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B A S I C P A C T S M E N U ITEM Date Basic Addition Basic Subtraction Basic Multiplication Basic Division
Adding Decimals Subtracting Decimals Multiplying Decimals Dividing Decimals
Problem Solving
Name Date
ddition Facts
Add.
1. 7
+ 9
6
+ 3
7
+ 5
6
+ 9
4
+ 4
5
+ 8
3
+ 8
2. 4
+ 7 9
+ 5
3
+ 5
6
+ 7
2 + 5
5
+ 4
8
+ 9
3. 8
+ 7
2
+ 7
6
+ 6
5
+ 6
8
+ 8
9
+ 1
3
+ 7
4. 6
+ 8
3
+ 9
0
+ 8
9
+ 9
4
+ 6
8
+ 4
7
+ 7
5. 3
+ 3
9
+ 8
1
+ 9
8
+ 5
5
+ 5
4
+ 9
6
+ 5
6. 7
+ 6
4
+ 8
7
+ 8
8
+ 3
9
+ 7
4
+ 2
8
+ 6
7. 9
+ 6
2
+ 9
9
+ 4
5
+ 7
5
+ 9
7
+ 4
9
+ 3
d e 6 .iy time. 159
Name Date
ddition. Whole Numbers (1)
Find each sum.
1. 4 2 2 . 3 5 3 . 4 0 4 . 6 2
+ 2 7 + 5 4 + 5 8 + 3 7
5. 5 8 6. 7 4 7. 3 9 8. 4 7
+ 1 9 + 1 7 + 2 2 + 2 7
9. 6 9 10 . 8 5 11 . 7 4 12 . 5 6
+ 6 3 + 3 7 + 8 6 + 7 8
4 8 2 14. 2 0 8 15 . 3 5 4 16 . 6 2
+ 5 0 7 + 5 6 1 + 2 4 + 2 5
17 . 2 3 8 18. 4 7 3 19 . 6 5 9 2 0 . 8 6 7
+ 4 0 5 + 1 9 2 + 3 3 7 + 171
2 1 . 5 1 7 22 . 6 6 4 2 3 . 3 2 8 24 . 145
+ 1 9 5 + 2 8 6 + 5 9 8 + 6 7 8
2 5 . 6 4 0 26 . 7 5 3 27 . 9 7 6 2 8 . 8 0 2
+ 7 8 3 + 5 6 7 + 2 9 6 + 9 4 8
d e 6 Use any time. 163
Name
A Date
ddition, Whole Numbers (2)
Find each sum.
1. 2 3
6 0
4 8
19
+ 5 4
2 . 8 4
4 9
2 6
12
+ 65
3. 3 6
9 2
7 7
6 8
+ 5 9
4. 4 8
19
2 6
8 5
+ 7 3
5. 2 7 8
4 3 6
7 0 4
+ 5 9 1
6. 3 9 4
9 2 5
2 7 7
+ 6 8 6
7. 5 2 8
6 9 1
6 8 7
+ 9 4 9
8. 6 5 1
7 5 9
4 4 8
+ 8 6 5
9. 7 0 2 8
+ 3 4 9 8
10. 6 4 6 5
+ 2 9 0 9
11 . 3 4 8 9
+ 2 9 1 4
12 . 5 8 1 4
+ 2 8 3 9
13 . 4 2 8 4 2
+ 15 2 9 7
14. 6 3 291
+ 2 8 3 9 2
15 . 7 7 5 5 5
+ 18 0 8 4
16. 9 0 3 4 0
+ 4 8 9 6 3
17. 8 9 3 4 6
+ 2 8 9 1
18. 4 0 9 7
+ 3 7 6 6 6
19 . 3 7 2 1 6
+ 9 8 3 7
20 . 5 2 7 3
+ 15 9 3 5
164 Grade 6 Use any time.
Name _ _ Date
ubtraction Facts
8 15 10 11 12 13
- 0 - 9 - 9 - 2 - 9 - 9
2 . 1 4 5 12 7 11 9 17
- 5 - 4 - 8 - 1 - 7 - 5 - 9
3 . 8 13 14 5 6 12 7
- 6 - 6 - 6 - 0 -_6 - _ 3 - 4
4. 16 11 8 18 9 11 12 £
- 8 - 8 - 5 - 9 - 7 - 6 - 5
5. 12 13 10 15 9 12 14
- 7 - 5 - 8 - 8 - 9 - 4 - 7
6. 17 11 13 14 10 15 11
- 8 - 5 - 8 - 8 - 5 - 7 - 4
1
7. 15 14 12 16 11 10 13 |
- 6 - 9 - 6 - 7 - 3 - 7 - 7 !
160 Grade 6 Use any time.
o
Name Date
ubtraction, Whole Numbers (1)
Find each difference.
