A
PRI M ARY
ARIT H M E TIC
WORK BOO K
A P r i m a ry A r ithmetic is a m a t h book published i n t he 1880’s a nd w as
a u t hored by E dw a r d O l ney . A fter look i ng a t a lot of publ ic dom ain
m a t h books, I li ked t he set up of t his one.
M y da ugh ter w a n t i ng a ‘m a t h book’ l i ke her cousi ns, I set ou t to t u r n
t his in to one.  T h is book is t he result. M y hope i n sh a r ing it w it h
ot hers is t h a t it w il l be useful in som e w ay to ot her homeschoolers.
P a r t I consists of N u m bers, A ddit ion, S ubt r act ion, M ult ipl ica t ion,
D ivision, a nd F r act ions. I t is designed for F irst a nd Second G r a des
(yea rs)
P a r t I I consists of a condensed cou rse for pr act ica l l ife, i ncl uding
ba r ter, a nd “cast ing in terest.” I t is designed for T hird a nd F ou r t h
gr ades.
E njoy,
C y n thi a
© 2007 A lbr igh t N ews
T his wor k book w as crea ted by C y n t hi a A lbr igh t a nd is t he proper t y of
A lbr igh t N ews. Copies m a y be m ade for use in you r ow n homeschool.
A
PRI M ARY
ARIT H M E TIC
WORK BOO K
P A R T I.
T H E F U NDAM E NTAL COMBINATION OF T H E
D I G I T S, A N D A P R I M A R Y C O U RS E I N C O M M O N
F R A C T I O N S A N D D E N O M I N A T E N U M B E RS.
F O R F I RS T A N D S E C O N D G R A D E S
(Y E A RS).
“T his p a r t is designed to gi ve t he p upil a t t he end of his second yea r, i.e., B Y
T H E T I M E H E I S A B L E T O R E A D , a good in tel ligen t k now ledge of t he A ddit ion,
Subt r act ion, M ult ipl ica t ion, a nd D ivision T ables; a k now ledge of t he n a t u r e
of Com mon F r act ions, a nd of t he Com mon D enom in a t ions of D enom i n a t e
N u mbers.”
M ultiplication
M ul t iplica t ion
71
M ultiplication
Pu rpose: To lea r n how to fi nd out the prod uct of a ny number less th a n 11
m ultipl ied by a ny num ber less th a n 11, a n d to fix the resu lts to memory; i.e.,
to lea r n the m u ltipl ica tion ta ble to 10 ti mes 10.
Method: Lea r n to fi nd out the product by a dd i ng the num ber to itself the
requisite num ber of ti mes.
F i rst E xercise.
1. If you pick a cher r y a nd p u t it i n you r
h a nd, a nd t hen pick a not her, how m a ny
cher r ies w il l you h a ve? H ow m a n y t i mes
h ave you pick ed 1 cher r y? T wo t imes 1
cher r y a re how m a ny cher r ies?
2. 1 + 1 = how m a ny? H ow m a n y t im es 1
a re 1 + 1? T wo t imes 1 a re how m a ny?
3. If you pick 1 cher r y, t hen a not her, a nd
t hen a not her, how m a ny t imes w i ll you h ave picked a cher r y? H ow m a ny
cher r ies w il l you h a ve? 3 t imes 1 cher r y a re how m a n y cher r ies?
4. 1 + 1 + 1 = how m a ny? H ow m a ny t imes 1 a re 1 + 1 + 1? 3 t imes 1 a re
how m a n y?
72
M ultiplication
5. If you r mot her gives you 1 cen t each d ay for 4 d ays, how m a ny t imes w il l
she h ave gi ven you 1 cen t? H ow m a n y cen ts w il l you h ave? 4 t im es 1 cen t
a re how m a ny cen ts?
6. 1 + 1 + 1 + 1 = how m a ny? H ow m a ny t imes 1 a re 1 + 1 + 1 + 1? 4 t imes
1 a re how m a ny?
7. If J a ne brea ks 1 needle each d ay, how m a ny does she brea k i n a wee k (6
days)? H ow m a n y a re 6 t imes 1?
8. T he sign x mea ns ti mes , a nd we r ead 3 x 2, t h ree t imes t wo.
9. Read 4 x 1, 3 x 1, 5 x 2, 6 x 4.
10. R ead 3 x 2, 4 x 7, 5 x 6, 8 x 9, 7 x 4.
1
1
1
1
1
1
1
1
1
1
=
+
+
+
+
+
+
+
+
+
1
1
1
1
1
1
1
1
1
=
+
+
+
+
+
+
+
+
1
1
1
1
1
1
1
1
=
+
+
+
+
+
+
+
1
1
1
1
1
1
1
=
+
+
+
+
+
+
1
1
1
1
1
1
=
+
+
+
+
+
1
1
1
1
1
=
+
+
+
+
1
1
1
1
1
2
3
4
5
6
=
7
+1=
8
+1+1=
9
+ 1 + 1 + 1 = 10
73
x
x
x
x
x
x
x
x
x
x
1
1
1
1
1
1
1
1
1
1
=
=
=
=
=
=
=
=
=
=
M ultiplication
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
10
0
1
0
4
Second E xercise.
1. T here a re 2 cher r ies in each bu nch, a nd 2 bu nches.
H ow m a n y t imes 2 cher r ies a re t here on t he t w ig?
H ow m a n y cher r ies a re t here? 2 t imes 2 cher r ies a r e
how m a n y cher r ies?
2. 2 + 2 = how m a ny? H ow m a n y t im es 2 is 2 + 2? 2 x 2 = how m a ny?
3. Joh n st ayed ou t of school 2 d ays to visit his u ncle, 2 d ays beca use he w as
sick, a nd 2 d ays he pla yed t r u a n t. H ow m a n y t imes did he st ay ou t 2 d ays?
H ow m a n y d ays did he st ay ou t i n al l? 3 t imes 2 d ays a re how m a n y d ays?
4. 2 + 2 + 2 = how m a ny? H ow m a ny t imes 2 a re 2 + 2 + 2? 3 x 2 a re how
m a ny?
5. J a ne fou nd 2 eggs on Mond ay, 2 on T uesd ay, 2 on W ed nesd ay, a nd 2 on
T h u rsday. H ow m a ny t imes did she find 2 eggs? H ow m a ny did she find i n
all? 4 t imes 2 eggs a r e how m a ny eggs?
6. 2 + 2 + 2 + 2 = how m a ny? H ow m a ny t imes 2 is 2 + 2 + 2 + 2?
4 x 2 = how m a ny?
74
M ultiplication
7. 4 t imes 2 a re how m a n y? If 4 t imes 2 a re 8, how m a ny a re 5 t imes 2?
H ow m a n y 2’s m ust you t a ke w it h 4 t i mes 2, or 8, to m a ke 5 t imes 2?
8. 6 t imes 2 a re 12. H ow m a ny a re 7 t imes 2? H ow m a ny 2’s m ust you pu t
w it h 6 t imes 2, or 12, to m a ke 7 t imes 2?
9. 8 t imes 2 a re 16. H ow m a ny a re 9 t imes 2?
2
2
2
2
2
2
2
2
2
2
2
+
+
+
+
+
+
+
+
+
2
2
2
2
2
2
2
2
2
2
3
=
+
+
+
+
+
+
+
+
2
2
2
2
2
2
2
2
=
+
+
+
+
+
+
+
2
4
2
2
2
2
2
2
2
=
+
+
+
+
+
+
2
5
2
2
2
2
2
2
=
+
+
+
+
+
2
2
2
2
2
2
6
=
+
+
+
+
2
2
2
2
2
7
2
3
4
5
6
=
7
+2=
8
+2+2=
9
+ 2 + 2 + 2 = 10
2
8
75
2
9
2
10
x
x
x
x
x
x
x
x
x
0
2
2
2
2
2
2
2
2
2
2
=
=
=
=
=
=
=
=
=
1
2
2
2
M ultiplication
T h i r d E xercise.
1. F r a n k spen t 3 cen ts each day i n t he wee k
except Su nd ay. H ow m a ny t imes did he spend
3 cen ts? H ow m a ny cen ts did he spend i n a ll?
6 t imes 3 cen ts a re how m a ny cen ts?
2. 3 + 3 + 3 + 3 + 3 + 3 = how m a n y? H ow m a n y t imes 3 is 3 + 3 + 3 + 3 + 3
+ 3? 6 x 3 a re how m a ny?
3. G eorge reads 3 p ages each d ay of t he wee k. H ow m a ny t imes 3 p ages
does he rea d? H ow m a ny a r e 7 x 3?
