4 3 9 8 4 14 26 ] 19 33 54 28 49 13 «x • - - -'^^■'■- "-"* 66 A KITH mi; ric. 9 3 ;{ r> 3 1 8 2 4 4 3 8 3 9 5 2 8 1 9 :{ 2 ;] »> 9 8 3 s 4 (i #> •5 6 A 3 3 5 9 iv' o I 3 i i) b 3 8 9 3 b 9 3 5 2 o 1 5 4 1 (> 3 2 6 4 4 7 8 9 (i 8 9 9 2 4 7 3 9 9 9 803 235 482 393 310 471 2700 462 788 545 225 300 43 1 2820 543 439 368 812 939 839 3940 349 870 843 133 134 753 3088 472 326 402 321 326 564 747 375 792 583 239 299 449 3484 Review of Sevens. (J487 1728 3569 4212 3339 8539 27874 2949 9035 6214 326J 1138 7581 30778 1382 9158 7869 9730 2129 6283 1422 4161 2724 2337 4534 6382 0060 37057 ADDITION. 67 82126 97738 29983 33679 93469 67263 68632 28328 39128 62632 16762 68199 74268 82289 21184 44469 66644 #4477 470986 38597 79322 92386 12363 88738 26225 62522 62886 66446 607874 8 86168 64389 38853 86833 33327 63722 16986 72966 28927 66667 466127 4 42 1+6,2+4, 4 + 2, 9+7, 7+9. Oral ExeicUes. 6 11 4 32 7 19 9 47 r 9 2 34 6 6 1 4 3 3 6 4 6 1 4 9 9 9 9 6 4 7 4 2 9 6 6 3 2 7 8 4 9 9 4 4 3 4 7 4 2 9 3 4 3 1 9 9 4 7 6 1 8 6 3 2 7 1 2 9 9 4 6 9 7 4 9 9 9 9 4 8 2 6 4 4 3 4 9 2 C 9 2 9 9 8 7 9 2 4 6 8 9 4 ' 8 7 ^^ *^ 32 *» *6 47 46 66 66 46 60 ^H ■--^*-^^- 68 ARITHMKTIO. h:l 989 686 243 371 397 282 2768 922 939 946 913 136 834 4690 297 686 762 946 227 669 3466 644 966 749 469 789 649 4266 614 466 678 398 344 288 448 3266 6486 3968 8728 9414 2734 4732 36062 39290 8972 6293 2323 1244 2646 6391 26868 6362 3823 9634 8264 6224 2692 36979 7472 3726 4892 2194 1327 6469 26070 ADDITION. 59 Review of Six—. 8 8 67664 42364 61896 83899 48129 49289 76439 429680 5 66893 43997 62624 92446 98128 42862 78186 44646 628680 76426 90683 47922 48982 66348 43674 23277 66477 462688 73767 96262 64126 78496 82637 28289 46448 468924 92363 74698 49272 48943 22447 43669 87179 44449 462820 7 46776 64984 62492 13442 43672 67498 17226 66663 362642 87764 88819 49249 43349 62763 46848 22224 64464 364460 8 48289 66727 27434 49674 48186 66194 17928 46646 360876 1+4, 3+2, 2+3, 8+7. 7+8, 9+6, 6+9. Oral FxerclMS. 4 II 4 31 2 23 9 46 3 42 1 18 — . — 7 58 8 27 8 47 2 33 6 19 3 72 9 36 9 26 60 ^ tiTHMETIO. 2870 2353 6760 7896 1565 27«7 24807 « 35o8S 9!i^864 86k 1 466:?7 7744 1 98141 411J8 166(1 600Ui.9 ADDITIOH k«> 1«W )f Fivt5. 2 i o227 7134 fc^34 4 M 92^2 If) 5 66 7 96.^ 5766 787^. 474;- «^ 5117 127- 408f 365( 1 74"66 81&46 dfi66P 83941^ 7^y 7^449 46o7 24-?. 7 45972 87499 28686 66845 98974 67721 96836 68173 42442 590647 688-i 96od 8399 9849 8269 6879 3449 2688 9 ti6543 97366 79272 23628 28388 82272 63288 27824 64444 522868 l+^i, 3+1, 9+6, 6+9, 8+6, 6+a Oral ExerclMs. 31 -3 .5 5 8 40 6 18 8 26 8 81 7 17 2 42 25 8 36 6 48 6 49 7 47 "— ^ -^ ■"" — 62 ARITHMETIC. 3 1 2 3 4 1 7 6 7 9 2 9 4 9 3 9 3 6 3 1 2 2 8 4 7 8 4 2 2 2 4 3 1 1 6 8 6 2 2 2 4 2 6 7 4 9 5 6 9 4 6 4 6 8 2 4 8 9 J 3 1 9 6 2 4 9 6 6 8 6 6 1 6 9 2 6 2 2 2 4 4 JO 11 6 6 9 t> 6 4 8 8 4 2 AODinoir. 62 Review of Four«. 1 8 S 4 6 6 9496 6668 6422 1744 8789 S736 6966 4689 1222 2444 2677 3647 20444 6649 2366 4682 9224 5388 8636 36;>i4 3966 3488 6622 9844 7287 7637 38744 6366 4867 7678 6486 4129 7646 36060 4994 8399 6299 2699 4429 9189 2639 34844 38448 9 10 86664 84689 47649 27669 88689 26689 43639 66449 94666 94496 71668 88472 84786 68784 32661 aWNiO 87944 72689 68865 37312 96664 87966 44268 88«9 67749 83829 88629 42369 36879 19673 66148 344948 645886 478544 377044 ./^^^^^^^^H 64 ARITHMETIC. 3 2 1 7 1 6 1+2, 8+6, 5+8, 4+9, 9+4, 6+7, 7+6. Oral ExereisM. ^345678 9 10 11 2 2 1 7 7 1 9 9 9 6 9 7 9 7 4 6 2 3 6 8 7 6 8 1 7 3 6 8 7 6 6 8 6 2 2 8 4 8 7 2 3 7 3 7 9 5 7 6 4 8 6 7 7 7 7 7 9 8 7 3 4 6 6 7 3 8 1 6 7 2 9 66 49 47 64 65 62 58 53 9 9 6 2 4 6 8 6 4 2 1 7 6 8 7 6 6 5 8 2 1 7 6 8 4 3 5 8 12 7 3 2 1 7 2 1 7 2 1 63 53 43 33 3 2 2 8 6 7 21 61 II 16 M 40 6 4 9 4 8 7 19 34 29 46 75 68 44 S3 S9 74 23 96 18 vr 47 76 25 67 36 47 38 46 63 26 88 67 44 39 333 356 268 306 88 26 43 99 44 34 97 66 44 13 34 39 45 87 16 26 27 38 8 69 89 79 99 49 89 69 333 283 236 633 ADDITION. 66 1 2 3 4 6 6 463 432 227 582 172 589 259 845 986 563 227 866 759 178 368 541 966 578 379 117 417 757 447 897 949 S29 937 929 378 744 429 534 236 234 436 979 669 2366 3365 : 3260 3035 3635 4033 7 8 9 10 U 6393 8676 6866 6293 7238 6946 6743 2557 3669 6896 7998 6911 7657 4684 3348 4876 6927 3563 7977 4827 6648 6429 7377 9692 7564 6799 6234 3676 7221 3739 6459 33636 33305 38788 29666 43563 Review of Threes. 2 3 77477 3M3g 66366 40668 64464 78353 39368 46646 46578 94633 77696 93644 19677 ^4643 7633 o9431 433333 37376 78737 36863 47476 fl8977 83866 36347 64697 460638 87843 83297 34843 99887 47886 84667 39334 66449 46883« 66 734629 872774 484861 326695 631663 274952 387576 929384 434671 ABITHMKTIC. 