1. 4 6 2 . 5 3 3 . 7 9 4. 9 0
- 18 - 2 7 - 2 9 - 2 8
5. 8 2 6 . 3 5 7 . 6 7 8. 8 6
- 6 4 - 16 - 3 8 - 5 9
9. 7 4 10 . 5 7 11 . 7 5 12 . 6 6
^ - 5 6 - _ 2 9 - 4 8 - 4 7
13 . 8 6 1 14. 7 6 1 15 . 5 0 5 16. 6 3 0
- 4 2 7 - 5 2 9 - 2 6 1 - 4 8 0
17 . 7 9 1 18 . 5 4 2 19 . 6 3 3 20 . 9 2 3
- 3 6 8 - 4 7 0 - 2 7 3 - 6 2 7
2 1 . 6 2 6 2 2 . 5 1 2 2 3 . 7 4 5 24 . 8 0 9
- 2 9 1 - 3 0 8 - 4 2 7 - 5 5 9
2 5 . 4 3 0 2 6 . 9 2 9 2 7 . 8 5 6 28 . 7 0 5
- 190 - 1 7 2 - 2 4 8 - 3 7 4
Grade 6 Use any time. 165
Name Date
ubtraction. Whole Numbers (2)
Find each difference.
1. 6 3 2 2 . 7 5 6
- 2 7 8 - 4 8 6
3. 5 4 0
- 3 7 2
4. 8 5 1
- 5 9 8
5. 6 5 7
- 3 6 7
6. 9 0 5
- 4 4 8
7. 4 4 0
- 2 6 1
8. 5 0 2
- 2 8 6
9. 4 5 8 6
- 1 9 4 8
10. 5 0 8 4
- 3 2 9 1
11. 9 3 1 7
- 3 0 8 8
12 . 6 0 4 0
1 9 2 8
1 3 . 7 0 1 0
- 4 3 0 3
14. 8 4 0 0
- 5 0 2 6
15. 3 1 0 4
- 1 6 5 4
16. 5 7 3 0
- 2 2 9 7
17. 15 2 8 4
- 7 9 0 7
18. 4 2 9 2 7
- 13 0 6 8
19. 9 0 142
- 18 4 0 9
20 . 3 7 2 0 0
- 15 9 8 9
2 1 . 6 6 3 0 5
- 4 7 2 3 8
22 . 5 0 0 4 1
- 2 7 8 9 0
2 3 . 8 4 2 3 7
- 8 4 2 8
24. 2 5 3 9 1
- 2 4 0 8 9
25 . 7 9 0 0 0
- 8 4 3 2
26 . 3 5 0 0 7
- 9 4 3 3
27 . 4 9 6 0 2
- 1 9 6 0 3
28 . 9 4 2 5 7
- 9 1 8 9 9
166 Grade 6 Use any time.
Name Date
4w ultiplication Facts
Multiply.
1. 9 4 5 6 3 2 8
x 5 x 7 x 3 x 9 x 3 x 6 x 8
2 . 8 6 9 6 8 0 4
x 3 x 4 x 3 x 7 x 1 x 6 x 8
3 . 6 8 8 4 4 7 9
x 6 x O x 6 x 5 x 9 x 7 x 8
4. 8 4 6 7 0 9 2
x 9 x 4 x 8 x 5 x 7 x 6 x 7
5. 8 5 4 9 9 5 7
x 7 x 8 x 3 x 1 x 7 x 5 x 9
6. 7 9 7 8 2 9 6
x 2 x 9 x 6 x 5 x 5 x 2 x 3
7. 9 5 8 6 8 8 9
x O x 9 x 7 x 5 x 2 x 4 x 4
Grade 6 Use any time. I 6 l
Name Date
^ M u l t i p l i c a t i o n , Whole Numbers (1)
Find each product.
1. 3 2 2 .
x 3
41
x 2
3 . 2 2
x 3
4. 5 0
x 2
5.
9 .
13.
6 3
x 3
5 7
x 7
9 3
x 9
6.
10 .
14 .
71
x 8
6 4
x 8
4 8
x 6
7.
11 .
1 5 .
9 2
x 2
7 5
x 6
3 9
x 7
8.
12 .
16.
5 4
x 2
8 8
x 5
2 6
x 9
17. 2 3 5
x 4
18. 186
x 7
19 . 7 2 0
x 5
20 . 8 1 5
x 6
2 1 . 3 0 7
x 8
2 2 . 4 1 7
x 6
2 3 . 5 5 0
x 7
24. 9 0 9
x 9
2 5 . 8 8 3
x 7
2 6 . 7 6 3
x 5
2 7 . 6 3 4
x 4
28 . 2 8 6
x 8
Grade 6 Use any time. 167
Name Date
t r ip l ica t ion . Whole Numbers (2 )
Find each product.
1. 9 4
x 12
2 . 8 3
x 13
3. 7 2
x 2 5
4. 6 5
x 4 3
5. 5 8
x 6 4
6. 4 7
x 7 5
3 9
x 9 3
8. 2 8
x 2 8
9. 19
x 9 4
10. 6 3
x 8 5
11. 8 6
x 4 7
12 . 5 5
x 7 9
13 . 2 2 7
x 31
14. 4 0 8
x 5 4
15. 6 3 9
x 7 6
16. 8 5 0
x 2 9
17. 7 0 5
x 4 4
18. 5 4 6
x 2 5
19. 3 9 0
x 8 4
20 . 182
x 5 7
2 1 . 9 0 0
x 6 5
2 2 . 3 2 7
x 4 0
23 . 4 1 3
x 7 9
214* • 8 6 5
x 8 6
168 Grade 6 Use any time.
Name Date
D Divide.
