Decimals/Multiplication and Division
Practice 11
Sweet Buggy Bites is a company that creates unusual kinds of candy. They make chocolate covered
ants, grasshopper kisses, sweet ’n sour crickets, beetle bites and other candy coated bugs. Use your
knowledge of multiplication and division with decimals to compute these answers.
Reminders
• Count all of the places to the right of the decimal
in multiplication and have the same number of
places to the right of the decimal in the answer.
• If the divisor has a decimal, move it to the right
of the divisor and move the decimal in the
dividend the same number of places to the right.
Example: 3.1 x 0.4 = 1.24
Example: .12 24.36 to 12. 2436.
= 203
1. A bag of beetle bites weighs 1.47 lbs. There are 7 candies in each bag. How much does each bite
weigh? _________________
2. A box of chocolate coated ants weighs 8.35 ounces. How much do 12 boxes weigh?
_________________
3. A bag of sweet ’n sour crickets weighs 9.81 ounces and holds 9 candies. How much does each
candy weigh? _________________
4. A large box of grasshopper kisses weighs 18.36 ounces. Each candy weighs 1.8 ounces. How
many candies are in the box? _________________
5. A super-sized bag of beetle bites weighs 2.255 lbs. What is the weight of 20 bags?
_________________
6. A mini-box of chocolate-coated ants weighs 4.025 ounces. Each candied ant weighs .05 ounces.
How many candy-coated ants are in each box? _________________
7. A large box of sweet ’n sour crickets weighs 13.467 ounces. How much do 72 boxes weigh?
_________________
8. A regular box of grasshopper kisses costs $4.83 for 21 candies. What is the cost for each candy?
_________________
9. A regular box of sweet ’n sour crickets costs $9.50 for 25 candied crickets. What is the cost for
each cricket? _________________
10. A box of beetle bites weighs 1.095 lbs. How much does a carton of 144 boxes weigh?
_________________
14
Answer Key
Page 4
1. 279 marbles
2. 146 marbles
3. 188 marbles
4. 55 marbles
5. 1,316 marbles
6. 37 marbles
7. 96 marbles
8. 222 marbles
9. 245 marbles
10. 468 marbles
11. 71 marbles
12 marbles
12. 444 marbles
Page 5
1. addition
19,056 bases
2. subtraction
1,689 at bats
3. addition
2,129 home runs
4. division
177 hits
5. multiplication
3,928,500 tickets
6. subtraction
1,578 strike outs
7. division
2,800 groups
8. subtraction
329 walks
9. division
175 hits (174 R13)
10. division
.600 or 60%
Page 6
1. subtraction
37,036 people
2. subtraction
14,443 people
3. addition
132,118 fans
4. addition
35,292 fans
5. division
860 packages
6. division
2,000 packages
7. subtraction
28,538 fans
8. division
8,250 packages
9. multiplication
601,536 fans
10. multiplication
3,649,050 tickets
47
Page 7
1. 7/12 lb.
2. 1 5/12 lb.
3. 1/8 lb.
4. 1/12 lb.
5. 5 lb.
6. 1/4 feet
7. 1 7/10 lb.
8. 11/24 feet
9. 6 cups
10. 1 19/30 lb.
Page 8
1. 15 ounces
2. 24 3/4 ounces
3. 21/40 ounces
4. 25 students
5. 14 students
6. 1/12 ounces
7. 1 7/10 ounces
8. 27 1/5 ounces
9. 9 3/8 ounces
10. 8 3/4 lb.
11. 1 1/2 ounces
12. 28 cups
Page 9
1. 10 3/8 inches
2. 32 3/4 inches
3. 7/8 inches
4. 51 5/8 inches
5. 83 7/8 inches
6. 3 1/4 lb.
7. 20 1/4 lb.
8. 24 1/6 inches
9. 14 1/8 ounces
10. 20 3/8 inches
Page 10
1. 76 inches
2. 52 1/5 inches
3. 10 prints
4. 8 prints
5. 150 inches
6. 355 inches
7. 23 1/3 inches
8. 7 prints
9. 451 inches
10. 8 prints
Page 11
1. 2 1/4 feet
2. 9 5/6 feet
3. 17 3/4 feet
4. 3 1/8 feet
5. 2 1/3 feet
6. 6 2/5 times
7. 12 lengths
8. 6 1/12 feet
9. 5 1/2 feet
10. 14 7/12 feet
Page 17
1. 467.476 mi.