6 6053S5 797621 639646 786669 622829 476799 237989 699889 328349 866879 436946 937963 683724 628683 882768 266839 724928 447741 892445 236898 644777 489677 726633 668969 786648 967868 992228 6 Oral Exercises. 8 ^ 13 4I 2I it ^ ,1 7 6 6 — — -.__ ^ 16 26 37 67 ADDITION. 67 1 1 1 1 6 8 3 6 6 6 6 8 8 6 6 8 6 8 3 7 9 3 8 9 3 6 4 3 7 3 7 9 3 8 3 9 1 9 3 3 4 8 3 4 8 4 9 9 3 6 7 8 7 6 8 5 7 8 9 9 3 6 7 9 8 8 3 6 7 7 7 6 4 8 8 8 8 3 6 7 4 6 1 3 9 8 8 7 6 6 6 a=JLJL_12_46 53 60 ^ el M 93 67 46 38 67 36 111 777 886 928 338 764 8803 71 89 33 18 39 33 91 39 89 33 37 36 52 99 S3 98 46 76 63 98 34 98 47 76 34 99 83 18 36 36 3 9 8 8 4 8 4 4 7 7 63 89 38 38 S3 S7 35 5M 943 384 893 637 686 4034 668 877 946 938 36tt 936 4604 778 856 578 647 929 794 4576 266 977 988 874 867 469 4480 383 789 889 849 689 789 659 3904 68 ARITHMETIC. Review of Two*. I: i m 64633 68677 68863 84777 26648 3884a 72646 27246 64968 68862 88887 29226 «3776 48637 23228 66469 279442 «73443 238848 782222 366967 377679 778666 458896 482797 866628 28369 82649 23529 37599 97639 83989 26839 62629 43367 87944 83834 87472 48486 81228 23639 62269 858672 882788 888922 832239 816908 856922 836246 867328 416679 248972 964918 378992 669988 823992 978999 963983 289948 838828 323654 37773 78687 82628 23272 73766 67688 83234 92464 769868 686988 297988 954938 967988 697948 666928 267468 946488 246789 346789 346789 846789 346789 346780 S46789 646789 ADDITION. gg 2+9,9^2,4+7.7 + 4,3+8.8 + 3,6+6.6+5. Oral Exercises. i! ^ ^ U ^ ^ d i ,1 3* ^ 9 32 2 49 7 24 4 17 8 23 8 43 6 16 6 66 9 42 2 9 9 9 2 9 9 2 7 2 9 9 9 2 2 9 9 61 58 2 8 9 2 6 4 6 7 7 4 5 6 7 4 3 9 4 8 2 7 9 8 2 3 2 7 9 8 7 8 7 7 3 4 7 8 5 6 8 1 6 5 8 1 8 3 2 8 2 8 2 9 8 2 3 7 7 4 1 9 9 6 9 S 6 9 7 9 9 2 8 9 8 2 9 4 3 9 6 9 9 6 9 9 6 99 12 39 .86 n 96 64 96 19 89 38 97 84 79 29 48 18 93 82 79 38 48 96 63 86 99 21 98 93 29 26 46 99 99 22 88 69 72 79 48 24 42 28 39 58 mMm ^Mtttt^iUtim'hd-iKknMriiirrT •«'••, ■iLj-.J^- '% 70 698 919 827 189 964 86» 989 Wr 499 784 7» AlWTHMETia 978 323 482 277 649 372 3121 4619 3081 962 698 637 974 629 689 672 671 647 925 888 338 834 948 926 196 999 343 778 6051 4153 4189 366 493 995 504 249 423 3118 8979 1999 8364 5869 6629 6342 38172 5722 4898 8982 3328 2432 4339 29701 7773 9929 8982 3928 2437 4834 37883 9934 2198 8846 2368 3287 3475 30108 7657 9929 2892 9388 2932 4839 37637 9646 2774 6339 4946 6266 5888 2336 456i( 42761 Review of Ones. 76887 38289 97529 12589 28839 83288 74769 411191 696171 471441 AODinoir. 71 411111 72689 98289 68889 68289 92889 28289 83989 22189 64229 673741 451111 98887 22933 93899 47822 76888 96288 66738 •5288 66668 611811 494180 6ll3n 1. (•) 43+7 16 f 8 29+9 47+7 68+8 13+3 BU5Y WORK. All Combinatloiu. (b) (0) (d) 11+9 34+6 46+3 4J+6 47+2 36;f 84 + 4 16+4 23+6 S+? 31+8 41 + 7 77+7 43+6 18+9 26+6 ]2;7 M+J (•) 48+6 11+6 19+7 47+9 38+4 11+8 *^ft^ 72 2. (.) «8 + 7 J6+9 32+3 41+4 19+6 57+8 17+7 28+6 36+8 10+9 49+6 41+3 ABITHMBTIC. (C) 14+9 31+2 15+8 48+6 17+6 56+7 (d) 18+4 2«+6 47+6 28+9 19+3 44+8 (•) 12+9 33+8 46+6 29+8 17+4 54+r 46 58 38 48 M 67 80 64 3. *+6+3+7+8+2+l+9+6= 9+9+2+9+9+8+G+2+4- 1+1+2+4+2+6+6+2+4= 4+6+1+2+7+9+8+3+9- 20+3+5+8+2+2+1+7+2- »+«+7+3+3+8+9+3+2+6-. 41+6+3+7+9+4+2+4+4- 17+7+6+2+2+4+6+6+9+5- 16+7+2+8+7+8+6+2+8+7+6+7-83 19+3+8+3+9+8+7+6+2+8= 73 16+6+8+9+3+8+6+7+2+8- 72 2+9+4+7+9+8+2+7+3- 51 3+8+8+2+7+3+4^6+9+6+6- 61 EXERCISES INVOLVINQ ALL THE COMBINA- TION*. hundred and fo^y one ^ ^^^ ^?S'*^V?l"""'>** '''^ wopd». ^ ^^- J«>76. Wnte anawer in fo^^ttu2':nd 2r^"'r« ^"»**«»d and three. Wrii»an.«?rTnio?d. ' ''*"'^J'-»«^«"- ^n.- 40155! 73 uiglit hundrod • Alls. V625'J. Ana. 401U4 3631U 86864a 604260 111168 439097 ADDITION. 3. Add togc'tlicr: Ihroe, forty sovon 4. Find the sum of • (bi s'^'irms' i?' '7^^^' 37312. / V /aA"' ^"3» 47, 1005. 6243 27Hnn (el 2Mnn^S' fi?'il<**'«- 600069. Exercl.es Involving All Comblnatloiu. 6. The addenda aru : 432, 207, 869, 100, 423. Find the sum 8. The addends are : ^^^ 2031. 