4. 3 + 3 + 3 + 3 + 3 + 3 + 3 = how m a n y? H ow m a ny t imes 3 is 3 + 3 + 3 + 3
+ 3 + 3 + 3? 7 t imes 3 a re how m a n y?
5. J a mes goes fish ing each day for 4 d ays a nd ca tches 0 fish each day. H ow
m a ny does he ca tch in al l? H ow m a n y a re 4 t imes 0? 5 t imes 0?
76
M ultiplication
6. 4 t imes 3 a re 12. H ow m a ny more 3’s a re 5 t imes 3 t h a n 4 t imes 3? H ow
m a ny a re 5 t imes 3?
7. 6 t imes 3 a re 18. H ow m a ny a re 7 t imes 3?
8. 8 x 3 = 24. H ow m a ny a re 9 x 3? 10 x 3?
9. If you k now how m a ny 5 t imes 3 a r e, how ca n you tell from t his how
m a ny 6 t imes 3 a r e?
3
3
3
3
3
3
3
3
+
+
+
+
+
+
+
+
3
3
3
3
3
3
3
3
+
+
+
+
+
+
+
+
3
3
3
3
3
3
3
3
3
3
=
+3=
+3+3=
+3 + 3 + 3
+ 3+ 3 + 3
+ 3+ 3 + 3
+ 3+ 3 + 3
+ 3+ 3 + 3
3
4
2
7
3
6
2
6
=
+
+
+
+
3
8
1
4
3
3
3
3
3
4
5
6
=
7
+3=
8
+3+3=
9
+ 3 + 3 + 3 = 10
3
7
3
5
3
4
1
8
77
3
5
2
9
3
8
0
3
x
x
x
x
x
x
x
x
3
3
3
3
3
3
3
3
=
=
=
=
=
=
=
=
0
5
1
3
3
7
2
3
3
10
3
3
M ultiplication
F ourth E xercise.
1. H ow m a ny legs h as 1 la m b? F i ve l a mbs h ave how m a ny t imes as m a n y
legs as 1 la mb? H ow m a ny legs h ave 5 la m bs?
2. H ow m a n y legs h ave 4 la mbs? H ow m a n y t imes as m a ny legs as 1 l a mb?
H ow m a n y a re 4 t imes 4?
3. H ow m a ny legs h ave 6 l a mbs? H ow m a n y t imes as m a ny legs as 1 l a mb?
Six t imes 4 a re how m a ny?
4. Seven l a mbs h a ve how m a n y t imes as m a ny legs as 1 la m b? 7 la m bs
h ave how m a ny legs? 7 x 4 = how m a ny?
5. J a mes bough t 8 or a nges a nd gave 4 cen ts for each. H ow m a n y t imes 4
cen ts did he give for all h is or a nges? H ow m a n y a re 8 t imes 4?
78
M ultiplication
6. 4 + 4 + 4 + 4 + 4 + 4 + 4 +4 + 4 = how m a n y? H ow m a n y t imes a re 4 + 4 +
4 + 4 + 4 + 4 + 4 + 4 + 4? 9 x 4 = how m a ny?
7. 3 t imes 4 a re 12. H ow m a ny more 4’s a re 4 t imes 4 t h a n 3 t imes 4? H ow
m a ny a re 4 x 4?
8. 5 x 4 = 20. H ow m a ny a re 6 x 4? 7 x 4? 8 x 4? 9 x 4? 10 x 4? H ow m a ny
more do you t a ke each t ime?
4
4
4
4
4
4
4
+
+
+
+
+
+
+
4
4
4
4
4
4
4
+
+
+
+
+
+
+
4
4
4
4
4
4
4
+
+
+
+
+
+
+
4=
4+ 4
4+ 4
4+ 4
4+ 4
4+ 4
4+ 4
=
+
+
+
+
+
4
4
4
4
4
=
+
+
+
+
4
4
4
4
4
5
6
=
7
+4=
8
+4+4=
9
+ 4 + 4 +4 = 10
x
x
x
x
x
x
x
4
4
4
4
4
4
4
=
=
=
=
=
=
=
4
5
4
7
4
4
4
6
4
8
4
10
4
9
3
3
3
7
3
4
2
7
1
8
3
6
2
8
3
5
1
5
3
8
0
4
1
4
2
4
3
1
4
1
79
M ultiplication
F ifth E xercise.
1. H ow m a ny poin ts h as one st a r? H ow m a n y h ave 5 st a rs? H ow m a ny
h ave 6 st a rs? 7 st a rs? 8 st a rs? 9 st a rs? 10 st a rs?
2. Six st a rs h ave how m a ny t imes as m a ny poi n ts as 1 st a r? Seven st a rs
h ave how m a ny t imes as m a n y poi n ts as 1 st a r? E igh t st a rs h a ve how
m a ny t imes as m a n y poin ts as 1 st a r?
3. 5 + 5 + 5 + 5 + 5 + 5 a re how m a n y t imes 5? 6 t imes 5 a re how m a ny?
4. 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 a re how m a n y t imes 5? 8 t imes 5 a re how
m a ny?
5. If Joh n ea r ns 5 cen ts each day, how m a n y cen ts ca n he ea r n i n 6 d ays?
H ow m a n y t imes as m a ny ca n he ea r n i n 6 d ays as i n 1 d ay? Si x t imes 5
a re how m a ny?
80
M ultiplication
6. H ow m a ny cen ts ca n Joh n ea r n i n 10 days, if he ca n ea r n 5 cen ts in 1
day? H ow m a ny t imes as m a n y cen ts ca n he ea r n i n 10 d ays as i n 1 d ay?
7. 3 t imes 5 a re how m a n y? H ow m a ny more a re 4 t imes 5? H ow m a ny a r e
4 t imes 5? 7 t imes 5? 8 t imes 5? 9 t i mes 5? 10 t imes 5? H ow m a n y more
5’s do you t a k e each t ime?
5
5
5
5
5
5
+
+
+
+
+
+
5
5
5
5
5
5
+
+
+
+
+
+
5
5
5
5
5
5
+
+
+
+
+
+
5+
5+
5+
5+
5+
5+
5
5
5
5
5
5
=
+
+
+
+
+
5
5
5
5
5
=
+
+
+
+
5
5
5
5
5
6
=
7
+5=
8
+5+5=
9
+ 5 + 5 +5 = 10
x
x
x
x
x
x
5
5
5
5
5
5
=
=
=
=
=
=
5
5
5
6
5
7
5
8
5
9
5
10
0
5
1
5
2
5
3
5
4
5
5
5
4
7
3
7
2
8
3
8
4
8
5
8
1
8
0
8
4
6
4
9
4
10
4
4
81
M ultiplication
S ixth E xercise.
1. H ow m a ny pet a ls h as one li ly? H ow
m a ny t imes as m a n y h ave 7 lil ies? H ow
m a ny pet a ls h ave 7 lil ies? 7 t imes 6 a re
how m a n y?
2. If 1 l ily h as 6 pet a ls, how m a n y pet als
h ave 8 li lies? H ow m a ny h ave 9 li lies? H ow
m a ny t imes 6 pet a ls h ave 10 li lies? H ow
m a ny pet a ls h ave 10 li lies?
3. If J a mes bu ys 6 or a nges for 6 cen ts apiece, how m a n y ce n ts m ust he p ay
for al l?
4. H ow m a ny t imes as m uch m ust J a mes pay for 9 or a nges as for 1? H ow
m uch m ust he p ay for 9 or a nges if 1 or a nge is wor t h 6 cen ts?
5. 6 + 6 + 6 + 6 + 6 + 6 a re how m a n y t imes 6? 6 t imes 6 a re how m a ny?
6. If each of 8 boys h as 6 n u ts, how m a ny h ave t hey al l? H ow m a ny t imes 6
n u ts h a ve t hey? 8 t imes 6 n u ts a re how m a ny n u ts?
82
M ultiplication
7. 2 t imes 6 a re 12. H ow m a ny more 6’s m ust you t a ke to m a ke 3 t imes 6?
H ow m a n y a re 3 t imes 6? H ow m a n y more a re 4 t imes 6? H ow m a ny a re 4
t imes 6?
8. 5 x 6 = 30. H ow m a ny a re 6 x 6? 7 x 6?
9. 8 x 6 = 48. H ow m a ny a re 9 x 6? 10 x 6?
10. W hen you k now how m a ny 7 t imes 6 a re, how do you fi nd ou t how m a n y
8 t imes 6 a re ?