•vision Facts
1. 7 ) 1 4 5 ) 3 0 6 ) 3 6 4 ) 2 0 8 )32
2 . 3 )9 9 ) 2 7 4 )4 9 ) 7 2 7 ) 7
3 . 8 ) 2 4 7 ) 6 3 4 ) 2 4 1)9 7 )56
4 . 6 ) 2 4 8 ) 4 0 5)5 8 ) 7 2 8 ) 6 4
5 . 6 ) 5 4 3 ) 2 T 7 )42 2 j l 2 5 )20
6 . 7 ) 4 9 2 ) 1 6 4 )16 4 ) 3 6 9 )18
7 . 9 ) 8 T 5 ) 3 5 9 )45 2 )8 5 )25
8 . 8 ) 4 8 3 ) 2 4 1)7 8 j l 6 3 )3
9. 3 ) 1 5 7 ) 2 8 7)0 6 ) 3 0 9 ) 5 4
162 Grade 6 Use any time.
Name Date
v is ion . Whole Numbers (1)
Find each quotient.
1 . 3 ) 9 6 2 . 2 ) 8 4 3 . 5 ) 5 5
9 . 3 ) 5 5 1 0 . 2 ) 8 3 1 1 . 5 ) 7 8
17 . 3 ) 6 3 9 1 8 . 4 ) 4 8 4 19.5)505
2 1 . 6 ) 7 2 6 2 2 . 7 ) 9 4 5 2 3 . 8 ) 8 2 4
2 5 . 9 ) 3 7 8 2 6 . 6 ) 2 9 3 2 7 . 5 ) 4 6 7
rade 6 Use any time.
4.1)94
5 . 4 ) 6 8 6 . 5 ) 6 5 7 . 6 ) 9 6 8 . 7 ) 8 4
12 . 8 ) 9 T
1 3 - 4 ) 3 8 1 4 . 9 ) 7 5 1 5 . 7 ) 6 0 1 6 . 6J5T
20 . 2 ) 8 2 4
24 . 5 ) 7 3 0
28 . 7 ) 5 2 8
169
Skill: Order of Operations
E q u a t i o n s N a m e
j h o w your work o n a n o t h e r sheet . Wr i te your answers he re .
1 . 2 + 7 - 3 2 . 16 + 4 + 3 =
3 . 4 + 6 - 7 = 4 . 2 x 6 + 3 = 5 . 6 x 4 + 12 =
6 . 1 0 - 7 + 6 = 7 . 36 + 6 + 4 = 8 . 7 x 4 + 2 =
9 . 5 x 5 - 5 = 1 0 . 12 + 4 + 7 = 1 1 . 6 + 9 - 3 =
1 2 . 13 + 6 - 7 1 3 . 14 + 2 x 3 = 1 4 . 4 + 8 - 7
1 5 . (16 + 9) + 5 = 1 6 . 9 x 4 + 6 = 1 7 . 3 x 9 - 17 =
1 8 . 5 + 5 x 3 = 1 9 . 6 x 6 - r 12 = 2 0 . 1 2 + 7 - 9 =
2 1 . 6 + 1 2 + 2 = 2 2 . 9 x 3 + 4 = 2 3 . 9 + 6 - 8 =
- ^ 4 . 64 + 8 + 9 = 2 5 . 16 + 2 + 9 = 2 6 . 18 + 2 x 3 =
2 7 . 16 + 1 8 - 8 = 2 8 . 1 4 - 7 + 3 = 2 9 . 6 x 7 - 6 =
3 0 . 24 + 6 x 7 = 3 1 . 32 + 8 x 5 = 3 2 . 16 + 4 + 2 =
3 3 . 9 x 9 + 6 = 3 4 . 13 + 5 - 7 = 3 5 . 15 + 3 x 2 =
3 6 . 7 + (3 x 9) = 3 7 . 6 + (2 x 4) = 3 8 . (4 + 8) + 2
3 9 . 9 + 9 x 2 = 4 0 . 6 x 3 + 4 = 4 1 . (9 + 16) + 5 =
4 2 . 16 + 1 8 - 7 = 4 3 . (60 + 5) + 4 = 4 4 . 36 + (4 x 8) =
4 5 . 9 x 9 + 12 4 6 . 32 + 4 - 3 4 7 . 12 + 3 x 9 _
4 8 . 6 + 9 - 7 =
Success ahoy! Just practice! 4 9 . 8 x 9 + 7 =
5 0 . 8 + 3 x 8 =
Math IF8741 97 © 1990 Instructional I air. Ir K
'ietu ternus Adding decimals
You can use dec ima l squares to he lp %CtfkLctM)l unders tand h o w t o add dec ima ls . 1 Sunt>~~ the CWSUferXjlM&itOfl
.32 * .+5»?