789, 053, 425, 838, 724, 163. Find the sum. 7. Find the sum of • ^n»- 3692. (a) r«3+8«+678+78C+8<)9+923+239 (d) 97843+87142^,428,^ .W+aste" """"^ Ans. 277656. SUBTRACTION. INTRODUCTION. iu^^^t? t««shinp{ the ULlea in addition, the oonreiw or tba UblM 111 subfraction h«i ve been Uught ineidmUatty. The method of treatment hu been aco(»dinff to tablea in the following progreMire order : First, the taUe in- Tolving oombinatimie of t«n ; then ui,.e ; then the table ending in eight; inwtien; innsB; iajim; inftmr: in thrm i in two ; m mte. " > ^ » In the table ending in tight the pupil is introdooed into the mtrioaoiee of bo/rovnng. Allow pupila to indicate the operation of borrowing and changing, until ther have be- come proficient enough to do without. Thie p^ntut ia neoeMary to beginner*. Indeed, with aooM papilaTthe use of the slate helps to make the 6iMMUe (J^iMTidaa much clearer. ^ At end of taWe ending in (m« wiU be found reriew ex. erotiee on all the combinations. TaM* Endiag la «• lo." 10 10 10 10 10 10 10 6 6 4 7 S 8 3 10 10 9 1 Oral Eubcisi. You have a ten-cefU piece and vou buy one oriieb. say a top, for 5 cents ; what change should you reoeiTet Monty. lArtieU. Ohangt, 10-OMit piece. 6 cents .4 oenU 10-o«nt inece 7 cents. f lO-eent piece 8 cents. ...'..'.'-. ? 10-oent piece. 8 cents. .....'. . ? 10-oent piece 4 cents. .'.'.'.*-? <74) Monty. lO-osnt pMca. lO^uttpiM*. lO^MntjMM*. 10-c«it pi«o«. l .(1) 6- -0. 666,666.666,666 610j06M6641l 166.600.111.665 6-3- 6-2= 6- -4 (8) 686,666,666,666 42a.44«.28S.243 J4 3.234.483.4^ (4) 166 83 6- 6-4- J3) 16-8- 666,666,666,666 482.616.006.132 234.160.660.634 166.666,666 84,236,601 82,431,066 81 16 7 mmM m\\ i ABITHMBTIC. (6) 7tt 38 38 48 (8) 16,666,676 8,423,618 8,243,168 (») 777,776 188,888 688,888 (10) 166 94 n 16-9. (IJ) 76 5 1 37 1,778,776 829,798 16-7. (12) 76 27 49 (13) 17,776 7,979 (16) 76,716,987,716 27,328.644,749 (14) 1,777,776 897,798 9,797 879,978 (17) 11,877,767,996 4,983,793,998 948.978 49.388,442.967 6,893,973.99 8 (18) 17,397,017,006 8,423,868,439 9,473,168,667 (19) 177,879,010,000 98,989,264,367 78,889.766,683 Table Ending In •• 5. Oral Exbrcus. 6 4 6 6 6 6 3 5 2 16 9 16 6 16 ,Q 16 7 5-1 = WuTTEir Exercise. 6-4^ 6-3= (1) 666,666,666 223,340,611 332^216,044 6-6- ; 6-0«= 6-2= . 689,966,688,976,666 124.^05.264,223.342 466,660, 434.763,213 ^tMii^M SUBTIUOnON. 15-9' 15-6. 16- -9; 15- 83 .6. (6) .(«) ^tSi J?'!!$ «.««.«» ?» jiW 24:639 ^Me 15-8- (7) 666 388 969 3,699,696 (8) 665 — HI 877 488 4 1 (9) 666 378 287 -7; 16- -8. (12) 6,166.660,005 3,273.638.288 2.892.921.767 (10) 566,665 tMi,769 127,811 (11) 665,605 187,229 478,376 (14) 601,006 238,320 362.679 (17) 7.689,010 3.889,245 3.799.765 (16) 1,690,005 632,638 957.467 (18) 866,010,016 497.542,348 368.467.667 (13) 1»,887,776.6W 9,898,979.687 ».988,796.978 (16) 9,658,017 2.864,539 6.793.478 (19) 15,601,000 7.342.643 8,258.357 4 3 Table Ending In *< 4.'* Oral £xerci.se. 4 4 4 4 1* 2 6 14 9 14 7 14 6 14 8 WRlTTEir EXRRCISB. 4-1=. ; 4_3^ . ^_^^ 4-0- ; 4-2- . #i 84 ARITHMETIC. 14-6 = (1) 444,444,444 204.032,231 240,412,213 ; 14-9. (3) 6,464,464 1.636,326 3.919.129 (5) 6,464,464 1.939,329 3.616,126 (7) 4,466,664 2,326,995 2.129 669 (9) 657,799,764 268,464.979 299,:)44.78o (11) 66.646,464 27.774.727 27.770,727 («) 894,787,666,444 462,234.130,241 442,663,626,203 14- .9; 14- 14-7= (*) 6,446,564 3.623.555 1,921,999 (6) 5,445,554 3.928.999 1,521.666 (8) 446,445,664 312.923.969 132.621.696 (10) 6,006,095,458 2,643,439.609 2.461,666,949 (12) 14,796,004 6.429.237 9,365.767 (13) 967,886.664 679.892.957 387.992,697 SUBTRACTION. 14-6. 3 1 ; 14-8. 6,464,464 1.636,326 3.818.128 (16) 6,446.664 3,823.888 1.621,666 (18) 666,^,664 286.862,697 268.682,967 14- -8; 14- (16) 6,446.664 3 .023.666 1.821.888 . (17) 446,446,564 312.823.868 132,621,686 (1«) 1,447,879,004 830.379.426 617.499,678 Table Endlns In •• 3.'* Oral ExsRcui:. 85 = «. 3 2 3 3 3 13 9 13 13 4 8 13 6 13 7 13 6 3-1. WUTTBN EXBKCUB. 13-9= (1) 4,433,33!^ 1.990,321 2,448,012 (3) 343.344.443 119,319,999 224.024,444 3-3- 13-4- 3-0> 343,8SB,443 129,230.299 214.108.144 (4) 434,434,343 141.440.484 292.998.909 ^^kUkm ft« ARITHIHnO. 443.444.443 149,iai.9»i a94,3«.449 a) 130,764.003 40 884.7W 90.360.344 13-8< (8) 4 443 2,888 1,666 (11) 14,443,333 6.984.032 8.469.301 13-6- (0) 444,334,443 288,880.888 166,603.666 (10) 144,488 06.861 48.682 13-7- 13-6- (13) 444,443 167.667 276.776 (16) 14,444,006 4.867.236 9,676.769 (17) 14,046,764,340 6.496,880,734 7,619,383.606 .839, W) .448 894,869 944.689 13- 13- -6 , (14) 1.364,448 726,078 638.366 ss. 197,944,013 98,476,327 99,467,886 (18) 1.400,434,433 636.071.898 766.388,640 •tJBTlUOTIOV. 9f! (W) 1.378,401,304.008 622,186.708.684 766.876.600.470 144.64§IS7,1 7H.804,a4g.840 68,849.820.640 8 1 a a T«bl« Emllns In "j." O&AL EXBBGUB. 8 13 18 18 18 18 18 18 06394867 WRIITBjr EXBKOZSB. «-l- ; 8-a- ; 2-0- (1) 828.222,222 100,822,111 122.000.]] 