6
6
6
6
6
+
+
+
+
+
6
9
6
6
6
6
6
+
+
+
+
+
6
10
6
6
6
6
6
+
+
+
+
+
6+
6+
6+
6+
6+
6
7
6
6
6
6
6
+
+
+
+
+
6
6
6
6
6
6
6
=
+
+
+
+
6
8
6
6
6
6
=
+6=
+6+6=
+ 6 + 6 +6 =
0
6
1
6
83
2
6
6
7
8
9
10
3
6
x
x
x
x
x
6
6
6
6
6
=
=
=
=
=
4
6
5
6
6
6
M ultiplication
Seventh E xercise.
1. T here a re 7 days i n one wee k. H ow m a ny t imes as m a ny days a re t here
in 4 wee ks? H ow m a ny days i n 4 wee ks? H ow m a ny d ays i n 2 wee ks? H ow
m a ny in 6 wee ks?
2. H ow m a ny d ays a re t here i n 8 wee ks? W hy? H ow m a ny days i n 9
wee ks? W h y: H ow m a ny days i n 10 wee ks? W h y?
3. If J a ne fi nds 7 eggs each day, how m a ny w i ll she fi nd in 6 days? W h y?
4. 7 + 7 = how m a ny? 7 + 7 a re how m a ny t imes 7? 2 t imes 7 a r e how
m a ny?
84
M ultiplication
5. H ow m a ny t imes 7 st a rs a re t here here? H ow
m a ny st a rs i n a row from left to r igh t? H ow m a ny
rows? H ow m a ny t imes as m a n y st a rs a re t here i n
8 rows as t here a re in 1 row? 8 t imes 7 st a rs a re
how m a n y st a rs?
6. H ow m a ny st a rs a re t here in 7 of t he rows from left to r igh t? W hy?
7. If 3 t imes 7 a re 21, how m a ny a re 4 t imes 7?
8. If 5 t imes 7 a re 35, how m a ny a re 6 t imes 7?
9. H ow m a ny more a re 8 t imes 7 t h a n 7 t imes 7?
10. 4 x 7 = 28. H ow m a ny a re 5 x 7? 6 x 7? 7 x 7?
7
7
7
7
+
+
+
+
7
7
7
7
+
+
+
+
7
7
7
7
+
+
+
+
7+
7+
7+
7+
7
7
7
7
+
+
+
+
7
7
7
7
+
+
+
+
7
7
7
7
=
7
+7=
8
+7+7=
9
+ 7 + 7 +7 = 10
85
x
x
x
x
7
7
7
7
=
=
=
=
M ultiplication
7
8
7
9
7
7
7
10
0
7
1
7
2
7
3
7
4
7
5
7
6
7
7
7
2
3
3
4
4
5
5
6
6
7
7
4
8
3
7
7
5
5
4
4
6
6
3
3
E ighth E xercise.
1. H ow m a ny o’s a re t here in a row? H ow m a n y e’s?
H ow m a n y b’s? H ow m a ny let ters in each row? H ow
m a ny rows? H ow m a n y t imes 8 let ters a re t here?
H ow m a n y let ters i n all? 9 t imes 8 let ters a re how
m a ny let ters?
2. If we w r ite a row of 8 m’s u nder t he g’s, how m a ny rows of let ters w il l
t here be? H ow m a ny t imes 8 let ters? 10 t imes 8 let ters a re how m a n y
let ters?
3. If we cover up t he row of g’s how m a ny rows of let ters w il l t here be? H ow
m a ny t imes 8 let ters? 8 x 8 = how m a ny?
4. If t here a re 9 boys, a nd each boy h as 8 cen ts, how m a ny t imes 8 cen ts
h ave t hey a ll? H ow m a n y cen ts h ave t hey a ll? 9 t imes 8 a r e how m a ny?
86
M ultiplication
5. If t here a re 10 gir ls i n t he class, a nd each gir l h as 8 bu t tons on her dress,
how m a n y bu t tons a re t here on al l t heir dresses? H ow m a ny t imes 8
bu t tons a re t here? 10 t imes 8 a re how m a n y?
6. 2 x 8 = 16. H ow m a ny a re 3 x 8? 4 x 8? 5 x 8? 6 x 8? 7 x 8?
8 + 8 + 8 + 8+ 8 + 8 + 8 + 8 =
8x8=
8 + 8 + 8 + 8+ 8 + 8 + 8 + 8 + 8 =
9x8=
8 + 8 + 8 + 8+ 8 + 8 + 8 + 8 + 8 +8 = 10 x 8 =
8
10
8
8
8
9
0
8
1
8
2
8
3
8
N i nth E xercise.
1. H ow m a ny br a nches h as t h is pla n t? H ow
m a ny lea ves on each br a nch? H ow m a ny t imes
9 leaves a re t her e on t he pl a n t? 10 t i mes 9
leaves a re how m a ny leaves?
2. If you were to brea k off t he lowest br a nch,
how m a n y br a nches wou ld be left? H ow m a ny
leaves? 9 x 9 = how m a n y?
87
4
8
5
8
6
8
7
8
8
8
M ultiplication
3. If you were to brea k off t wo of t he lower br a nches, how m a ny br a nches
wou ld rem ai n? H ow m a ny leaves? 8 x 9 = how m a ny?
4. If you were to brea k off 3 of t he br a nches, how m a n y br a nches would
rem ain? H ow m a ny lea ves? 7 t imes 9 a re how m a ny?
5. H ow m a ny fi ngers h as a boy on bot h h a nds, w it h h is t h u mbs? H ow m a n y
h ave 10 boys? 10 tens m a ke w h a t?
6. H ow m a ny fi ngers h ave 8 boys? 7 boys? 6 boys? 9 boys?
7. If a boy ea r ns 10 cen ts each da y, how
m a ny cen ts does he ea r n in 2 days? 3
days? 6 days? 8 da ys? 10 d ays? 10 x 10 =
how m a n y?
88
M ultiplication
8. 2 x 9 = 18. 3 x 9 = ? 4 x 9 = ? 5 x 9 = 45. 6 x 9 = ? 7 x 9 = ? 8 x 9 = ?
9 + 9 + 9 + 9+ 9 +
9 + 9 + 9 + 9+ 9 +
10 + 10 + 10 + 10
10
9
9
+
+
9
9
2
9
9
10
10
10
0
9
0
10
1
9
1
10
2
10
+9+9+9=
9x9=
+ 9 + 9 + 9 +9 =
10 x 9 =
10 + 10 + 10 + 10 + 10 x 10 =
10 =
3
9
3
10
4
9
4
10
5
9
5
10
6
9
6
10
Tenth E xercise.
1. H ere a re t wo piles of money. I n t he upper
t here a re 5 3-cen t pieces. H ow m a n y cen ts a re
in it? 5 t imes 3 a re how m a ny? I n t he lower a re
3 5-cen t pieces. H ow m a ny cen ts i n it? 3 t imes
5 a re how m a ny? I n w hich pile is t here t he
most money? 5 t imes 3 is t he sa me as w h a t?
89
7
9
7
10
8
9
8
10
9
9
9
10
10
9
10
10
M ultiplication
2. J a mes ea r ned 3 cen ts each da y for 4 d ays. H ow m a ny cen ts h ad he?
Joh n ea r ned 4 cen ts each da y for 3 da ys. H ow m a n y cen ts h a d he? W hich
h a d t he mor e?
3. 4 t imes 3 a re how m a n y? 3 t imes 4 a re how m a n y? W hich is t he most, 3
t imes 4 or 4 t imes 3?
4. M a r y h as 10 5-cen t pieces a nd J a ne h as 5 10-cen t pieces. W hich h as t he
most? W hy?
5. If you cou n t t he rows of st a rs from left to r igh t,
how m a n y st a rs a r e t here in a row? H ow m a n y
rows of 7 st a rs e ach? H ow m a ny st a rs? If you cou n t
t he rows of st a rs dow n t he p age, how m a ny st a rs
a re t here in a row? H ow m a n y rows of 8 st a rs each?
8 t imes 7 a re how m a ny? 7 t imes 8 a r e how m a ny?
W hish is t he most, 8 t imes 7 or 7 t imes 8?
6. 5 t imes 3 a re how m a n y? T hen how m a n y a r e 3 t imes 5? W h y?
90
M ultiplication
7. 6 t imes 4 a re how m a n y? T hen 4 t i mes 6 a re how m a ny? W h y?
8. 7 t imes 6 a re how m a n y? T hen 6 t i mes 7 a re how m a ny? W h y?