» • • • • •
.32 + AS = .7S
f i
on + 05 = / . z
T h e p a t t e r n : A d d t h e n u ^ f o e r s inthe sane places together tenths to -tenths, hundredths to hundredths.
Shade in the dec ima l squares to f i nd each sum.
. 4 + .3 =
Find the sums
.3 + .8 =
0.5
+ 0.4
0.8
0.7
0.23
+ 0.34
0.72
+ 0.86
7. 1.2
+ 4.5
8. 3.9
+ 6.4
11 2.53
+ 0.34
12. 9.12
+ 0.02
3.42
+ 4.25
10. 6.74
+ 1.32
13. 1.642
+3.853
14. 2.561
+3.429
15.
17.
0.3 + 0.6 =
0.9 + 0.6 =
19. It ra ined 1.65 c m o n M o n d a y and
. 2.08 c m o n Tuesday . H o w m u c h
rain in a l l?
16. 0.14 + 0.72 =
18. 0.25 + 0.94 =
20. A c o n t a i n e r ho ld i ng 0.7 l i ters of o i l
was m i x e d w i t h 5.6 l i ters of gas.
H o w m u c h l iqu id in al l?
T e a c h e r Use base ten blocks to build each number. Use flats for ones, longs for * * 0 ! G * tenths and units for hundredths. Put the numbers together ( with
necessary exchanges) to show addition.
e Math T tachm Pr«e«
Name Date
AddifIoB' De«iM«,s
Find each sum.
1. 4 .2 2 . 5 .6 3 . 8 .8 4 . 7.3
+ 7.3 + 9 . 2 + 1 . 8 + 4 . 7
5 . 6 9 . 4 6. 3 7 . 5 7 . 9 2 . 7 8 . 64 .3
+ 7 2 . 8 + 8 1 . 5 + 18 .5 + 2 9 . 8
9. $ 8 . 4 0 10 . $ 9 . 2 7 11 . $ 4 . 5 6 1 2 . $5 .02
+ $ 6 . 2 7 + $ 2 . 9 1 + $ 8 . 1 8 + $ 6 . 1 8
1 3 . 18 .45 14. 5 7 . 9 3 15 . 7 . 88 16 . 85 .26
+ 2 3 . 9 1 + 8 .45 + 16 .09 + 1 9 . 5 5
17 . 8 . 017 18. 4 . 7 0 9 19 . 7 . 0 5 6 2 0 . 6 .845
+ 1.948 + 2 . 6 2 3 + 0 . 3 8 6 + 8 . 9 1 7
2 1 . 4 2 . 0 7 2 2 . 5 6 . 9 2 3 . 6 . 8 4 2 4 . 10 .393
+ 2 7 . 9 1 5 + 6 4 . 1 8 2 + 1 9 . 2 9 3 + 3 .966
2 5 . 3 .958 26 . 7 2 . 2 8 3 27 . 8 4 . 4 2 8 . 6 .76
+ 1 1 . 4 7 + 6 6 . 5 + 9 . 9 0 7 + 2 5 . 0 4 8
Grade 6 Use any time. 171
Name
Mentally Adding Hundredths and Thousandths o o o o o o o o o o o o o o o o o o o o o o o o o
Add the decimal at the beginning of each line to each decimal to the right. Write the answer on the line below.
1 . . 2 .35 .463 2.545 5.4 7.863
2 . . 0 0 2 .391 6.2077 5.3567 2.939 2.460
3 . . 0 5 .623 9.718 3.2763 8.4043 .6853
4 . . 0 0 5 2.967 7.766 4.833 2.397 .6853
5 . . 0 9 .006 1.04 2.111 4.583 9.921
6 . . 0 0 9 3.157 .4245 6.408 3.3556 1.7281
6 8
A D D I N G D E C I M A L S Name Add center number to number in first circle to find the answer. Next add all answers on wheel. Then, add all wheel answers to get total of all wheels.
w h e e l answer w h e e l answer
Math IF8744 80 © 1990 Instructional Fair Jnc.
Subtracting decimals
Use base ten b locks to unde rs tand h o w
to sub t rac t dec ima ls .
f?evteu> terms subtraction-Ukes things apart: difference -ansuxr in siStractioi'
2%q BuiUthttwr^r i ) ^ The pattern:
- 7 AO R € m ° V e ^ e
s m > U * r WMb*r A d d o r subtract numbers with the same
' » , . . i / . ... p lace value. T h e decimal point in the ones
• 0 tenths 0000
Hoiv mucA 6 s left ?
hundredths o © o o
i
answer c o m e s under the other decimal
point.
2.87 -7.42
Find the d i f fe rences .
1. 0.9
- 0.5
1.2
0.7
0.32
0.21
1.58
- 0.72
5.7
1.2
10.3
6.4
7.67
4.25
8. 7.06
6.74
4.75
4.36
10. 0.577
-0.314
11 1.162
-0.433
12. 5.984
-2.568
13. 0 . 9 - 0 . 6 =
15. 1 . 5 - 0 . 6 =
17. The d i s tance to s c h o o l is 1.5 k m .
Nhat w a l k e d 0.8 k m of t he way .
H o w m u c h d i d he have lef t t o
wa lk?