2. 2,246.8 mi.
3. 32.422 feet
4. 94.14 mi.
5. 15.23 mi.
6. 44.636 mi.
7. 177.813 m.p.h.
8. 3,030.957 lb.
9. 91.05 mi.
10. 880.431 mi.
Page 12
1. $5.04
2. $0.56
3. $63.68
4. $43.45
5. $5.51
6. $5.04
7. $29.25
8. $0.96
9. $10.13
10. $20.15
11. $18.35
12. $17.10
Page 13
1. 7.9 centimeters
2. 87.6 centimeters
3. 30.25 centimeters
4. 220.89 centimeters
5. 204.26 centimeters
6. 347.863 centimeters
7. 24.99 centimeters
8. 1.201 centimeters
9. 56.899 centimeters
10. 59.663 centimeters
11. 26.989 centimeters
12. 181.91 centimeters
Page 14
1. 0.21 lb.
2. 100.2 ounces
3. 1.09 ounces
4. 10.2 candies
5. 45.1 lb.
6. 80.5 ants
7. 969.624 ounces
8. $0.23
9. $0.38
10. 157.68 lb.
Page 15
1. 75%
2. 72%
3. 75%
4. 60%
5. 75%
Page 16
1. $34.00
2. $4.00
3. $1.32
4. $9.52
5. $7.00
6. $2.48
7. $22.80
8. $4.00
9. $18.00
$42.00
10. $5.24
$29.71
6.
7.
8.
9.
10.
80%
64%
67%
70%
82%
Page 18
1. 60 m.p.h.
2. 50 m.p.h.
3. 30 m.p.h.
4. 60 m.p.h.
5. 50 m.p.h.
6. 55 m.p.h.
7. 52 m.p.h.
8. 40 m.p.h.
9. 40 m.p.h.
10. 80 m.p.h.
Page 19
1. 3,200 feet
2. 40 min.
3. 10,000 feet
4. 7,128 feet
5. 396 min.
6. 7,740 feet
7. 24,000 feet
8. 503 min.
9. 410 min.
10. 30,400 feet
Page 20
1. $1
2. $1
3. $11
4. 7
5. $21
6. 2
7. -$6
8. -24
9. 17
10. -72
11. -32
12. $226
Page 21
1. -$12
2. -$20
3. +42
4. -$7
5. -9
6. +10
7. $270
8. +156
9. 64
10. +5
11. -$5
12. +20
Page 22
1. polar bear
2. leopard/camel
dog/cat
3. 2 yr.
4. pig
5. 9 yr.
6. 15 yr..
7. 1 yr.
8. 9 yr.
9. 55 yr.
10. 70 yr.
Page 23
1. 30%
2. 5th/8th
3. 60%
4. no
5. 45%
6. 40%
Page 24
1. 1960
2. 1990–2000
3. 1960
4. 1950–1960
5. 1990–2000
6. 1970–1980
7. 1960–1970
8. the same
9. 10/11
10. 12/13
11. 16
12. 7/8/9
13. taller
14. 14
Page 25
1. 12
2. 1
3. 4
4. 2
5. 2
6. 12
7. 18
8. 1
9. 4
10. dog
11. snake
12. 5
13. 41
14. 27
Frequency
Cat 8
Dog 12
Snake 2
Bird 3
Mouse 3
Hamster 4
Fish 6
Other 3
Page 26
1. 10 m.p.h.
2. the scale starts at 20
rather than 0
6
How to
• • • • • • • • • • • • • • • • • • Multiply Decimals
Facts to Know
You multiply decimals the same way you multiply whole numbers. Also, the decimal points do not
have to be lined up. However, you must be careful to correctly place the decimal point in the product
for multiplication. The number of decimal places in the answer must equal the total number of places
to the right of the decimal point in the problem.
Decimal Points in the Final Answer
Multiplying decimals is the same as multiplying whole numbers. The key is to count the decimal
places in each factor.