1 18-6- 8,883,339 1.618,666 1.610.666 18-3- I ia-9- (*) 3,222,838,382 1,608.188.833 1,680,199.999 13 -4. ia-8> 138, ,888,888, .838 89.848.618.844 43.980.614,488 18- -6. (3) 8,883,388 1.660.666 1.668.666 18- -9i 18- -SL .2M, W 143.303,333,888 79,909.966.193 63.800.366.139 13- -4 13- -8. (7 ,883,908,838 136.431.400.138 106.891,808,104 MHii MICROCOPY RESOIUTION TEST CHART (ANSI and ISO TEST CHART No. 2) 1.0 I.I 1.25 ^ IP-' ■ 3.2 71 y^ a ■ 4.0 1.4 23 m III 2.0 1.8 A APPLIED IN/MGE Inc 1653 East Main Street Rochester. New York 14609 (716) 482 -0300 -Phone (716) 288- 5989 -Fax USA 88 ARITHMETIC. 12-6= ; 12-7 = (8) 123,323,332 72,771,666 60.661,777 (10) :^,333,332 16,768.493 16,674,839 (12) 13,483,002,812 7.791.936.324 5.691.066,488 (14) 612,932,064,434 26.136.019.166 487.797.036.268 1 1 12- =6i 12- =7, 12,233,332 7.01^,767 6,217.676 (11) 333,333,332 168.673.649 174.669.683 (13) 432,833,383,000 17.339,726.924 415.493.657.076 (16) 833,432,963,802 646.637.698,346 287.796,366.466 Table Ending in "i.»» Okal Exercise. 1 11 2 11 9 11 3 11 8 11 4 11 7 11 6 1-1= 11-3. Writt^jn Exercise. ; 1-0= ; 11-8= 11- = (1) 122,221,111 83,922.101 38.299,010 11-2= ; 11- =2; 11- =8. 11-9= 11- = 11 6 3; (2) 21,222,221 3,199.283 18,022,938 SU<3TKACTI0N. 89 11-4= 11 7 = 11- =4; 11 - =: (3) 11,222,221 7.177.444 4 044.777 11-5= ; 11-6= 12,221,221 6,665.165 6,666,066 (7) 1,222,222,221 966,748,392 266,473,82 9 (9) 722,863,223,001 34,872,629.248 687,990,693.753 (4) 1,112,222,221 401,987.324 710,234.897 11- =5; 11- -.6. (6) 122,210,121 67,660,016 64,660.106 (8) 222,222,221 182,463,697 39.768.624^ (10) 13,010,602,700 101 9.250,223.723.654 3.760.318,976 447 Review Work on any Combination. JliXEBCISE 1. (1) 80,008 31,243 48,766 (3) 1,000,000 293.784 706,216 (4) 1,000,000 467,312 532,688 (2) 180,009 93.624 86.4 86 (6) 1,000,000,103 101.092,028 898.908,076 *1 90 AR1THMKTK3. 8,000,0(4), lei 2.080,109.173 6,919,890,928 840.000,364,201 1 20,731.89 2,109 71068^472^092 Exercise II. (2) 484,030,298,046 128,910,012,031 355.120.286,015 (4) 420,790,010,112 124 730,913.871 306.059.096.241 (5) 3,000.801,800,103 1.287.121.073.109 1.713.680.726.994 PROBLEMS. _, , Exercise I. Find the sum of . 1. 160, 23, 47, 8 and 31. [Ans. 269.] 2. Thir^-six; Forty-eight ; Tvrenty ; Fifty-nine ; Three. [Ans. 166. j ' ' •> ' 3. One hundred and twenty-one ; Three hundred and e^ht ; Seventy-nine ; One hundred and fifteen. [Ans. 4. The odd numbers between 2 and 12, [Ans. 36.] 5. The even numbers between 1 and 11. [Ans. 30.] Exercise 11. Find the value of : 1. 19-3-f6-f-8-5-J-17-14. [Ans. 28.] 2. 84-13-27 -f76-4H- 12. [Am 91.] .S. 12-1-16-15 + 97-34-29. [Ans. 47.] 4. 76-39-H98-I-84-25-.23. [Ans. 171.1 5. 274 + 153-326-f-282-108. [Ans. 276.] Exercise III. I add to 84 to make 113? 1. What number must [Ans. 39.] 2. What number must I add to 638 to make nine hun- dred and nine? [Ans. 37lJ 3. What number must I add to four hundred and seven to make 1,074 ? [Ans. 667.] 4. What number must I add to five thousand and seventy to make ten thousand ? [Am,. 4,930.] 5. What number must I add to seventy-one thousand three hundred and one to make 100,000 ? Write answer m words. [Ans. Twenty-eight thousand six hundred and ninety-mne.] (91) i j ? 92 ARITHMETIC. Exeixise IV. [An8.^7.f '"""'^'' ™"** ^ '"** ^""" ^21 to make 34? 2. What number must I take from 6,372 to make two thousand one hundred and .eventy-six ?' [In.. sflM ] 3. What number must . take from thirty-eight thoi.- f wi".' ^ T^^ '^'^39 ? [Ami. 19,667.1 iiev^nT.^ilT*^!?'!!^^ **^« ^^^"^ o«« niiiiontomake 6. What number muflt I take from one miUion and one to make eight huD<'red thousand and two ? Write W^ Zd Si:ri?"' .f^"- ?"^ ^"^^^ aud^JtySfthT saiid mne hundred and ninety-nine, j Exercise V. 1. Take the sum of 56 and 93 from 618. fAns 469 1 f«>m JCtSd"* lis? irr '"""" " "■» ^ K«f* '^*'^on*^VU^,''' *" **»« numbers ending in "2" between 30 and 70 from 286. [Ans. 98.1 *^ 5. lake the sum of one hundred and one ; two hundred and mnety ; fifteen ; four hundred and eightVlIromTSS? ^JurtTenJ '"'''"' '" ^'•^" f^^' ^"« hundredCd Exercise VI. »,„L ?*"* 1^® """^ ^'^ ^'^5 a»»d two thousarid three PROBLEMS. 93 fchl^Tr^Slti^'^^ ^* *^« difference between tnem. [Ans. 35,878 j Exercbe VII. 1. How much leas is 293 than 621 ? [Ana. 328 1 a. How much leas is 2,004 than 29.001 ? [Ans. 26.997 1 3. How much greater is 866 than 389 ? fAns. 467 1 rxt. «°«1L?"*'** ^'■*"**** " '®^- l^ouaand than 8,004 ? l_A.ns. OjVWo.j 6. How many more in ten thousand than in two thous- and and two? [Ans. 7,998.J i»n m cwo tnous- • Exercise VIII. 2 Sti? ^;k^'^ ^'**" 8 376.420. [Ans. 2.679,08a] l»il^^o^®rA'^®Tt*'fn5!'''®«° 3,421,008.001 an^ Q iS?' - • ^^' ^' ^ ' ^ 364,074. ] 1 air^S? '^^ thousand five hundred and four take i!ll' 1 ""''®' "^ ^°'^«- C-^n* Six hundred and TA** ^a ?