14. 0 . 8 6 - 0 . 1 4 =
16. 1 . 1 9 - 0 . 2 5 =
18. A gaso l i ne tank ho lds 80 l i ters.
A f te r A n n e had p u m p e d 56.2 l i ters
of gas in to the tank, it was f u l l . How
m u c h gas was a l ready in the tank?
T E A C H E R Use base ten blocks to build the larger number. Remove the smaller N O T E : number. Start at the place having the least value (farthest right) and
make exchanges as necessary
78 © Math Teachers Press
Reoroduction bv anv means strictly orohibited
Name Date
ubtraction. Decimals
Find each difference.
1. 7 .9
- 3 . 4
2 . 6.5
- 3 . 8
3. 8.7
- 2 . 9
4 . 4 .8
- 1.6
5. 3 8 . 3
19.1
6. 4 3 . 8
- 2 8 . 9
7. 5 6 . 2
- 18 .7
8. 9 3 . 3
17.6
9.
1 3 .
17 .
2 1 .
$ 9 . 4 2
- $ 7 . 6 7
5 5 . 0 5
- 2 6 . 1 8
0 . 7 2 4
- 0 .551
4 7 . 5 1 5
- 2 5 . 6 6 5
10. $ 8 . 0 5
- $ 2 . 1 6
14. 6 2 . 4 8
- 18 .29
11
18.
22 .
7 .256
- 6 . 0 6 7
6 3 . 0 7 4
- 3 7 . 5 2 7
15 .
19.
23 .
$ 7 . 2 5
- $ 4 . 7 5
8 7 . 3
- 6 9 . 5 2
9 .041
- 2 . 8 0 8
8 4 . 0 0 5
- 2 . 8 4 6
12 .
16 .
2 0 .
24 .
$ 5 . 2 0
- $ 3 . 8 4
9 1 . 5
- 7 5 . 8 6
8 .103
- 5 .829
7 0 . 5 0 2
- 6 3 . 4 8 8
2 5 . 5 9 . 2 7
- 1 1 . 1 9 2
26 . 18.45
- 6 .593
27. 3 6 . 6
- 18 .926
2 8 . 9 0 . 8 5
- 7 .065
172 Grade 6 Use any time.
Name
Using Money to Subtract Decimals Mentally o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
Our money system is a decimal system. THINK of subtracting decimals as you would THINK of subtracting money mentally. The subtraction is much easier without resorting to borrowing or renaming.
EXAMPLE: 5 - 1.75 Think $5.00 - $1.75.
Subtract the decimal from the number in the IN column. Write the answer in the OUT column.
1. Subt rac t . 2 5
I N
.75
1.50
3.50
4.75
5.00
6.25
4.35
3.40
O U T
.50
1.25
2 . Subt rac t . 5 0
I N O U T
5
4.25
3.75
6.5
7.0
6.6
4.80
3.65 j
3 . Subt rac t 1.50
I N
10
2.8
O U T
4
3
2.75
4.25
5.50
1.6
Subt rac t . 7 5
I N OUT
1.00
2.0
3.75
4.50
1.25
6.80
3.90
2.86
7 0
Name
Subtract.
A. H- li |
- 3 . 8 7
B. $143.79
- 88.81
Decimal Differences
0.85
0.68
26.85
15.97
$51.04
- 22.63
71.35
- 4.661
Subtracting decimals
70.
- 1 6 . 9 5
636.336
173.854
$73.21
- 56 .56
54.135
27.95
$95.41
- 8.72
21.06
- 4.79
Rewrite the problems vertically. Then find the differences.
D. 3.74 - 1.88 52.67 - 24.7
2 ib
57 .19 -19 .88
E. 3 0 . 2 9 - 1 9 . 5 2 .718-0 .884 92 .16-34 .423
F. 7 .506 -4 .968 $164.78-$59.99
© Frank Schaffer Publications, Inc. 4 9 FS-32072 Rfth Grade Math Review
Multiplying decimals by a whole number
Review terms rmLtipliccrtiAK—puts things together in Groups product—tfa£ answer in mJiHipiication
To m u l t i p l y 3 x .2, t h i nk of pu t t i ng
toge the r 3 g r o u p s of 2 ten ths e a c h .
.2 tenths
rate
Say: 3 t imes 2 ten ths is 6 ten ths
W r i t e : 3 x . 2 = . 6 o r ^ A
. 6
Find the p roduc t s .
1. .3
x 3
.4
x 3
3. .25
x 3
4. .42
x 3
.9
x 9
.97
x 7
7. 3.97
x 5
8. 5.265
x 2
7.06
x 4
10. 9.003
x 8
11 8.6
x 5
12. .092
x 4
13. $0.12
x 3
14. $0.34
x 6
15. $0.05
x 13
16. $0.40
x 20
17. 24 x $0.32 =
19. B o b b y b o u g h t 16 penc i l s f o r
$0.08 e a c h . H o w m u c h d id al l
the penc i l s cos t?
18. 4 x $0.63 =
20. One h a m b u r g e r pat ty uses .4
p o u n d of hamburger . How many
p o u n d s w i l l be needed to make
48 h a m b u r g e r s ?