Sample: 458 x 7.3 = ?
Step 1
Line up the digits.
Step 2
Multiply as with whole numbers.
Step 3
Count the decimal places in each
factor. The product must have
an equal number of decimal
places as the problem.
Zero as a Place Holder
Remember, the product has the same number of decimal
places as the factors. Sometimes you have to add zeros as needed.
45.8
x 7.3
1374
+ 32060
3,343.4
21.45
x 0.0321
2145
42900
+ 643500
0.688545
Multiplying Decimals by Whole Numbers
When multiplying decimals by whole numbers, counting off decimal places is the key.
Sample: One inch contains 2.54 centimeters. How many centimeters are there in four inches?
You must multiply the number of centimeters in one inch by four.
Step 1
Step 2
Step 3
Line up the numbers for easy multiplication. You don’t need to line up the
decimal points, however.
Multiply the numbers as you would multiply whole numbers.
Count the number of decimal places in both numbers that you multiplied. Make
sure the decimal places in the product equal the number of decimal places in the
problem.
2.54
x 4
10.16
(2 decimal places)
(0 decimal places)
(2 decimal places)
So the final answer is 10.16 cm
25
.
6
How to
• • • • • • • • • • • • • • • • • • Multiply Decimals
Facts to Know (cont.)
Multiplying Decimals by Decimals
When multiplying decimals by decimals, counting off decimal places is the key again.
Sample: John can run 4.30 miles in an hour during an ultramarathon. How far does he run in
7.5 hours?
You must multiply the distance John runs in an hour by 7.5.
Step 1
Step 2
Step 3
Line up the numbers for easy multiplication. You don’t
need to line up the decimal points, however.
Multiply the numbers as you would multiply whole
numbers.
Count the number of decimal places in both numbers
that you multiplied. Make sure the decimal places in
the product equal the number of decimal places in the
problem.
We can drop the final zero to make the answer easier to read. So the final answer is 32.25 miles.
Multiplying Decimals by 10, 100, and 1000
When you multiply by powers of 10, do the following:
Multiply by 10
Move the decimal point 1 place to the right.
3.63 x 10 = 36.3
Multiply by 100
Move the decimal point 2 places to the right.
3.63 x 100 = 363.
Multiply by 1000
Move the decimal point 3 places to the right.
3.63 x 1000 = 3,630.
Multiplying Money
Amounts of money are multiplied the same way other decimal numbers are multiplied. The number of
decimal places in the answer must equal the number of decimal places in the problem.
Sample
$155.73 (2 decimal places)
x 31
$4,827.63 (2 decimal places)
26
6
Practice
• • • • • • • • • • • • • • • Multiplying Decimals
Directions: Multiply the decimals by whole numbers.
1.
9 x .3 = _____________
6.
.75 x 8 = _____________
2.
4 x .035 = _____________
7.
50.3 x 3 = _____________
3.
482 x .009 = _____________
8.
2.125 x 5 = _____________
4.
45.63 x 40 = _____________
9.
.814 x 2 = _____________
5.
634 x 6.5 = _____________
10.
15.94 x 2 = _____________
Directions: Multiply the decimals by decimals.
11.
.08 x .7 = _____________
16.
4.26 x .508 = _____________
12.
.234 x .03 = _____________
17.
1.23 x 45.6 = _____________
13.
.14 x .6 = _____________
18.
29.7 x 1.64 = _____________
14.
73.6 x 8.14 = _____________
19.
19.04 x .4 = _____________
15.
43.65 x 3.7 = _____________
20.
.802 x .23 = _____________
Directions: Multiply the decimals by 10, 100, and 1000.
21.
.180 x 10 = _____________
26.
.00922 x 100 = _____________
22.
.53 x 100 = _____________
27.
52.475 x 10 = _____________
23.
.145 x 1000 = _____________
28.
893.155 x 1000 = _____________
24.
.00091 x 100 = _____________
29.
.00023 x 1000 = _____________
25.
11.234 x 10 = _____________
30.
167.945 x 10 = _____________
27
.
6
Practice • • • • • • • • • • • • • • • Multiplying Decimals
Keys to Multiplying Decimals
• Line up the numbers. You don’t need to line up the decimal points, however.