® *° ^® difference between 1,123 and 249. 6. Fmd the differenc between 847 aud 468 and to the rematncterotWonehund'^d. [Ans. 479.] Exercise IX. 1. The addends are :— Eight hundred and four ; four hundred and five ; five Jnd'Stf^^ *** ""^ fourteen ; seven thoiisand Find Uieir wm and take it from one hundred thousand |_Ans. oo,o41. 1 I l?'?'*f"'"''°'*'«8+'.3<»-<.379.[AML6,37ill 3 871] ' "* ^'^^^-I-OM+Z-ISB. [Am. ^'Sk- 94 ARITHMETIC. ExerciM X. 1. Subtract 216 from 691. [Ans. 476 ] 2. Subtract 135 from 225 + 882. [Ans. 972.] 3 The minuend is 2.040 and the subtrahend ia 1.191. Fmd the remainder. [Ang. 849.] 4. The minuend is 1,763 and the subtrahend is 984. What IS the difference 1 [Ans. 779.1 tJlmA^ *^'?^ "^VJ' ^ and from the remainder take 10,424. [Ans. 17,272 Exc.^ise XI. 1. How many days altogether in the three months. March, Apnl and May / Give your answer in words ; XCn? ^" numerals. [Ans. Ninety-two days; 2. How many days in the mmmer mo; , 1 In the (Mtvmn months? Give the mm of the two answers in Jioman numerals. [Ans. CLXXXIIL] 3. Add 25 cents ; 33 cents ; 82 cents ; 10 cents : 8 cents ; 18 cents ; 60 cents. [Ans. ^2.26.] [kmf'm.llf'' ^'^' •*"*' ^^<»"^5 ^08; $0.03. 6. Out of a ten dollar bill a farmer spent 17. 08. What money had he left ? [Ans. $2.92.] Exercise XII. 1. Make the largent number that can be made from the three figures 1, 5 and 9 ; and from it take 237. [Ans. 2. Make the ma^hst number that can be made from the %ires 8, 0, 4 and 6 ; and from it take 189. [Ans. 3. From the iar^ number that can be made from the figures 4, 5 and 3 take the smallest number that can be made from the same figures. [Ans. 198.] 4. Take the amaUest number to be made from the J^^x^'J *°° ^ ^^ ^fae largest number to be made from the figures 1, 6 and 3. [Ans. 602.J :?■ PBOBLXMS. 95 6. SnbtnMst the largut number to be made from the fiflurM 0, 0, 2 and 5 from ten thoaaand and one. [Ana. BxardM XIII. 1. John had read in hia Reader as far aa leaaon XXXIV. Write thia in figures. [Ana. 34.] 2. Write in Rom an nnmertUs : 18 ; 13 : 4M : 81 : 100 : ^JAna. XVm. ; XIH. ; XLIX. ; LXXXI. ; C. I 8. Write injmtret : XLHI. ; LXVni. : CIV. ; XCIX.: M.; DCC3XXXI. [Ana. 43 ; 68 ; 104 ; 99 ; 1000 ; 731.] 4. I had three Bontan eoins on which were theae dates : DLV.; CCVm.; CDX. Write fkjlgure*. [Ans. 666: 208 ; 410.] 6. In dieae books I saw theae datea : Andersen's Fairy Tales. . . ^ . . .DCCCXL. ; Robinson Crusoe OMLXXXVIII. Write in .^^M. (Ans. 840 ; 988. J Exercise XIV. 1. Sam'a father gave him for a Xmas present 6 ten- cent pieces. He spent 26 cents on a book for his sister and 11 cents on marbles. How much had he left? [Ana. 14centa.j 2. Tom had a dollar bill and he gave his 2 brothers 30 cents each. How much had he left ? [Ana. 40 oenU,] 3. How much would I have left out of a hoo doUar bill if I gaye 60 cents for a knife, 16 centa for a ball and 10 cents for a slate ? [Ana. 91.25.1; 4. A boy had 96 ; his sister 96 ; his mother 960 and hia father 9100. How much money had they idtosether ? [Ana. 9161.] / •«» 6. Fanny had 76 cents. She gave her brother 86 cents and her sister 16 cents. How much had she left for her- aelf? [Ans. 36 cents.] ExerdM XV. 1. Willie's brother is 16 years old ; how much longer must he live to be 27 years of age 1 [Ans. 12 years.] M ARITHMETIC. w*/*'"^"^^ *".""*/■•'■'*'•■ •" •>•' examination than her friend Aim,e. who had M marks. Low many marki had Jennie ? f Ans. 77 marks] 3. Our school had 23 boys and 20 girls on openirre came and 2 boys left% Jj aS MhdarH 1 "" ""*"^ "cholnrs are in the school / [Aiw. 4. John was born in 1876 and lived till 1894. How old was he? [Ans. 19 vears.] wmU^*"**""®'" "'"'•'^^ ^^ *" o^d ^^^ of fwry tales, which was given to her in the year 1864. She gave it [IZ S ye'arlT' ^'^''' """ "^ ''*** '^' '^*'^^' Exercise XVI. fhf "^u/"""' " ^^ f«®^,*«de and 24 feet wide. What is the distance around it ? f us. 80 feet 1 more'^^TSln^'** '^^ """"u'''' ^'« ""^'''^^ S^ve him 19 rlr^ I *r1 u *"*" ,?*o^^r^'* °°""" 27. How m«iy hai! James left for himself? [Ans. 67 marbles. J ^ 3. lorn 8 father bought a house and lot for $4,750 9i!mr "^^ • ^^^ ^^ '^^ ^"* cost? [C: !««; ^ n ^*" *" ^/'* '*''"^® ^ * f®et wide and 18 feet long. How many feet will May walk to go around the hall once? [Ans, 44 feet.] ""« i-ue (J: 7^® *''^i?' °" ''"'' <«^her'8 table is 2 feet wide and 6 feet long. How many feet of fringe will it take fw tnmmmg ? [Ans. 14 feet.] Exercise XVII. thiw^jrX *'«£««'««ng.at pitching the ball. He sux*?"