91
M ultiplication
1x2=
, hence
2x1=
2x2=
1x8=
, hence
8x1=
2x8=
, hence
8x2=
1x3=
, hence
3x1=
3x8=
, hence
8x3=
2x3=
, hence
3x2=
4x8=
, hence
8x4=
5x8=
, hence
8x5=
3x3=
1x4=
, hence
4x1=
6x8=
, hence
8x6=
2x4=
, hence
4x2=
7x8=
, hence
8x7=
3x4=
, hence
4x4=
4x3=
1x5=
2x5=
3x5=
4x5=
, hence
, hence
, hence
, hence
8x8=
1x9=
, hence
9x1=
2x9=
, hence
9x2=
3x9=
, hence
9x3=
4x9=
, hence
9x4=
5x9=
, hence
9x5=
6x9=
, hence
9x6=
7x9=
, hence
9x7=
8x9=
, hence
9x8=
5x1=
5x2=
5x3=
5x4=
5x5=
1x6=
2x6=
3x6=
, hence
, hence
, hence
6x1=
6x2=
6x3=
9x9=
4x6=
, hence
6x4=
92
M ultiplication
5x6=
, hence
6x5=
6x6=
1x10=
, hence 10x1=
2x10=
, hence 10x2=
1x7=
, hence
7x1=
3x10=
, hence 10x3=
2x7=
, hence
7x2=
4x10=
, hence 10x4=
3x7=
, hence
7x3=
5x10=
, hence 10x5=
4x7=
, hence
7x4=
6x10=
, hence 10x6=
5x7=
, hence
7x5=
7x10=
, hence 10x7=
6x7=
, hence
7x6=
8x10=
, hence 10x8=
9x10=
, hence 10x9=
7x7=
10x10=
E leventh E xercise.
1. 6 + 6 + 6 + 6 a r e how m a ny t imes 6? H ow m a ny a re 4 t imes 6?
2. 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 a re how m a n y? H ow m a n y t imes 3? 8 t imes
3 a re how m a ny?
93
M ultiplication
1+1=
, hence
2x1=
6+6=
, hence 2x6=
2+2=
, hence
2x2=
7+7=
, hence 2x7=
3+3=
, hence
2x3=
8+8=
, hence 2x8=
4+4=
, hence
2x4=
9+9=
, hence 2x9=
5+5=
, hence
2x5=
10+10=
, hence 2x10=
1+1+1=
, hence
3x1=
2+2+2=
, hence
3x2=
3+3+3=
, hence
3x3=
4+4+4=
, hence
3x4=
5+5+5=
, hence
3x5=
6+6+6=
, hence
3x6=
7+7+7=
, hence
3x7=
8+8+8=
, hence
3x8=
9+9+9=
, hence
3x9=
10+10+10=
, hence
3x10=
94
M ultiplication
3. F il l t h is t able ou t to 4 t imes 10, a nd w r ite in al l t he resu lts. So a lso of t he
follow i ng, 5, 6, 7, 8, 9, a nd 10.
1+1+1+1=
,
hence
4x1=
2+2+2+2=
,
hence
4x2=
3+3+3+3=
,
hence
4x3=
4+4+4+4=
,
hence
4x4=
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
95
M ultiplication
4.
1+1+1+1+1=
,
hence
5x1=
2+2+2+2+2=
,
hence
5x2=
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
96
M ultiplication
5.
1+1+1+1+1+1=
,
hence
6x1=
2+2+2+2+2+2=
,
hence
6x2=
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
97
M ultiplication
6.
1+1+1+1+1+1+1=
,
hence
7x1=
2+2+2+2+2+2+2=
,
hence
7x2=
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
98
M ultiplication
7.
1+1+1+1+1+1+1+1=
,
hence
8x1=
2+2+2+2+2+2+2+2=
,
hence
8x2=
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
,
hence
99
M ultiplication
8.
1+1+1+1+1+1+1+1+1=
, hence 9x1=
2+2+2+2+2+2+2+2+2=
, hence 9x2=
, hence
, hence
, hence
, hence
, hence
, hence
, hence
, hence
100
M ultiplication
9.
1+1+1+1+1+1+1+1+1+1=
, hence 10x1=
2+2+2+2+2+2+2+2+2+2=
, hence 10x2=
, hence
, hence
, hence
, hence
, hence
, hence
, hence
, hence
101
M ultiplication
T welfth E xercise.
1. Repea t t he 2’s of t he m u lt iplica t ion t able 5 t imes,
t h us:
1 t imes 2 is ______.
2 t imes 2 a re ______.
3 t imes 2 a re ______, etc.
2. Repea t t he 2’s 5 t imes in t his w a y:
2 t imes 1 a re _______.
2 t imes 2 a re _______.
2 t imes 3 a re _______, etc.
3. Repea t t he 3’s 5 t imes t h us:
1 t imes 3 is ______.
2 t imes 2 a re _______.
3 t imes 3 a re _______, etc.
4. Repea t t he 3’s 5 t imes t h us:
3 t imes 1 a re _______.
3 t imes 2 a re _______.
3 t imes 3 a re _______, etc.
5. A nswer t he follow i ng 5 t imes.
2x3?
3x5?
1x2?
4x2?
4x3?
1x3?
2x7?
3x4?
5x2?
7x2?
2x8?
3x5?
3x1?
8x2?
9x3?
6x3?
7x3?
9x2?
5x3?
2x7?
3x9?
6. If 1 or a nge costs 4 cen ts, how m a n y cen ts w ill 3 or a nges cost?
(If 1 or a nge cost 4 cen ts, 3 or a nges w i ll cost 3 t imes 4 cen ts, or 12 cen ts.
7. If 1 penci l costs 5 cen ts, how m a ny cen ts w i ll 3 penci ls cost?
102
M ultiplication
8. If a boy lea r ns 2 lessons each day, how m a n y lessons does he lea r n i n 6
days? I n 9 d ays?
9. T here a re 7 days i n one wee k. H ow m a ny d ays a re t here i n 2 wee ks? I n
3 wee ks?
T h i rteenth E xercise.
1.Repea t t he 4’s 5 t imes i n each of t he t wo w a ys, t h us:
1 t ime 4 is _____________.
2 t imes 4 a re ___________.
3 t imes 4 a re ___________,
etc., etc.
4 t imes 1 a re ___________.
4 t imes 2 a re ___________.
4 t imes 3 a re ___________,
etc., etc.
2. Repea t t he 5’s 5 t imes in each of t he tow w ays, t h us:
1 t ime 5 is _____________.
2 t imes 5 a re ___________.
3 t imes 5 a re ___________,
etc., etc.
5 t imes 1 a re ___________.
5 t imes 2 a re ___________.
5 t imes 3 a re ___________,
etc., etc.
3. Repea t t he 6’s 5 t imes in each of t he t wo w ays, t h us:
1 t ime 6 is _____________.
2 t imes 6 a re ___________.
3 t imes 6 a re ___________,
etc., etc.
6 t imes 1 a re ___________.
6 t imes 2 a re ___________.
6 t imes 3 a re ___________,
etc., etc.
103
M ultiplication
4. M ult iply.
6
4
4
7
7
5
8
6
9
6
6
7
7
6
8
5
5
8
4
9
6
9
9
6
7
6
5
7
9
4
6
10
6
8
4
10
5
10
10
5
2
4
6
2
6
6
5
5
5. J a mes wor ked 7 hou rs for 5 cen ts a n hou r. H ow m uch did he ea r n?
6. Joh n wor ked 6 hou rs for 4 cen ts a n hou r, a nd H en r y wor k ed 4 hou rs for 6
cen ts a n hou r. W hich ea r ned t he most?
7. J a ne bough t 7 or a nges for 6 cen ts each. H ow m uch did t hey cost?
8. M a r y bough t 4 spools of t h rea d for 5 cen ts a spool, a nd gave t he cler k 25
cen ts. H ow m uch ch a nge shou ld he give her? H ow m uch did her t h read
cost? 25 is how m uch more t h a n 20?
104
M ultiplication
F ourteenth E xercise.
1. Repea t t he 7’s 5 t imes in each of t he t wo w ays, t h us:
1 t ime 7 is _____________.
2 t imes 7 a re _______, etc.
7 t imes 1 a re ___________.
7 t imes 2 a re ______, etc.
2. Repea t t he 8’s 5 t imes in each of t he t wo w ays, t h us:
1 t ime 8 is _____________.
2 t imes 8 a re _______, etc.
8 t imes 1 a re ___________.
8 t imes 2 a re ________, etc.
3. A nswer t he follow i ng 5 t imes.
8x7?
7x9?
7x4?
8x9?
6x9?
8x3?
6x8?
9x6?
3x8?
7x6?
7x7?
6x3?
8x6?
8x8?
4x6?
9x8?
9x9?
3x7?
9x7?
7x5?
3x9?