• Multiply the numbers as you would multiply whole numbers.
• Count the number of decimal places in both numbers that are being multiplied. Make sure the
decimal places in the product equal the number of decimal places in the problem.
Directions: Multiply to solve each problem.
1.
$46.98
x
2
7.
$45.03
x 13
13.
$10.50
x 0.60
2.
$1.49
x 3
8.
$17.10
x 15
14.
47.8
x 0.1
3.
$21.06
x 5
9.
0.84
x 3.15
15.
14.2
x 9.7
4.
$9.99
x 7
10.
2.08
x 0.9
16.
$5.75
x 0.24
5.
$1.57
x 34
11.
0.28
x 9.51
17.
$5.58
x 1.5
6.
$105.13
x
4
12.
0.0076
x 0.30
18.
0.14
x 0.87
28
7
How to
• • • • • • • • • • • • • • • • • • • Divide Decimals
Facts to Know
Take a look at these two division problems and notice the difference.
2
3 6
.2
3 .6
In the first problem, a whole number is being divided into a whole number. In the second, a whole
number is being divided into a decimal. Notice that the decimal point is placed directly above in the
quotient.
In fact, dividing decimals by whole numbers is simple if you place the decimal point in the
quotient first.
Directions: Mixed review—solve the problems.
0.85
Sample: 5.95 ÷ 7 = ?
7 5.95
–56
Step 1
Place the decimal point in the quotient.
35
Step 2
Divide as with whole numbers.
– 35
Multiplying Decimals by 10, 100, and 1000
When you multiply by powers of 10, do the following:
Divide by 10
Move the decimal point 1 place to the left.
3.63 ÷ 10 = 0.363
Divide by 100
Move the decimal point 2 places to the left.
3.63 ÷ 100 = 0.0363
Divide by 1000
Move the decimal point 3 places to the left.
3.63 ÷ 1000 = 0.00363
Zeros as Placeholders
When you cannot divide, use zeros to hold the decimal point.
Sample: .410 ÷ 5 = ?
In your first step, you cannot divide 5 into 4, so place a zero above
the 4. It serves as a placeholder. Don’t move the decimal point.
Next divide 5 into 41 and complete the problem.
.082
5 .410
– 400
10
– 10
0
Adding Zeros Inside the Division Box
Sometimes you cannot divide without adding zeros to the dividend (the number being divided). You
can add as many zeros as you need after the decimal point without changing the value of the number.
Sample: 3 ÷ 6 = ?
Step 1
Step 2
Step 3
6 will not divide into 3. Add a decimal point and a zero after the 3.
Place the decimal point in the quotient now, so you don’t forget.
Divide 30 by 6, which is 5. Place the 5 after the decimal point, just as you put a zero
after the decimal point in the problem.
.5
6 3
6 3.0
6 3.0
–3 0
0
29
.
7
How to • • • • • • • • • • • • • • • • • • • Divide Decimals
Facts to Know (cont.)
Dividing Decimals by Decimals
Dividing decimals by decimals means you must move the decimal point by changing the decimal
number to a whole number. Multiply the divisor (the dividing number) and the dividend (the number
being divided) by the same power of 10. This will make the divisor a whole number.
Sample: 2.6 20.8
Step 1
The divisor has sixth tenths. Multiply the
divisor and the dividend by 10 to get a whole
number divisor. What you do to the divisor
7 5.95 number, you must do to the dividend.
Step 2
8
26 208
– 208
0
2.6 20.8
Divide 208 by 26, which is 8.
Note: If the divisor has hundredths, move the decimal point 2 places. If the divisor has thousandths,
move the decimal 3 places.
More About Adding Zeros Inside the Division Box
You can make a divisor that is a decimal into a whole number by moving the decimal. To do so, you
may need to add zeros to the dividend.
Sample: 3.15 6.3
Step 1
Step 2
3.15 has hundredths. Change 3.15 to the whole
number 315 by moving the decimal 2 places.
Remember, that you must do to the dividend what you
did to the divisor. However, you must add a zero to
the dividend as a placeholder in order to move the
decimal 2 places.
3.15 6.3
2
315 630
– 630
0
Divide 630 by 315, which is 2.