[risirj ''' ''-'' ''^-^ ^« '^^ la^S^f ^l?'"'^ i". the orchard and he threw an apple 13 feet to his rujht, and another apple 15 feet to^^Kis ^Jt. How many feet apart wer« the apples ? [Ans. 2» PBOBLIMS. 87 3. A Im^ slingg a stone 35 feet wp the roed and another ■tone 29 feet down the road. How far apart are the tw^ ■tonee ? [Ana. 64 feet.] 4 Mr. Smith Hvee 98 miles east of Toronto, and Mr. Brown livet 47 miles toett of Toronto. How far apart do they lire ? fAns. 145 miles.] 6. Edith lived 176 yards north of the school and Mabel lived 228 yards amUh of the school. How much nearer the school did Edith live ? [Ans. 62 y&.ds.] Exercise XVIII. 1. Maggie and Ettie picked 123 pints of berries in the holidays ; if Maggie picked 79 pints, how may pinta did Bttie nick 1 [Ans. 44 pints.] 9. Annie's Sunday School prise book has 468 pages in It She has lead 189 pages. How many haa she still left to read 7 [Ans. 274 pages.] 3. Ii^n orchard there were 68 more apple trees than peach trees. There were 113 peach trees. How many trees altogether in the orchard ? [Ans. 284 trees.] 4. A farmer had 260 sheep. He sold 116 to a butcher and 17 of the others took sick and died: How many had he left ? [Ans, 118 sheep.] 6. Fred is making a collection of stamps. He has 67 now. How many more must he get to have 123 ? [Ana 66 stamps ] ExerdM XiX. 1. Dr. Brown left his office and rode 7 miles to see a little boy who had hurt his foot Then he returned to his omee and went out a^ain, riding 12 miles to a sick man. After returning to his office the second time how many pules had the doctor ridden altogether ? And how much 18 It lass than 60 miles ? [Ans. 38 miles ; 12 miles. ] 2. A newsboy buys 36 papers on Monday, 47 on Tues- day, M on Wednesday, 61 on Thursday, 70 on Friday and 83 or Saturday. How many papers did he sell that week if he sold all but 18 ? [Ans. 337 papers ] 3. In a box of chestnuts there w«re five hundred and eleven nuta. Fxank took 123 out and his sister took out 98 ARITHMRTIC. 34 lesi tluii he did. How many were left in the box ? [Ans. 299 ch'^atnute.] 4. Jim drives the cow» twice a day to be milked. How many times will he have driven them in the aummer months? [Ans. 184 times.] ^. In what year was ii man bom who died in 1871 at the age of 94 / [Ans In 1777.] Exercise XX. 1. A grocer has three boxes filled with eggs ; the first contains 2,(X)7 ; the second contains 128 less than the first ; and the third contains as many as the first and second toj^ether less .». How many eggs in the three boxes ? [Ans. 7,703 eggs.] 2. Tom bad 416 marbles, his aunt gave him 29 less than 227, then he gave his brother Jack and his cousin Bort ir.M each. How many had Tom left ? [Ans. 297 marbles.! 3. A bicycle dealer owes f 1 ,860 ; if he had |8 less than fVAM) he could pay all he owes. How much money Raa he ? [Ans. $1,258. J 4. A man bought a farm for $8,790 ; he spent 1638 for new sheds and »807 for cattle. He then sold out the whole for $12,000. Did he gain or lose, and how much ? [Ans. $1,775 gain.] 6. Mr. and Mrs." King and their two children, Fred and Maud, got weighed. Mr. King weighed 150 pounds more than his daughter ; Mrs. King weighed 108 pounds less than Mr. King ; Fred weighed 42 pounds more than his mother; Maud weighed 97 pounds. What did the others weigh, tnd how much did the whole family weigh -alt«)gether ? [Ans. Mr. King 247 pounds ; Mrs. King 139 pounds ; Fred 181 pounds ; whole family 664 pounds. J Exercise XXi. 1. Mr. Brown, a farmer, had $1,225.75 in the Bank of Commerce . He drew out eighty-five dollars to buy a bi- cycle for his son John. In a week. Mr. Brown put in the bank throe hundred dollars .tnd sixty- five cents. He drew out again ninety dollars and sixteen cents for r^- PROBLEMS. 99 pniring hit bftrn. How much had he left in the bank ? lAn.H. «I,361.24.] li. WillUm, Fred ;»nd John are three brotherB. Their rather died leaving his money willed tri them in this way : William was to receive $11,985 ; Fred, one hundred and 3ighty-nme drJlara leu than William ; and the sum of Nyihiam's and Fred's money less nine thousand and eighty-four dollars was what John was to receive. Whut was Frod to receive ? What was John to receive i What was thu.r father worth ? TAns. Fred, $11,796 ; John. $14,697 ; Father was wortli $38,478.] ' ^ ' ' y. A man bought a house and ground for $9,266 ; he built an extension to the house which cost him $1,836. The house w..