T E A C X E S , i j O T B ^ W o r k P r o b l e m s 1 - 4 w i t n b a s e t e n blocks. Show the exchange of 10 tenthsi
* for 1 whole in problem 2 and 10 hundredths for 1 tenth in problem 3.
C Math Te«ch#f» Prwt Ftooroduction bv any m#«n* strictly oroMbitsd
Name Date
ultiplication. Decimals (1)
Find each product.
1. 6 .4 2 .
x 2
5.3
x 3
4 . 2
x 4
4. 0.6
x 4
5. 5 .7
x 5
6. 8.4
x 9
7. 7.6
x 8
8. 6.5
x 6
9.
13 .
16 .8
x 7
3 .25
x 8
10.
14 .
28 .9
x 9
4 .76
x 3
11.
15 .
3 5 . 4
x 6
8 . 2 4
x 5
12 .
16.
7 2 . 7
x 4
6 .93
x 6
17. 4 2 . 6 1
x 7
18. 5 5 . 0 7
x 8
19. 8 4 . 9 2
x 4
20 . 7 9 . 0 4
x 5
2 1 . 18 .26
x 7
2 2 . 33 .83
x 9
2 3 . 4 0 . 6 6
x 8
24. 6 1 . 8 2
x 3
Grade 6 Use any time. 173
Multiplying decimals by 10,100 or 1000
The same s h o r t c u t used to m u l t i p l y w h o l e n u m b e r s by 10 ,100 or 1000 can be used
to mu l t i p l y dec ima ls .
C o u n t the n u m b e r of zeros in the opera to r . Move the dec ima l po in t that m a n y
p laces in the greater d i rec t i on (to the r igh t ) .
( N o t i c e J \NhzYithe decimaL poini is moi/ed to the. r i g h t , tht number becomes greccben ^
I btco/nes ^6 ^ 45b^ be&>ms46()0 r
A , . Whole, Muntbers A.fA\jLltiplijin% hu 10 JO x
0 ~zfjco' m>ve Tjplace to ih\ ( * & >
Miiitidxjing by 100 \ 100*4-2= *2jD0 100^2-420 & zeros ** mvc Zplotes tp the rty)tt) (42,^^ ) (4,^^ )
Cl/W:ipkiing by WOO 7000x£h*S6000 7oa>x£fr5l>d\ (3zen&mve,3places-fatf\trcjhy (56-^^^) (Zt^^^)
1. 1 0 x 4 6 = 2. 1 0 x 7 . 8 3. 1 0 x . 3 9 =
4. 1 0 0 x 5 2 = 5. 1 0 0 x 3 . 9 = 6. 1 0 0 x 78 =
7. 1 0 0 0 x 6 = 8. 1000 x . 6 5 9. 1000 x . 7 9 4 = .
10. 1 0 x 9 . 6 = 11. 9.64 x 1000 = 12. 63.6 x 100 =
13. 3 .14x 10 = 14. .072 x 100 15. .064 x 1000 =
16. 25.2 x 100 = 17. 1 0 x 8 . 7 3 = 18. 1 0 0 0 x 2.68 =
19. A b ike s tore buys b ikes f r o m the 20. Ju l ie can wa lk 2.4 mi les in 1 hour .
. manu fac tu re r fo r $42.35. How m u c h H o w far can she wa lk in 10 h o u r s ?
wi l l 100 b ikes cos t?
82 © Math Teachers Press
Reoroductlon bv any moans strictly orohibited
Multiplying Decimals by .1, .01, and .001 o o o o o o o o o o o o o o o o o o o o o o o o o
Study the examples below to find a pattern.
6 x 1 = 6 .6 x 1 = .6 . 6 x .1 = .06 .6 x .01 = .006 .6 x .001 = .0006
6 x . l = .6 6 x .01 = .06 6 x .001 = .006
Did you notice that in each answer: ^ . .
* there is 6. the number with which you started? ^ *
* the number of decimal places is equal to the total number of decimal places m the
two factors?
Do the following multiplication mentally:
1 . 7 x .1 = 2 . 9 x .01 =
3 . . 9 x . U 4 . 2.5 x .1 =
5 . 2.5 x . 0 1 = _
7 . .23 x .001 =
9 . 41.5 x .01 =
1 1 . .1 x .1 =
6 . .23 x .01 =
8 . .415 x . 0 1 =
1 0 . 415 x .01 =
1 2 . .01 x .1 =
1 3 . .01 x .01 = 1 4 . .001 x .01 =
1 5 . .001 x .001 =
1 7 . .01 x . 0 0 6 = _
1 9 . .004 x . 2 »
2 1 . .01 x .03 x .02 =
2 3 . .45 x .02 =
1 6 . .0001 x . 3 5 =
1 8 . .0023 x . l =_
2 0 . .005 x .02 - .
2 2 . .06 x .007 x .01 =
2 4 . 3.25 x .03 =
7 4
Rule for multiplying decimals
Multiply a s with whole numbers. T h e product should have the s a m e number of
p laces (to the right of the decimal point) a s the s u m of the p laces In the two
numbers being multiplied.