Sometimes, you need to add more than one zero to the dividend, depending on how many places you
move the decimal in the divisor.
Dividing Money
Money is divided in the same way as other decimals. Add a
dollar sign and put the decimal point in the quotient directly
above the one in the dividend. Look at the sample on the right.
30
$0.30
6 $1.80
– 18
0
7
How to
• • • • • • • • • • • • • • • • • • • Divide Decimals
Facts to Know (cont.)
Changing Fractions to Decimals
To change fractions into decimals, divide the numerator by the denominator.
Sample: Change 3– to a decimal.
4
Step 1
Set up the division problem. Divide the numerator 3
by the denominator 4.
Step 2
Step 3
Notice that you must add a zero because 3 is not
divisible by 4 unless you do. Place the decimal
point in the quotient now, so you don’t forget.
Divide 3.0 by 4, which is 0.75.
0.75
4 3.00
– 2 80
20
– 20
0
Sometimes you must add several zeros to the dividend. If the answer has a remainder and a number
–
turns into a repeating decimal, such as .333, write the remainder in fraction form—.33 1–.
3
Changing Mixed Numbers to Decimals
To change a mixed number to a decimal number, work with only the fraction first. You can include the
whole number in your answer.
Sample: Change 2 6– to a decimal.
7
5
0.85 –7
Step 1
Set up the division problem. Divide 6, the numerator
of the fraction, by the denominator 7.
7 6.00
–56
Step 2
Notice that you must add a zero. The number
40
6 isn’t divisible by 7 unless you do. Place the decimal
– 35
point in the quotient now, so you don’t forget.
5
Step 3
Divide 6.0 by 7. Add another zero.
Turn the remainder into a fraction.
Step 4
Add the whole number to the answer.
The final answer is 2.85 5–
7
Changing Decimals to Fractions
To change a decimal into a fraction, do the following three things:
Step 1
Step 2
Step 3
Drop the decimal point and place the number into
the numerator of a fraction.
Make the the denominator a 1 followed by as many
zeros as there were decimal places.
Reduce the fraction if you can.
31
35
.35 = —
—
100
7—
.007 = —
—
—
1000
.
7
Practice • • • • • • • • • • • • • • • • • Dividing Decimals
Directions: Solve the division problems.
1.
.7 =
—
.14
6.
9.2
—
— =
230
11.
45.6
—
—
—
— =
8
2.
6— =
—
43.2
7.
.8—
—
—
—=
27.2
12.
.258
—
— =
6
3.
4— =
—
—
—
—
.3704
8.
$30
—
— =
.04
13.
3.43
—
—=
.7
4.
3—
.— =
—
—
—
.0048
9.
$42
—
—=
.24
14.
7.2
— =
.09
5.
.8 =
—
60
10. $65 ÷ 4– =
5
15.
60
—
— =
1.2
Directions: Change each decimal to a fraction or a mixed number. Reduce to the lowest terms.
16.
.35 =
20.
18.33 =
24.
.318 =
17.
.064 =
21.
4.625 =
25.
.0625 =
18.
3.4 =
22.
.0084 =
26.
4.25 =
19.
3.125 =
23.
66.75 =
27.
1.10 =
Directions: Change each fraction to a decimal.
28.
4– =
5
30.
2– =
3
32.
5– =
6
34.
1– =
3
29.
3– =
8
31.
7– =
9
33.
5– =
8
35.