4. If 7 w hite hens h ave 8 chickens each, a nd 8 bl ack hens h ave 7 chickens
each, w hich h ave t he most ch ickens, t he w hite hens or t he black hens?
W hy?
5. Joh n ea r ns 6 cen ts a n hou r a nd wor ks 7 hou rs, a nd H en r y ea r ns 7 cen ts
a n hou r a nd wor ks 6 hou rs. W hich ea r ns t he most money?
6. W hich costs t he most, 8 or a nges a t 9 cen ts each, or 9 or a nges a t 8 cnets
each? W h y?
105
M ultiplication
7. I n t he first col u m n t here a re 4 wor ds, w it h 7 let ters i n each word, a nd i n
t he second a re 7 words, w it h 4 i n each wor d. I n w hich col u m n a re t here t he
most let ters? W hy?
F ifteenth E xercise.
1. Repea t t he 9’s 5 t imes in each of t he t wo w ays, t h us:
1 t ime 9 is ________.
2 t imes 9 a re _______, etc.
9 t imes 1 a re _______.
9 t imes 2 a re ______, etc.
2. Repea t t he 10’s 5 t im es i n each of t he t wo w a ys, t h us:
1 t ime 10 is _______.
2 t imes 10 a re ______, etc.
10 t imes 1 a re ______.
10 t imes 2 a re ______, etc.
3. A nswer t he follow i ng 5 t imes. W r it e t hem on a sep a r a te piece of pa per.
9x3?
10x3?
4x9?
3x10?
10x7?
9x8?
8x9?
9x6?
106
6x9?
9x7?
7x9?
3x9?
9x6?
1x9?
M ultiplication
4. A nswer t he follow i ng:
3x5=
3x7=
2x2=
7x8=
3x2=
3x3=
6x7=
5x8=
4x4=
9x8=
9x4=
5x5=
4x7=
9x3=
6x6=
7x5=
4x9=
7x7=
6x9=
3x9=
8x8=
10 x 8 =
2x8=
9x9=
5x7=
3x8=
10 x 10 =
7x6=
10 x 4 =
1x1=
9x6=
3 x 10 =
5x0=
8x7=
10 x 10 =
0x3=
107
M ultiplication
S ixteenth E xercise.
1. H ow m a ny t imes m ust you m a k e 3 st a rs to h a ve 12
st a rs? H ow m a ny t imes 3 is 12? 4 t i mes 3 a re how
m a ny?
2. H ow m a ny t imes m ust you m a k e 4 m a r ks to h ave 20 m a r ks? H ow m a ny
t imes 4 is 20? 5 t imes 4 a re how m a n y?
3. T h ree t imes w h a t n u mber m a kes 12? T h ree t imes w h a t n u mber m a kes
18?
4. 4 t imes w h a t n u m ber m a kes 20?
5 t imes w h a t n u m ber m a kes 30?
7 t imes w h a t n u m ber m a kes 21?
8 t imes w h a t n u m ber m a kes 56?
5. F il l i n t he m issing n u mbers to complete each equ a t ion.
2 x ________ =
2
3 x ________ =
21
4 x ________ =
20
2 x ________ =
6
3 x ________ =
15
4 x ________ =
16
2 x ________ =
8
3 x ________ =
18
4 x ________ =
4
2 x ________ =
4
3 x ________ =
12
4 x ________ =
12
2 x ________ = 10
3 x ________ =
3
4 x ________ =
24
108
M ultiplication
2 x ________ = 14
3 x ________ =
9
4 x ________ =
40
2 x ________ = 20
3 x ________ =
27
4 x ________ =
8
2 x ________ = 18
3 x ________ =
6
4 x ________ =
36
2 x ________ = 16
3 x ________ =
30
4 x ________ =
28
2 x ________ = 12
3 x ________ =
24
4 x ________ =
32
6. H ow m a ny t imes 5 does it t a ke to m a ke 15? H ow m a ny 5’s a re t here in
15?
7. H ow m a ny t imes 6 does it t a ke to m a ke 24? H ow m a ny 6’s i n 24?
Seventeenth E xercise.
1. H ow m a ny cen ts do 6 5-cen t pieces m a ke? H ow m a ny
5-cen t pieces does it t a ke to m a ke 30 cen ts? 6 t imes 5
a re how m a ny? 6 t imes w h a t n u mber m a kes 30?
2. H ow m a ny cher r ies a re t here in t he pict u re? H ow
m a ny bu nches? H ow m a n y i n each
bu nch? 7 t imes w h a t n u mber m a k es
42?
109
M ultiplication
3. F il l i n t he m issing n u mbers to complete each equ a t ion.
5 x ________ = 15
6 x ________ =
18
7 x ________ =
28
5 x ________ = 10
6 x ________ =
12
7 x ________ =
14
5 x ________ = 20
6 x ________ =
42
7 x ________ =
35
5 x ________ = 35
6 x ________ =
48
7 x ________ =
63
5 x ________ = 50
6 x ________ =
24
7 x ________ =
70
5 x ________ = 45
6 x ________ =
30
7 x ________ =
42
5 x ________ =
5
6 x ________ =
6
7 x ________ =
21
5 x ________ = 25
6 x ________ =
54
7 x ________ =
7
5 x ________ = 30
6 x ________ =
36
7 x ________ =
56
5 x ________ = 40
6 x ________ =
60
7 x ________ =
49
4. H ow m a ny t imes m ust Joh n br i ng i n 4 eggs a t a t ime, i n or der to br ing i n
24 eggs? H ow m a n y t imes 4 does it t a ke to m a ke 24?
5. If H en r y ea r ns 5 cen ts a n hou r, how m a n y cen ts w i ll he ea r n i n 7 hou rs?
6. If H en r y ea r ns 5 cen ts a n hou r, how m a n y hou rs w i ll it t a ke h im to ea r n
35 cen ts? W hy?
110
M ultiplication
E ighteenth E xercise.
1. H ere a re t wo squ a r es of bl ack gl ass, w it h 9
fla kes of snow on each. H ow m a n y squ a res
wou ld it t a ke to h ave 72 fl a kes of snow? 8 t imes
9 a re how m a ny?
2. A cl ass of boys h a d 90 fingers, i ncl uding t heir t h u mbs. H ow m a ny boys
were t here i n t he class? H ow m a ny 10’s does it t a ke to m a ke 90? 9 t imes
10 a re how m a ny?
3. F il l i n t he m issing n u mbers to complete each equ a t ion.
8 x ________ = 16
9 x ________ =
36
10 x ________ =
40
8 x ________ = 40
9 x ________ =
27
10 x ________ =
70
8 x ________ = 24
9 x ________ =
18
10 x ________ =
90
8 x ________ = 56
9 x ________ =
45
10 x ________ =
30
8 x ________ = 64
9 x ________ =
63
10 x ________ =
10
8 x ________ =
8
9 x ________ =
81
10 x ________ =
20
8 x ________ = 72
9 x ________ =
9
8 x ________ = 32
9 x ________ =
54
10 x ________ =
50
8 x ________ = 80
9 x ________ =
90
10 x ________ =
80
8 x ________ = 48
9 x ________ =
72
10 x ________ =
60
111
10 x ________ = 100
M ultiplication
4. If Joh n ca tches 7 fishes each d ay, how long w i ll
it t a ke him to ca tch 42 fishes? 6 t imes 7 a re how
m a ny?
5. If Moses l ays by 10 cen ts a wee k, how m a ny
wee ks w i ll it t a ke him to la y by one dolla r, or 100
cen ts? H ow m a ny tens does it t a ke to m a ke 100?
Defi n ition E xercise.
1. If one cu r r a n t bush produces t wo
qu a r ts of cu r r a n ts, how m a ny qu a r ts
w ill 3 cu r r a n t bushes produce? W h a t is
t he product of 3 t imes 2? W h a t is t he
prod uct of 3 t imes 7? W h a t is t he
prod uct of 4 t imes 5?
2. W h a t n u m ber does 6 t imes 4 m a ke? W h a t is t he product of 6 t imes 4?
W h a t is t he prod uct of 6 t imes 7? W h a t is t he product of 7 t imes 6?
112
M ultiplication
3. W h a t is t he prod uct of 4 t imes 8? Ask t h is quest ion w it hou t using t he
word prod uct.
4. W h a t is t he prod uct of 3 a nd 4? As k t his quest ion w it hou t using t he
word prod uct.
5. H ow m a ny a re 8 t imes 6? As k t h is quest ion w it hou t usi ng t he wor d
prod uct.
6. W h a t is t he prod uct of 7 a nd 3?
W h a t is t he prod uct of 6 a nd 9?