^ then destroyed by fire and he received three thousand seven hundred and five dollars from the insurance company. How much did he lose ? fAns. $7,396.] *• 4. A man had four money boxes. He put two thou- sand five hundred and six dollars in the first box ; one thousand nine hundred and eighteen dollars in the second box. In the third box he put as much as in the first and second together. How much was in the fourth box, sup- posing he was worth ten thousand dollars ? [Ans. $1,162!.] 6. A wholesale tea merchant buys six thousand and wxty pounds of tea. He has four ches t» put it in. The first holds one thousand and ten poui ; the second holds one hundred and one pounts lens .uan the first : the third holds as much as the firiit ■.«J second less ninety pounds. How much muft the foi-'^h hold ? fAns. 2 312 {K)und8.] ' Exe^..ieXXIl. 1. John Porter owed James Smith $8,000 leu $179. He paid his debt by giving some property and two thousand eight hundred and fifty three dollars in cash. How much was the property supposed to be worth ? [Ans. $4,968. ] 2. I purchased a house, paying eight thousand dollars. I then spent one hundred and eighteen dollars less than SIX hundred dollars in improvements ; after this I decided to sell. Mr. Clark bought from me for nine thousand and fifty dollars How much did I make ? [Ans. $568.] 100 ARITHMETIC. 3. WiUiamhwi $201.63; John haa «13.49 lea. than Wilham and $9.39 more than James. Fred has as much FredMr^.te9T'" ^^ "^^ ^^^ »^- 4. James Robertson, hardware mercliant, had at the begmnmgof the day $648.25 in his safe; he received during the d.y $237.19; he paid out thewmeday^ loss ] 1 cents. How much cash had he in his safe at S end of the day ? f Ans. $855.55.] 5. A bicycle dealer received durmg the day $5ia He ^t f°^-/l!""« ,*^^'" /^*y. ^^^ «"•» «^ $18.19 and $13.08. What did he make that day ? [Ans. $478.73.] Exercise XXIII. 1. Mr. Thompson has $175 worth of poultry. He sold them so as to make $20 loss 91 cents ; what wL the selling price of the poultry ? [Ans. $194.09.] ^ .^'■^.^l^^^^^^'^^^i^'^ifi^ted by ten thousand two hun- dred and fifty-one persons on Monday ; nine thou and and SIX persons on Tuesday ; 3,984 persons on Wednes- day ; the diflFerence between Monday and Wednesday will give the number who attended on Thursday ; the sum of Tuesday and Thursday will give the number who atten™ ^ *uday. On Saturday there were ninety persons less in attendance than on Friday. How many Arsons visited the exhibition on Saturday ? [Ans. 15,174 persons 1 A.h A^u ^'^i^S ^""'^ thousand dollars less three hun- filf *" »,J J"^^J*°^iT,P*''* "^ *'"« <=»'»*' «l«^«n dolllarsless than eight hundred dollars, and at another time five hun- dred dollars. How much does he still owe ? [Ans. $408 1 f ,•,;• it "^ u "^^^ ""r^ ?'*^'" hundred dollars paid at one S!l •ff''^^ ''^ u'^'"^'* *"!«"« *^°"*" 5 "'d at anther time the difference between $820 and $349 ; and the third time te [tr^'^^r """ ™"' ""' '' ^^ ''' '"""^ ««w ^ T!" ^"«ht » farm for $6,987 ; he spent two thous- J?,i^*!j^ T.^"^y. '*''"*™ ^^'^ improvements and three hundred dollars for stock. He then sold the whole for nme thousand two hundred and fifty doUars ; did he gain or lose, and how much 1 [Ans. He lost $67 ] ^^'' PROBLEMS 101 Exercise XXIV. 1. A farmer's horses, cattle and sheep number nineteen leu than one hundred and fifty. He has IS-horses ; 68 more cattle than horses. How many sheep has he? [Ans. 33 sheep.] 2. A man who had to collect money from four men re- ceived altogether $1,639 ; from the first he got four hun- dred and fifty-eight doUars ; from the second sixty -nine collars more, and from the third ninety-three dollars less than thw. How much did he receive from the fourth ? [Ans. f289.] 3. A span of horses weigh 2,476 pounds. One weichs the sum of 618 and 689 pounds. What does the other weigh ? \V rite answer in words, also in Roman numerals I Ans. 1,168 pounds ; one thousand one hundred and sixty eight ; l&CLXVIII.] area ana 4. rae population of three towns is as follows : The first IS nmeteen thousand three hundred and eighty-five ; the second is one thousand and nineteen less than the Imt ; and the third is nine hundred and eighty-nine less than the second. What is the population of the third town? [Ans. 17,377.] 5. John Reid bought of Thomas Gibson 923 acres of land for twenly-five thousand doUars. For 41 6 acres he paid thu^en thousand three hundred and seventy-one dollars. How many acres were in the remainder ? And what money did it cost ? [Ans. 507 acres ; $11,629.] Exercise XXV. 1. A farmer bought two hundred and fifty cows for five thousand three hundred and thirty doUars. He fed them for one year at an expense of $2,000 less fifty dollars, and then «)ld the entire herd for six thousand one hundred and nmety-nine dollars. How much did he sain or lose? [Ans. He lost $108.] *^ , ^iJ^L ^^l^^ ^"«1»*' one hundred and nineiy-three sheep *u •^•. ^ ^' °?