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18. How much will 7 arithmetics cost at $.82 apiece ? 19. At $.35 apiece, how much will 24 chickens cost ? 20. A rod is 16.5 feet. How many feet are there in 9 rods?

21. When a man earns $3.65 per day, how much does he earn in 26 days?

22. A pound of cream cheese costs $.115. How much do 126 pounds cost ?

23. If an automobile averages 17.75 miles an hour, how far will it travel in 14 hours ?

Multiplying a decimal by a decimal.

1. Multiply 1.5 by 4. When a decimal is multiplied by an integer, what do you observe about the number of decimal places in the product ?

2. Multiply .1 by .01; 1 x 100 = 1000 .001. Multiply 1.5 by .5; 1.5= 15; 14x B= 16 = .75. When a decimal is multiplied by a decimal, what do you observe about the number of decimal places in the product ?

To bo = .001.

Written Work 1. Multiply .75 by .3.

Since there are two decimal places in the multiplicand and 1 in the multiplier, point off 3 decimal places in the product, making the answer .225.

2 25 1000

.75

Test: .75 = 105, and .3 = x x x = .3

or .225, a decimal. .225 Multiply as in integers, pointing off as many decimal places in the product as there are decimal places in both factors.

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7. 3.21 x 4.5 13. 11.4 x 150 19. 1.33 X 44

20. Find the cost of 11.5 yards of cloth at 124 cents a yard.

21. Mrs. Crane bought 3.5 pounds of steak at $.16 per pound, 6 pounds of sugar at $.05 per pound, 4 pounds of coffee at $.28 per pound, and 3 quarts of cranberries at $.10 per quart. She gave in payment 3 one-dollar bills. How much change should she receive ?

22. How much will 41.25 yards of linoleum cost at $1.25 per yard ?

23. A train between Los Angeles and San Francisco runs 13.5 hours at the rate of 35.7 miles per hour ? What is the distance between the two cities?

24. A mail carrier averages 3.25 miles per hour while delivering mail. If he spends 5.25 hours delivering each day, how far does he walk per day ?

25. Find the cost of 5.125 yards of silk at $1.75 a yard. At the same price per yard find the cost of 8.875 yards.

26. At $ 2.50 per day, how much will 4 men earn in 6.5 days ?

27. A cubic foot of water weighs 62.5 pounds. How much do 12.75 cubic feet of water weigh ?

DIVISION OF DECIMALS

Dividing a decimal by an integer.

Written Work

1. Divide .84 by 4 in this way:

4).84

.21 Divide and test, placing a decimal point in the quotient, before beginning to divide: 2. 6).66 5. 7).714

8. 7).847 3. 3).96 6. 5).535

9. 6).936 4. 8).808

7. 4).848 10. 8).896 11. Explain why adding naughts to the right of a decimal does not change its value; thus, .8=.80, .05 = .050.

It is sometimes necessary to add naughts to the right of the dividend to complete the division. 12. Divide .12 by 5. 5).12 =5).120

.024

.08

Find the quotients and test: 13. 4).3 14. 8).6 15. 6).27 16. 5).28 17. .6 : 2 25. .024 6 33. .108 _ 3 18. .9+ 3 26. .102 + 3

34.

2 19. .12; 6

27. .039 13 35. .125 + 5 20. .005 - 5 28. .144 - 12 36. .008 • 4 21. .008; 4 29. .015 + 3

37. .35+ 7 22. .27 + 9 30. .063 · 7

38. .077 11 23. .2 + 4

31. .904 - 8 39. .022 4 2 24. .6 + 8

32. .72 +10 40. .036 + 6

Dividing a mixed decimal by an integer.

Written Work

Divide in this way:
1. 6)6.648 2. 8)24.600 3. 9)729.83
1.108
3.075

81.09 Observe that in dividing a decimal or a mixed decimal by an integer, the dividend is simply separated or partitioned into equal parts. 4. Divide 39.25 by 25. 5. Divide 12.648 by 24. 1.57

.527 25) 39.25 24)12.648 How many times is 25 contained 25 12 0

in 39? in 14.2 ? in 1.75 ?

In practice, we simply divide as 14.2

64

in the division of integers. Since 12.5

48

24 is larger than 12.648, the quo1.75

168

tient must be a decimal. 1.75

168

Place a decimal point in the quotient directly above or below the decimal point in the dividend before beginning to divide; then divide as in the division of integers.

Divide and test : 6. 69.92 + 23 14. .945 • 35 22. 8.437 59 7. 29.54 - 14 15. 60.32 - 52

23. 233.32 + 38 8. 195.2 + 32 16. .968 +44 24. 283.88; 47 9. 401.4:18 17. .828 ; 23

6.497

-73 10. 3.434 _ 34 18. 5.18 37 26. 16.150 : 34 11. 156.4 +46

19. .0833 : 49 27. 55.660 + 92 12. 1.014 – 26 20. 1.566 : 54 28. 5.460 : 84 13. 5.084 + 41 21. 2.546 – 67 29. 1.6272 + 18

25.

30. Divide 12 by 16. 12 + 16 = 12.00 - 16.

.75

12 is equal to 12.00, which divided by 16 16)12.00 equals .75. 112 A decimal point must be placed after an

80 integer before naughts are annexed.

80 Divide: 31. 20 : 75

44 ; 99 39. 605 by 1210 32. 60 : 150 36. 110 : 220

40. 513 by 2052 33. 24 : 228 37. 340 ; 1700 41. 208 by 1664 34. 30 : 375 38. 510 - 1020

42. 111 by 8888

35.

Dividing a decimal by a decimal. 1. 8; 4= 80 - 40.

5:10 = 50 - 100.

6; 3= 600 ; 300. 2. Compare the quotient of 8• 4 with the quotient of 80 = 40. Compare the quotient of 5 - 10 with the quotient of 50 - 100. Compare the quotient of 6 = 3 with the quotient of 600 : 300.

.8 x 10 8 .08 x 100 8
.2 x 10 2 .02 x 100 2

3. Does multiplying both dividend and divisor by the same number affect the value of the quotient?

4. Multiplying by 10 moves the decimal point how many places to the right ? multiplying by 100 ?

5. In what short way may a decimal be multiplied by 10? by 100? by 1000, etc. ?

6. Multiply .5, .25, .025 each by 10; each by 100; each by 1000.

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