W h a t is t he prod uct of 8 a nd 7?
W h a t is t he prod uct of 3 a nd 9?
W h a t is t he prod uct of 3 a nd 3?
W h a t is t he prod uct of 8 a nd 8?
7. Supply t he proper word in t he follow ing?
W h a t is t he ____________________ of 6 a nd 4?
T he _____________________ of 7 a nd 5 is w h a t?
9 t imes 5 gives w h a t ____________________?
W h a t is t he ______________________ of 2 a nd 9?
113
M ultiplication
Second Defi n ition E xercise.
1. H ere a re some cu r ious on ions. If you pla n t a
lit t le one l i ke one of t hose in t he first row, it w il l
grow a nd m u lt ipl y i n to 4 or more li ke t hose i n t he
second row. If you pl a n ted t he 3 i n t he first row,
a nd each one m ult iplied so as to m a k e 4, how m a n y
wou ld you h ave? H ow m a ny t imes as m a ny as you
pla n ted? 3 m ult iplied by 4 produces how m a n y?
W h a t is t he prod uct of 3 m ult iplied by 4?
2. If I pla n ted 6 of t hese cu r ious on ions, a nd each one m ult ipl ies in to 5, how
m a ny t imes as m a n y sh al l I h ave as I pl a n ted? 6 m ult ipl ied by 5 prod uces
how m a n y?
3. If I m ult iply 5 by 6, w h a t is t he product? W hen I m u lt iply 6 by 5, w h a t is
t he product? W hen I m ult iply 5 by 6, how m a n y t imes do I t a ke 5? 6 t imes
5 a re how m a ny?
4. If I m ult iply 4 by 8, w h a t is t he product? As k t h is quest ion w it hou t using
eit her of t he words m u lt ipl y or prod uct.
114
M ultiplication
5. If I _______________________ 7 by 3, w h a t is t he ___________________?
If I _______________________ 6 by 9, w h a t is t he ___________________?
T he _______________________ of 5 _____________________ by 8 is w h a t?
W h a t is t he _______________________ of 7 ______________________ by 6?
6. W hen you m u lt iply 8 by 9, how m a ny t imes do you t a ke 8?
W h a t is t he _______________________?
7. W h a t is t he _________________________ of 8 a nd 7?
6 _______________________ by 4 gives w h a t __________________________?
W h a t ________________________ does 4 ______________________ by 10
gi ve?
8. F i nding w h a t t he product of t wo n u mbers is, is ca lled M U L T I P L I C A T I O N .
9. W e h a ve now st udied C O U N T I N G , A D D I T I O N , S U B T R A C T I O N , a nd
M U L TIP LIC A TIO N.
W hen I find ou t t h a t 6 t a ken from 11 leaves 5, w h a t is it? ________________
_________________ W hen I find ou t t h a t 5 t imes 6 is 30, w h a t is it? ________
_______________________ W hen I n a m e al l t he n u mbers in order from one to
t wen t y–t h us, one, t wo, t h ree, fou r, etc.–w h a t is it? ______________________
W hen I find ou t t h a t 7 a nd 8 a re 15, w h a t is it? _________________________
115
M ultiplication
D r i l l E xercise.
1. A dd 4 a nd 3 a nd 6; from t his su m subt r act 8; m u lt iply t h is rem a inder by
2. W h a t is t he r esu lt?
2. A dd 2 a nd 6 a nd 3 a nd 7; from t his su m subt r act 9; m ult ipl y t he
rem ainder by 3. W h a t is t he product?
3. A dd 5 a nd 7; from t h is su m subt r act 8; to t h is rem ai nder a dd 5; from t his
su m subt r act 7; m ult ipl y t his rem ai nder by 4; m ult ipl y t h is product by 3; to
t his prod uct add 6. W h a t is t he r esul t?
4. F rom 8 subt r act 3; from t his rem ai nder subt r act 2; to t h is rem a inder add
5 a nd 7; from t his su m subt r act 8; to t his rem ai nder add 2; m u lt iply t h is
su m by 4. W h a t is t he result?
116
M ultiplication
5. B egin w it h 5, a dd 2, add 6, subt r act 9, m u lt iply by 3, a dd 5, subt r act 8,
subt r act 6, m u lt ipl y by 7. W h a t is t he result?
6. B egi n w it h 11, subt r act 6, subt r act 2, m ult iply by 8, add 5. W h a t is t he
result?
7. B egin w it h 6, m u lt iply by 2, subt r act 5, a dd 3, subt r act 4, a dd 1, subt r act
6, a dd 8, m ult iply by 7. W h a t is t he r esult?
8. B egin w it h 5, a dd 7, subt r act 3, subt r act 4, m u lt ipl y by 3, a dd 8. W h a t is
t he resu lt?
9. B egin w it h 4, a dd 9, subt r act 7, m u lt ipl y by 2, subt r act 1, subt r act 3,
m ult iply by 9. W h a t is t he resu lt?
117
M ultiplication
10. B egi n w it h 6, add 8, subt r act 7, a dd 2, m ult iply by 8. W h a t is t he
result?
P r actica l E xercise.
1. Joh n bough t 2 or a nges for 4 cen ts each, a nd gave t he cler k 10 cen ts.
H ow m uch ch a nge did he receive?
2. M a r y bough t 3 spools of t h rea d for 6 cen ts each, a nd one ya r d of cal ico for
9 cen ts. H ow m uch did she p ay for a l l?
3. H en r y wor ked 3 hou rs for 5 cen ts a n hou r, a nd t he m a n for w hom he
wor ked gave him a bal l wor t h 8 cen ts, a nd t he rem ai nder i n money? H ow
m uch money did H en r y get?
4. H ow m a ny d ays a re t here i n one wee k? H ow m a n y i n 6 wee ks? H ow
m a ny da ys i n 4 wee ks?
118
M ultiplication
5. Joh n wor ked 1 wee k (6 d ays) a nd 4 days more? H ow m a n y d ays did he
wor k in al l? If he ea r ned 4 sh il li ngs a day, how m a ny sh ill ings d id he ea r n?
H ow m a n y more days would he h ave h a nd to wor k to m a ke 2 wee ks? H ow
m uch more would he h ave ea r ned if he h a d wor ked 2 wee ks?
6. Sa r a h sews 3 hou rs each da y. H ow m a ny hou rs does she sew i n a wee k
(6 days)?
7. H ow m a ny d ays a re t here i n 8 wee ks? H ow m a ny Su nd ays i n 8 wee ks?
H ow m a n y wor k-days i n 8 wee ks?
119
Division
D ivision
Division
Pu rpose: To develop the i dea of D ivision i n its T wo F or ms, a nd the n ature
of D ivision as the converse of M ultipl ication, a nd to ded uce the quotient of
a ny n umber less th a n 100, d ivi ded by a ny n umber less th a n 10, from the
rel ation of D iv ision to M ultipl ication.
F i rst E xercise.
To be done or a l. T he use of cou nters is a grea t w ay for the stu dent to
visu a l ize the problem.
1. H ow m a ny lit t le d ucks a re t here i n t he pict u re? A re t hey al l toget her?
I n how m a ny groups a re t hey? H ow m a ny in each group? 3 groups w it h 4
in each group, m a ke how m a ny? H ow m a ny 4’s in 12?
2. If you h ave 12 ducks a nd p u t t hem in 3 groups, w it h t he sa me n u mber in
each group, how m a ny w il l be i n each group? 12 div ided i n to 3 equ a l p a r ts
m a kes how m a ny i n each pa r t?
3. H ow m a ny a’s a re t here i n t he next li ne?
If you divide t hese 6 a’s in to groups w it h 3 i n a group, how m a ny groups
w ill t here be?
. H ow m a ny 3’s i n 6? I f you div ide 6 a’s
in to 2 equ a l groups, how m a ny w i ll t here be in each group? 6 div ided by 2
a re how m a ny?
4. 3 t imes w h a t n u m ber m a kes 12? H ow m a ny t imes does 4 go i n 12? 4
t imes w h a t n u mber m a kes 12? H ow m a ny t imes does 3 go i n 12? 12
div ided by 4 a re how m a n y? W hy? 12 divided by 3 a re how m a ny? W hy?
5. 2 t imes w h a t n u m ber m a kes 6? H ow m a n y a r e 6 di vided by 3? W hy? 3
t imes w h a t n u mber a re 6? 6 di vided by 2 a re how m a ny?