. 0 9
x . 0 4 .09 (2 decimal ptaces)
x.04-(2 decimal ptoucc^) » A ^ & m dearna-l places)
. 0 0 3 k |St e r - f spaces. 4ddfztro\ mededn
Find the p r o d u c t s
1. 3.25
x 3
dec ima l p laces
dec ima l p laces
dec ima l p laces
2. 3.2
x .8
dec ima l p laces
dec ima l p laces
dec ima l p laces
3. 29.8
x .06
dec ima l p laces
dec ima l p laces
dec ima l p laces
4. .32
x .06
dec ima l p laces
dec ima l p laces
dec ima l p laces
.5
x .3
.23
x .4
.27
.04
8. .19
x 6
.014
x .4
10. .17
x .07
11 4.9
x 5
12. 2.7
x .6
13. 3.5
x .04
14. 65.1
x .03
15. 2.3
x .6
16. 59.8
x .05
17. . 8 x 3 . 1 2
19. . 0 7 X . 0 4
18. 40.7 x . 0 5
20. . 1 6 X . 0 6
C Mam T«*eh#r» Pmtti Reoroduetton bv any meant strictly oroMbltad 85
Name Multiplying decimals
B.
0.75 7.3 0.2 5.03
x 9.3 xO.08 x 0 . 3 x 7.1
4.24
x 7.2
24.6
x 3.5
6.9
xO .64
18.5
x 1.6
D. 7.6
x 0.8
27.43
x 2.3
5.43
x 8.6
8.31
x 9.4
E. What rule can you write about the placement of the decimal point in the product?
© Frank Schaffer Publications, Inc. 5 6 FS-32072 Rfth Grade Math Review
A Rule For D i v id ing
Ask yourself what you did each step as you divided the blocks into the containers on page 87. You will find the four steps in division.
Step 1. H o w d id y o u get the f i rs t d ig i t in the q u o t i e n t ? (D iv ided 4 by 3)
Step 2. H o w d id y o u f i nd h o w m a n y had been taken a w a y ? (Mu l t i p l i ed 1 x 3)
Step 3. H o w d id y o u f i nd h o w m a n y were left over? (Sub t rac ted 3 f r o m 4)
Step 4. Wha t happened to the a m o u n t left over?
T h e Four Steps can be abbrev ia ted : D M S ^
(Exchanged and
r e g r o u p e d . Th is
is some t imes
ca l led b r i ng i ng d o w n )
Here's h o w to wr i te the p r o b l e m
Use D M S ^ t o d iv ide the
ones .
Use D M S + t o d iv ide tenths.
Use DMS4"to d iv ide
h u n d r e d t h s .
f p o r V t f o r g e t t o puX\ V n e i/L (/ouranswer IJ
3 i f -62 * 3 / f .62 Find the quo t i en t s
1. 2)2.84 2. 1)21.23 3. 5^183.5 4. 6 / 1 9 ^ 2
5. 3 / 1 0 2 6 " 6. SlWm 7. 8 I 5 8 4 T 8. 9J&282
9. 6>>$32.22 10. 9 ;$1.17 11 . 8 / 3 Z 8 0 " 12. 5>>$23.05
88 © Math Teachers Press
Ffeoroduction bv anv means strtcttv orohlblted
N a m e D a t e
^Recognizing Quotients
Ci rc le e a c h co r rec t quo t ien t
1.
2 .
3.
4 .
5.
6 .
7.
8 .
9.
17.4 + 2 8 7 8.7 0 .87 8 7 0
22 .5 + 5 4 5 0 4 5 4 .5 0 .45
4 3 . 2 + 8 0 .54 5.4 54 5 4 0
13 .04 + 4 3 .26 32 .6 3 2 6 0 .326
2 2 2 . 3 + 3 0 .741 741 7.41 74 .1
17 .08 + 2 8 .54 0 .854 8 5 4 8 5 . 4
3 6 1 . 2 + 6 6 .02 60 .2 602 0 .602
2 0 . 7 2 + 4 5 1 8 51 .8 5.18 0 .518
6 4 7 . 5 + 7 9 2 5 0 .925 9.25 92 .5
4 8 Grade 6 Use with Unit 3, Activity 8.
Name Date
iv is ion. Decimals (1)
Find each quotient.
1 .4 )33 2 . 3)§3 3 .2 )53 4 . 1)9/7
5. 5 ) 1 5 3 6 . 7 ) 2 0 1 7. 3 )183 8 . 4 ) 2 0 8
9 . 8 ) 5 3 10.9)7\2 1 1 . 6 ) 4 3 1 2 . 7 ) 4 3
13 . 5)5T3 14. 4)3l3 15.8)333 1 6 . 7 ) 4 0 6
17 . 3)713 18 .2)034 19.5)§7TO 2 0 . 6 )024
2 1 . 4 )434 2 2 . 7 ) ^ 6 4 2 3 . 8 ) 2 ^ 4 24 . 9)33$
176 Grade 6 Use any time.
The difficult zero
Here are t w o test papers .
W h i c h s tuden t answered co r rec t l y?