**= •l^O to get them to market. Eight sheep died on the way, which was a loss of $40. Hewld the remainder for $1,480. What did he gain? [Am. f3o5 gain.] " '- MHiilil nil jnn 102 ARITHMETIC. K ^FV^^ workman earned $79 by working a certein number of days He bought a coat which cort $11.69 : a mlway tijket which cost f4.86 ; and a pair of boot, for • Vu V ,0 r. ^®i®^*= ^ ■P®***! after putting 126.00 in the bank ? [Ana. $33.96.^ f a v-w-w 4. There were two candidates in an election. The whole number of votes was two thousand four hundred and eighty-six. The defeated person got nine hundred and two votes ; what was the majority? [Ans. 682 1 Tif 'n.u'^o JCr^**^ * steamer for thirty thousand doliirs. He paid $12,696 m cash, and $3,898 less in goods. The fAm"S^^508 f '*'*" P'^'P^^'^y- What was thehuid worth? Exercise XXVI. 1. In a battle the number of soldiers in the regiments was ten thousand and eighty ; of these 419 were killed : SIX hundred less twenty-three were wounded. How many uninjured remained ? [Ans. 9,084 1 AK^'i^ ^}^ "^ ^'^''^ **"' ^^'^^5 my furniture for $4,- 060 less than my house ; my bam and contents for $760 more than my furniture. How much cash did I receive ? ru^l^edTlTar:^]"^''"- C^- Twelve thousand three 3. Frank White decided to sell hU farm. The auc- tioneer s charges were five dollars and three cents. The ^wyer s expenses were fifteen dollars and sixty-nine cents How much did he receive if the farm sold for seven thou^ sand dollars less twenty-three dollars ? [Ans. $6,966 28 1 •B^tTf^^^P"*.^" T"]^^ ^^ 8*^'^ mines gaine'^ f6,d95. But the next day he lost $127 + $396. In a few months, however, he made three thousand and ten doUars and immediately lost two hundred and five dollars. How much more did he gain than lose on the whole ? [Ana. 6. A man bought five houses for twenty thousand dol- lars. For the first he paid $260 moria than for the •^•ujJ?®",**'^*"**^^^e8«*han the third. Bow much did he pay for the fourth house ? [An^ $4,467. j "SCHOOL HELPS" SERIES CAHAOIAM HISTOBT MOTES, for Srd, 4th and 6th CUhm. Bjr G. B. Hendenon, Editor of Th^ CamaoiaH Tbachbk tuti Tub Emthancs ; and C G. Fnier, AsdfUat liuMr ia Glad- ■tgos Av«. School, Toronto. Pric«, 15 nnta. BimSH BISTORT NOTES, for Spd. 4th and 5th CIu set. By G. E. Heodenon and C G. Frasor. Prioa, 15 cantb 6I06SAPHT NOTES, for 8Pd, 4th. and 6th Claues. Bjr G. E. Hendenon, and G. A. ^nrnt, Hawketvilk, Obi. iSoeata. EXERCISES IN ARITHMETIC FOR FIFTH CLASSES. B7 G. E. Hendeiion and E. W. Bruce, M.A. Price, 15 Teachers' edition, containbg answers, ao cents. EXEBCISBS IN ARrrHMETIC FOR FOURTH CLASSES. By G. E. Henderson, and W. E. Groves, Principal Church Streal Model School, Toronta Price, 15 cents. Teachers' Bditioa, earn- laininK Answers, eo cents. EXERCISES Of ARITHMETIC FOR THIRD CLASSES. By G. Henderson, and E. W. Bruce, M.A., Prindpd Hnraa Street School, Toronta Price, 15 cents. Teacher^ Editioa, yarn- taining Answers, so cents. EXERCISES or ARITHMETIC FOB SECOND CLASSES. By G. E. Henderson and B. W. Bmce, M.A. Prioa* u oaaliL TeacheiB' Editioa, containing Answers, is cents. EXERCISES IN ARITHMETIC FOB FIBST BOOK TBACBBBS. By G. E. Henderson, and Miss R. Church, Mks A. Haidiag, Teachers in Church Street School, Tonmto. Price, ao ewta. (This book is devotad to the teaching of NotatiaB, ^ HMm am Snbtraction.) MOTES CM PHTSIOLOOr AND TBHPBBANCB. ■yaK.Headeiaaoa>dC.anaaw. PrisikieceiM. ;^- miCISIS Dl OlABMAl FOI TBIIO A>D f OUITB CLAaUl BraB.H«id«mMdOM.A.FraMi. PriM.isenti. LANOgiai LB8S0MS POR FUST. UCOMD AID TBIU CLA88IS Bjras. ■ad C O. FraMr. Prioa, s$ ( IXBICISIS IH COMPOSITION POl POURTH AMD PIPTI CLAS8R8 B]raB.H«MUtMaMidCC. PrsMr. Orfoa, «5 PB0HIC8. TOCAL EXPRBSSION AMD SPILUNG Bj Mi« R. If. Chnrah and MiM A. A. Hwdii«. T( 9Hm, ■AIUAL O** PimCTUAnOII. By Xa.ftot. Priot.isetati. •UHMART OP CAKADIAM BISTORT IN 9y a W. Johun. Uppw C RNTRAMCS I3CAMINATI0N PAP] ▼RRSB. Geilaga. Priea, momMl »RRS POR THR PAST SIX TRARS PatqiUM §otm wfoh Mibjtcts trovpad for cImb ma%. By G. R. H iBdi w w. Pika,Mo«b:ar.ia aliilM«riwo«r POBUC SCHOOL LRAVINO PAHRS. Amacad SUM M Rattmaea. M HMM fri» THE EDUCATIONAL PUBLISHINQ Ca ROROmO. CMT ■^'^ ^ H KuH^iWm^ U'WC J. / '■'■NllVapMM,-'^*^ ' '^? il- ■: Y\ 'At ':i^. :'''^^:4]