121
Division
6. T he sign for “di vided by” is ÷ . Copy, fi ll ou t a nd lea r n t he follow i ng:
2 ÷ 2 = _______
3 ÷ 3 = _______
8 ÷ 2 = _______
4 ÷ 2 = _______
6 ÷ 3 = _______
9 ÷ 3 = _______
6 ÷ 2 = _______
9 ÷ 3 = _______
10 ÷ 2 = _______
8 ÷ 2 = _______
12 ÷ 3 = _______
6 ÷ 3 = _______
10 ÷ 2 = _______
15 ÷ 3 = _______
6 ÷ 2 = _______
12 ÷ 2 = _______
18 ÷ 3 = _______
12 ÷ 3 = _______
14 ÷ 2 = _______
21 ÷ 3 = _______
12 ÷ 2 = _______
16 ÷ 2 = _______
24 ÷ 3 = _______
15 ÷ 3 = _______
18 ÷ 2 = _______
27 ÷ 3 = _______
20 ÷ 2 = _______
20 ÷ 2 = _______
30 ÷ 3 = _______
18 ÷ 3 = _______
4 ÷ 2 = _______
2 ÷ 2 = _______
30 ÷ 3 = _______
3 ÷ 3 = _______
14 ÷ 2 = _______
27 ÷ 3 = _______
16 ÷ 2 = _______
18 ÷ 2 = _______
21 ÷ 3 = _______
24 ÷ 3 = _______
122
Division
Second E xercise.
1. H ow m a ny fi ngers, i ncl uding t h u m bs,
h ave t wo boys? H ow m a ny 5’s i n 20? If
you di vide 20 i n to 5 equ a l p a r ts, how
m a ny w i ll t here e in each p a r t?
2. 20 ÷ 5 = how m a ny?
3. 20 ÷ 4 = how m a ny?
4. H ow m a ny legs h ave 6 ca ts? H ow m a ny 4’s i n 24? 24 ÷ 4 = how m a ny?
W hy?
5. Joh n h as 28 cen ts; how m a n y lemons ca n he buy a t 4 cen ts each? H ow
m a ny 4’s i n 28? 28 ÷ 4 = how m a ny? W hy?
6. M a r y h as 15 pa nsies, a nd she w ishes to m a ke 5 bouquets a nd p u t t he
sa me n u mber of pa nsies i n each. H ow m a n y ca n she pu t in each bouquet?
If you divide 15 t hi ngs i n to 5 equ a l groups, how m a ny w i ll t here be i n each
group? 15 ÷ 5 = how m a ny?
123
Division
7. Copy, fi ll ou t a nd lea r n t he follow i ng:
4 ÷ 4 = _______
5 ÷ 5 = _______
12 ÷ 4 = _______
8 ÷ 4 = _______
10 ÷ 5 = _______
15 ÷ 5 = _______
12 ÷ 4 = _______
15 ÷ 5 = _______
16 ÷ 4 = _______
16 ÷ 4 = _______
20 ÷ 5 = _______
28 ÷ 4 = _______
20 ÷ 4 = _______
25 ÷ 5 = _______
25 ÷ 5 = _______
24 ÷ 4 = _______
30 ÷ 5 = _______
30 ÷ 5 = _______
28 ÷ 4 = _______
35 ÷ 5 = _______
36 ÷ 4 = _______
32 ÷ 4 = _______
40 ÷ 5 = _______
20 ÷ 4 = _______
36 ÷ 4 = _______
45 ÷ 5 = _______
20 ÷ 5 = _______
40 ÷ 4 = _______
50 ÷ 5 = _______
8 ÷ 4 = _______
4 ÷ 4 = _______
40 ÷ 5 = _______
5 ÷ 5 = _______
40 ÷ 4 = _______
10 ÷ 5 = _______
45 ÷ 5 = _______
35 ÷ 5 = _______
24 ÷ 4 = _______
32 ÷ 4 = _______
50 ÷ 5 = _______
124
Division
T h i r d E xercise.
1. T h is l a rge bas ket con t ai ns 42 eggs. H ow
m a ny t imes ca n t he lit t le gir l fi ll her sm all
bask et from it, if her sm all basket holds 6
eggs? H ow m a n y t imes ca n she fil l her sm a ll
bask et if it holds 7 eggs? H ow m a ny 6’s i n 42?
H ow m a n y t imes 6 m a ke 42? 42 ÷ 6 a re how
m a ny? W h y? H ow m a n y 7’s in 42? H ow m a n y
t imes 7 m a ke 42? 42 ÷ 7 m a ke how m a ny?
W hy?
2. H ere a re 30
C ross ou t 6
. T hen cross ou t 6 more. T hen a not her 6. H ow m a ny t imes
ca n you cross ou t 6
? H ow m a n y 6’s i n 30? H ow m a n y t imes 6 m a ke 30?
30 ÷ 6 a re how m a ny? W h y?
3. If Joh n h as 35 cen ts a nd spends 7 cen ts each d a y, how m a ny da ys before
all his money w ill be spen t? 35 ÷ 7 = how m a n y? W hy?
4. If H en r y h as 56 cen ts, how m a n y or a nges ca n he buy a t 7 cen ts each?
56 ÷ 7 = how m a ny? W h y?
125
Division
Copy, fi ll ou t a nd lea r n t he follow i ng:
6 ÷ 6 = _______
7 ÷ 7 = _______
36 ÷ 6 = _______
12 ÷ 6 = _______
14 ÷ 7 = _______
42 ÷ 7 = _______
18 ÷ 6 = _______
21 ÷ 7 = _______
42 ÷ 6 = _______
24 ÷ 6 = _______
28 ÷ 7 = _______
30 ÷ 6 = _______
30 ÷ 6 = _______
35 ÷ 7 = _______
35 ÷ 7 = _______
36 ÷ 6 = _______
42 ÷ 7 = _______
49 ÷ 7 = _______
42 ÷ 6 = _______
49 ÷ 7 = _______
24 ÷ 6 = _______
48 ÷ 6 = _______
56 ÷ 7 = _______
12 ÷ 6 = _______
54 ÷ 6 = _______
63 ÷ 7 = _______
70 ÷ 7 = _______
60 ÷ 6 = _______
70 ÷ 7 = _______
60 ÷ 6 = _______
6 ÷ 6 = _______
54 ÷ 6 = _______
7 ÷ 7 = _______
56 ÷ 7 = _______
14 ÷ 7 = _______
48 ÷ 6 = _______
18 ÷ 6 = _______
63 ÷ 7 = _______
21 ÷ 7 = _______
28 ÷ 7 = _______
126
Division
F ourth E xercise.
1. H ere a re 18 a’s.
M a r k t hem off i n to groups of 9 each. H ow m a n y such groups w ill you h ave?
H ow m a n y 9’s in 18? H ow m a ny t imes 9 a re 18? 18 ÷ 9 = how m a n y?
2. H ere a re 36 a’s.
M a ke 9 l a rge circles. C ross ou t one a a nd p u t it i n one of t he circles. T hen
cross ou t a not her a a nd pu t it in a not her circle. T hen a not her a nd a not her ,
t ill you h a ve one a i n each circle. T hen go rou nd agai n a nd p u t a not her a i n
each of t he circles, t il l you h ave 2 a’s i n each circle. T hen go rou nd agai n,
pu t t i ng a not her a in each circle, t il l a l l t he 36 a’s a re used up. H ow m a ny
a’s w i ll t here be i n each circle? If you div ide 36 i n to 9 equ al groups, how
m a ny a re t here i n each group? 36 ÷ 9 = how m a ny? W h y?
127
Division
Copy, fi ll ou t a nd lea r n t he follow i ng:
8 ÷ 8 = _______
9 ÷ 9 = _______
72 ÷ 9 = _______
16 ÷ 8 = _______
18 ÷ 9 = _______
72 ÷ 8 = _______
24 ÷ 8 = _______
27 ÷ 9 = _______
8 ÷ 8 = _______
32 ÷ 8 = _______
36 ÷ 9 = _______
9 ÷ 9 = _______
40 ÷ 8 = _______
45 ÷ 9 = _______
80 ÷ 8 = _______
48 ÷ 8 = _______
54 ÷ 9 = _______
90 ÷ 9 = _______
56 ÷ 8 = _______
63 ÷ 9 = _______
16 ÷ 8 = _______
64 ÷ 8 = _______
72 ÷ 9 = _______
18 ÷ 9 = _______
72 ÷ 8 = _______
81 ÷ 9 = _______
24 ÷ 8 = _______
80 ÷ 8 = _______
90 ÷ 9 = _______
48 ÷ 8 = _______
6 ÷ 9 = _______
54 ÷ 8 = _______
7 ÷ 8 = _______
56 ÷ 9 = _______
14 ÷ 9 = _______
48 ÷ 8 = _______
18 ÷ 8 = _______
63 ÷ 9 = _______
21 ÷ 9 = _______
28 ÷ 9 = _______
128
Division
F ifth E xercise.