Student A StudentB
I
2I./6 2I./6
i 41.76
5. 6 r i 8 6. 2J4M
9. 6>/$24.06 10. 5 ^ 0 5
13. Seung ea rned $26.80 fo r w o r k i n g 8
hou rs . H o w m u c h d i d she earn per
h o u r ?
15. N ine s tuden ts ea rned $48.15 by
se l l ing baked g o o d s . Wha t was the
average a m o u n t ea rned by one
s tuden t?
n n T T T T
C u t o u t t he 16 c m n u m b e r s t r ip at t he
b o t t o m of the page to he lp dec ide .
1. 2) .16
Fo ld y o u r s t r i p i n to 2 equa l par ts . Wha t
n u m b e r is o n t he f o l d l ine? 16 h u n
d r e d t h s d i v i ded b y 2 is 8 h u n d r e d t h s so
the co r rec t answer is .08
2. 4) .16
Fo ld y o u r s t r i p i n to 4 equa l par ts . Wha t
n u m b e r is o n the f o l d l ine c losest t o t he
zero? 16 h u n d r e d t h s d iv ided by 4 is 4
h u n d r e d t h s so the co r rec t answer is .04
4. 4 1 3 7 2
7. 9A783 8. 8 1 3 6 0
11 . 9 ;$1.17 12. 8 ;$12.80
14. Mark d rove h is car 574 k i lomete rs
in 7 h o u r s . H o w m a n y k i l omete rs
per h o u r d id he average?
16. A package of 6 pops ic les
costs $1.32. H o w m u c h does
1 pops ic le cos t?
I — I — 1 — i — i — i — C — r ~ " S 9 10 rt 11 13 14 15*
Find the quo t i en t s . Be sure to pu t zeros in w h e n needed .
1. 8 ^ 2 4 2. 3A252 3. 5A375
89 e Math Teachers Preea
Reoreduetion bv any mean* ttrfctlv orohlbited
Dividing decimals by 10 ,100 or 1000
Dec ima ls can be d i v ided by 10 ,100 o r 1000 us ing the same sho r t cu t as w i t h w h o l e
n u m b e r s . C o u n t the n u m b e r of zeros in the ope ra to r . Move t he dec ima l po in t tha t
m a n y p laces in the lesser d i r ec t i on (to the le f t ) .
IVotLot how numbers become Less as -ike decimal point is rrwutd to the, Itit.
4£6 becomes 4S6 becomes A5G 4.SB<-4S:S &6 < f 56
/[.Dividing by 10 4&+IO=42& Ozero, 1 pLacctolhele^i) -423 = 4.Z3
(Z zeros, 2placet io # w left) - 4 . 2 3 - . 4 2 3 CMidim bu 100 4-23±70M=j22. 423+7M-4£3 (3 zeros, 3ptaces Me. Uft) =A23 =.0423
C o m p l e t e the tables.
4-10 -MOO 4-1000 -f-10 4-100 4-1000
1. 187 5. 18.7
2. 1382 6. 138.2
3. 86 7. 8.6
4. 314 8. 3.14
9. 74.2 4 -100 =
12. 368.5 4 -1000 =
15. 709 4-10 =
10. 7.2 4 -10 =
13. 5.88 4 -100 =
16. 439 4 -1000 =
1 1 . 27 4 -100 =
14. 92.7 4 -1000 =
17. 4.56 4 -100 =
90 © Math Teachers Press
Reoroduction bv anv means strictly won I bi led
Name
Dividing Decimals by .1, .01, and .001 o o o o o o o o o o o o o o o o o o o o o o o o
To learn a quick and easy strategy for dividing by .1, .01, and .001, look at the examples below. Observe the movement of the decimal point.
5 . 2 3 - r .1 = 5 2 . 3 5.23 + .01 = 523.0 5.23 -r .001 = 5230.0
S T R A T E G Y : The decimal point is moved to the RIGHT as many decimal places as there are in .7, .07, .007.
Notice that the answers are larger because you are dividing by a smaller quantity. Also, notice that dividing by .1 is the same as multiplying by 10. Dividing by .01 is the same as multiplying by 100. Dividing by .001 is the same as multiplying by 1,000.
Use your new strategy to divide mentally.
1. 1.84 + .1 =
3 . 1.84 - .001 =
2 . 1 . 8 4 * .01 =
4 . 3 4 . 7 * .1 =
5 . 34.7 - .01 =
7 . 4 5 8 - .1 =
6 . 34.7 * .001 =
8 . 458 * .01
9 . 458 - .001 =
1 1 . 4.8 - .01 =
1 0 . 36 1 =
1 3 . 8.84 * .001 =
1 5 . .230 * .001 =
1 7 . .78 ~ .01 =
1 2 . 367.2 * .10 =
1 4 . .96 - .01 =
1 6 . .45 -r .10 =
1 9 . 3.42 * .001 =
1 8 . 2.46 - .01 =
2 0 . .05 H- .01 =
2 1 . .4 * .1 = 2 2 . .036 - .001 =
2 3 . 14.1 - .01 = 2 4 . 6 - .1 =
7 7