7 =
—
10
32
1– .50
50%
2
20. 0.15; 0.51; 5.01;
50.1
21. 4
22. 27
23. 21
24. 5.6
25. 0.2
26. 7.6
27. 18.7
28. 304.81
29. 1.06
30. 27.39
31. 356.14
32. $13.02
33. $163.76
34. 4,567.83
Page 27
1. 2.7
2. .14
3. 4.338
4. 1825.2
5. 4121
6. 6
7. 150.9
8. 10.625
9. 1.628
10. 31.88
11. .056
12. .00702
13. .084
14. 599.104
15. 161.505
16. 2.16408
17. 56.088
18. 48.708
19. 7.616
20. .18446
21. 1.8
22. 53
23. 145
24. .091
25. 112.34
26. .922
27. 524.75
28. 893,155
29. 0.23
30. 1679.45
Page 28
1. $93.96
2. $4.47
3. $105.30
4. $69.93
5. $53.38
6. $420.52
• • • • • • • • • • • • • • • • • • • • • • Answer Key
7. $585.39
8. $256.50
9. 2.646
10. 1.872
11. 2.6628
12. 0.00228
13. $6.30
14. 4.78
15. 137.74
16. $1.38
17. $8.37
18. .1218
Page 32
1. 5
2. 0.139
3. 10.80
4. 625
5. 0.013
6. 0.04
7. 0.03
8. 750
9. 175
10. $81.25
11. 5.7
12. .043
13. 4.9
14. 80
15. 50
16. 7/20
17. 8/125
18. 3 2/5
19. 3 1/8
20. 18 1/3
21. 4 5/8
22. 21/2500
23. 66 3/4
24. 159/500
25. 1/16
26. 4 1/4
27. 1 1/10
28. .8
29. .37 1/2 or .375
30. .66 2/3
31. .77 7/9
32. .83 1/3
33. .62 1/2 or .625
34. .33 1/3
35. .7
Page 36
1. 7%
2. 75%
3. 3.5%
4. 33 1/3%
5. 90%
6. 150%
7. .4%
8. 65%
9. 10%
10. 66 2/3%
11. .09
12. .35
13. .048
14. .22 2/9
15. .6
16. 1.25
17. .003
18. .95
19. .2
20. .33 1/3
21. 3/4
22. 2/5
23. 1/20
24. 4/5
25. 3/50
26. 9/100
27. 2/25
28. 1/5
29. 7/20
30. 43/50
31. 37.5%
32. 33 1/3%
33. 40%
34. 87.5%
35. 66 2/3%
36. 20%
37. 50%
38. 12.5%
39. 5%
40. 25%
41. 5%
42. 600%
43. 20%
44. 16 2/3%
45. 25%
46. 80
47. 90
48. 63.6
49. 130
50. 85.71
Page 39
1. $45.00
2. $45.42
3. $10.00
4. $30.00
5. $135.00
6. $73.75
48
7. $19.90
8. $9.12
9. $298
10. $54.08
Page 40
1. $42.29
2. $196
3. $16.20
4. $0.25
5. $1372.70
Chart
1 , .10, 10%
1. —
10
2. 1– , .25, 25%
4
9 , .45, 45%
3. —
20
3 , .15, 15%
4. —
20
4 , .80, 80%
5. —
5
5 , .833, 83.3%
6. —
6
77
7. —
— , .77, 77%
100
1 , .20, 20%
8. —
20
11 , .222, 22%
9. —
50
10. 2– , .40, 40%
5
Pages 41 and 42
1. 24 pieces of pie
2 1/4 yard
3. 4 miles
4. 1 1/8 miles
5. 2 1/2 pieces of
taffy
6. 3 weeks
7. 75 ounces
8. 66 1/4 inches
9. $287.65
10. $21.79
11. $114.26
12. $81.16
13. $300; $90; $210
14. $26.45
15. 25 students
16. 150 children
17. 20 homes
18. 225 cards
19. $0.87
20. $1.50
21. 26 minutes
22. 288 boxes
23. 6 pounds
24. 6.25%
Pages 43 and 44
1. $500 every six
months. Take a
salary of $10,000
for Sample:
1st year: $5,000 +
$5,500 = $10,500
vs. $10,000
2nd year: $6,000
+ $6,500 =
$12,500 vs.
$12,000
2. about 18,000
miles
3. house numbers
4. $0.20
5. 100%
6. Choco-Chunk and
Nuts to U are
equal in value.
Goodie TwoShoes is the better
buy.
7. 200 miles a day
8. $4,250.00
9. $1.25 to break
even; $4.38 to
make $25,000.
10. a. $14.00
b. $42.00
c. $52.50
d. $87.50
e. $49.00
f. $105.00
Yes, he saved
$350.00
11. b
12. a
13. a
14. a
15. After 31 years,
the system will
still be worth
$10!
16. 52 bushels of
wheat, 55 bushels
of corn, and 34
bushels of oats.