1. H ow m a ny 10’s a re t here i n 20? H ow m a ny in 30? I n 40?
2. 40 ÷ 10 = how m a ny? 30 ÷ 10 = how m a n y?
3. H ow m a ny 1’s in 6? 6 ÷ 1 = how m a ny? H ow m a ny 1’s i n 7? 7 ÷ 1 = how
m a ny?
4. M a r y h as 80 needles in 8 pa pers, w it h t he sa me n u mber i n each pa per.
H ow m a n y needles i n each pa per?
5. If M a r y pu ts her 80 needles up i n p apers of 10 needles each, how m a ny
papers w i ll she h a ve? 80 ÷ 8 = how m a ny? 80 ÷ 10 = how m a ny?
6. Joh n h as 60 cen ts i n his ba n k. If he t a kes ou t 10 cen ts each day, how
m a ny da ys before his money w ill be gone? H ow m a n y t imes ca n you t a k e
10 ou t of 60? 60 ÷ 10 = how m a ny?
129
Division
7. Copy, fi ll ou t a nd lea r n t he follow i ng:
10 ÷ 10 = _______
1 ÷ 1 = _______
50 ÷ 10 = _______
20 ÷ 10 = _______
2 ÷ 1 = _______
8 ÷ 1 = _______
30 ÷ 10 = _______
3 ÷ 1 = _______
30 ÷ 10 = _______
40 ÷ 10 = _______
4 ÷ 1 = _______
70 ÷ 10 = _______
50 ÷ 10 = _______
5 ÷ 1 = _______
7 ÷ 1 = _______
60 ÷ 10 = _______
6 ÷ 1 = _______
4 ÷ 1 = _______
70 ÷ 10 = _______
7 ÷ 1 = _______
10 ÷ 10 = _______
80 ÷ 10 = _______
8 ÷ 1 = _______
1 ÷ 1 = _______
90 ÷ 10 = _______
9 ÷ 1 = _______
20 ÷ 10 = _______
100 ÷ 10 = _______ 10 ÷ 1 = _______
40 ÷ 10 = _______
3 ÷ 1 = _______
90 ÷ 10 = _______
2 ÷ 1 = _______
6 ÷ 1 = _______
60 ÷ 10 = _______
9 ÷ 1 = _______
80 ÷ 10 = _______
100 ÷ 10 = _______
5 ÷ 1 = _______
10 ÷ 1 = _______
130
Division
S ixth E xercise.
1. H ere is a bea u t iful pa nsy. H ow m a ny
blossoms a re t here on it? If you m a ke 2 bouquets
a nd p u t 3 of t heses pa nsies in each of t hem, how
m a ny pa nsies w i ll rem ai n? H ow m a n y 3’s i n 8,
a nd how m a ny over?
2. Joh n h ad 15 cen ts a nd gave 4 cen ts apiece for 3 or a nges. H ow m a ny
cen ts did he h a ve rem a in ing? H ow m a ny t imes ca n you t a ke 4 from 15?
H ow m a n y w ill rem ai n after you h a ve t a ken 4 from 15 as m a ny t imes as
you ca n?
3. A re t here 4 2’s in 7? H ow m a n y 2’s a re t here i n 7? Is t here a n y
rem ainder after you h a ve t a ken 3 2’s from 7? W h a t is it?
4. H ow m a ny a re 5 t imes 7? 6 t imes 7? H ow m a ny 7’s a r e t here in 38, a nd
how m a n y over? H ow m a ny 7’s i n 40, a nd how m a n y over? H ow m a ny 7’s
in 37, a nd how m a ny rem a in ing?
131
Division
5. If you di vide 12 i n to as m a ny 5’s as you ca n, how m a ny 5’s w il l you h a ve,
a nd how m a ny rem ai ni ng? If you div ide 23 i n to as m a ny 6’s as you ca n,
w h a t w il l t he rem ai nder be? 3 x 6 = how m a ny? 4 x 6 = how m a ny? A re
t here 4 6’s i n 23?
6. Say t he “3 t imes” of t he M ult iplica t ion T able. A re t here 2 3’s i n 17? A re
t here 3 3’s i n 17? A re t here 4? A re t here 5? A re t here 6? H ow m a n y 3’s
a re t here in 17, a nd how m a ny over?
7. Say t he “6 t imes” of t he M ult iplica t ion T able. A re t here 3 6’s i n 27? A re
t here 4? A re t here 5? If you div ide 27 i n to as m a n y 6’s as you ca n, how
m a ny 6’s w ill you h ave, a nd w h a t rem ainder?
8. Say t he “8 t imes” of t he M ult iplica t ion T able. A re t here 3 8’s i n 47? A re
t here 4? A re t here 5? A re t here 6? H ow m a n y t imes is 8 con t ai ned i n 47,
a nd how m a ny rem ai n?
132
Division
Seventh E xercise.
1. Say t he “4 t imes” of t he M ult iplica t ion T able. A re t here 3 4’s i n 27? A re
t here 5 4’s i n 27? A re t here 6? A re t here 7? H ow m a n y 4’s in 27, a nd w h a t
is t he rem ai nder? 27 ÷ 4 a re how m a ny, a nd w h a t is t he rem ai nder?
2. Joh n h ad 35 cen ts a nd bough t 8 lea d-penci ls, a t 4 cen ts each. H ow m uch
money h a d he left? H ow m a n y 4’s in 35, a nd how m a n y rem a in?
3. F il l ou t t he fol low ing?
14 ÷ 3 = __________ a nd __________ rem ainder.
22 ÷ 4 = __________ a nd __________ rem ainder.
18 ÷ 4 = __________ a nd __________ rem ainder.
37 ÷ 5 = __________ a nd __________ rem ainder.
40 ÷ 6 = __________ a nd __________ rem ainder.
51 ÷ 7 = __________ a nd __________ rem ainder.
133
Division
78 ÷ 9 = __________ a nd __________ rem ainder.
67 ÷ 8 = __________ a nd __________ rem ainder.
80 ÷ 9 = __________ a nd __________ rem ainder.
D r i l l E xercise.
1. A dd 2, 3, 4, subt r act 6, m ult ipl y by 7, divide by 3, subt r act 5, a dd 7,
div ide by 3, m ult iply by 8, di vide by 6, add 9, a dd 7, di vide by 5, di vide by 2,
add 8, 3, 9, 2, 4, divide by 7. W h a t is t he resu lt?
134
Division
2. A dd 5 to 7, subt r act 8, m ult ipl y by 3, a dd 9, di vide by 7, add 8, subt r act 9,
add 6, m ult ipl y by 7, a dd 8, div ide by 8. W h a t is t he r esu lt?
3. F rom 13 subt r act 8, m u lt ipl y by 4, add 6, add 4, a dd 2, di vide by 4, di vide
by 2, m u lt iply by 7, a dd 8, di vide by 9. W h a t is t he result?
4. D ivide 54 by 6, dive by 3, m ult iply by 9, a dd 8, add 10, div ide by 9,
m ult iply by 6, add 5, di vide by 7, m u l t iply by 2, m ult iply by 7, add 2, divide
by 8, m u lt iply by 6, a dd 9, di vide by 7, di vide by 9, subt r act 1. W h a t is t he
result?
135
Division
5. D ivide 27 by 9, m ult iply by 3, add 5, add 4, divide by 6, m ult iply by 8,
add 8, add 4, divide by 6, m ult iply by 7, a dd 7, di vide by 7, m ult ipl y by 9,
add 1, di vide by 8. W h a t is t he result?
6. D ivide 56 by 7, m ult iply 6, add 6, divide by 9, m u lt iply by 7, a dd 7, 3, 6,
4, 1, divide by 9, m u lt iply by 8, a dd 10, 10, 5, div ide by 9. W h a t is t he
result?
7. F rom 15 subt r act 9, a dd 2, m ult ipl y by 8, add 6, divide by 10, m ult ipl y by
9, a dd 1, di vide by 8, subt r act 1, m ult iply by 7, add 7, divide by 9. W h a t is
t he resu lt?
136
Division
8. D ivide 56 by 7, div ide by 2, m ult ipl y by 8, add 3, divide by 7, a dd 4,
m ult iply by 6, add 9, di vide by 7. W h a t is t he resu lt?
9. F rom 13 subt r act 8, m u lt ipl y by 6, add 6, di vide by 9, m u lt ipl y by 8, a dd
4, divide by 6, subt r act 6, m u lt iply by 3. W h a t is t he r esu lt?
137