ADDITION AND SUBTRACTION OF DECIMALS

1. Why must and be changed to twelfths before they can be added or subtracted?

2. What kind of fractional units, then, can be added or subtracted?

3. Observe that decimals are only so many 10ths, 100ths, 1000ths, etc., of a unit expressed by placing a period before the numerator and omitting the denominator. In adding or subtracting decimals, then, the decimal must be written so that like units are under each other.

Do naughts annexed to an integer change its value? Do naughts annexed to a decimal change its value?

15.000

6.387

8.613

Add:

8.445, .875, .05,

3. 25,005, .75, .005, .72, 7., 8.445, .0745, .6475.

4. Subtract 75.005 from 485.007.

5. Subtract .8075 from 23.

6. Subtract .5075 from 23.004.

7. Add 2.5, 11.25, 18.042, 27.0548.

8. Add 1.45, 3.06, 6.605, .09. 9. Add 4.24, 8.2, 6.006, 19.098. 10. Add 11.01, 3.7, 10.01, 2.005. 11. Add .7, .4285, 18.054, 8.0108. 12. Add .002, 22.5607, 1.114, 18.

13. Add 126, 2578, 9.009, .00101, 2.02, .0245. 14. Add .0402, 48.0148, .07089, .1607, 17.0017. 15. Add 89.4004, 75.8002, 761.0612, 1245.0005.

30. From .06.0875+ 49.03 take .025 +2.0025+43.701.

31. From the sum of .2305 + .9105 take 1.

32. From the sum of 27.045 and .7001 take their differ

34. How many yards equal 5 pieces of cloth containing 25.25 yd., 32.625 yd., 40.81 yd., 45.5 yd., and 48.75 yd. respectively?

35. A clerk's income for one year is $600. He spends $487.75. How much does he save?

36. The sum of two numbers is 118.6, and one of the numbers is 14.247. What is the other number?

37. What is the weight in tons of 4 loads of coal, which weigh respectively 1.5 T., 1.1875 T., 1.3125 T., and 1.9 T.?

38. If a tailor uses 4.375 yards of cloth in making a suit, how much remains of a piece of cloth containing 12.25 yards? 39. Find the cost of three tables at $9.50, $12.75, and $15.80.

40. A meter contains 39.37 inches. How much larger is a meter than a yard?

41. How many feet of lumber are there in three piles measuring 2675.25 ft., 6785.875 ft., and 5674.5 ft.?

42. A farmer bought 75.5 pounds of clover seed and sowed 54.25 pounds. How much had he remaining?

MULTIPLICATION OF DECIMALS

Multiplying a decimal by an integer or by a decimal. 1. How many are 5 x .3? 5 x .03? 5 x .003 ?

2. Multiply by and express the product decimally. ==.15. Hence, .3 x .5.15.

3. Multiply by 15 and express the product decimally. 10 × 180 = 1880.015. Hence, .3 x .05 .015.

=

In the above examples compare the number of decimal places in the multiplicand and multiplier together with the number of decimal places in the product.

Written Work

1. Multiply 5.8 by 6.

5.8

6

6 x .848 tenths or 4 ones and 8 tenths.

.8 and carry 4. 6 x 5 = 30; 30+ 4 = 34. 34.8 = 34.8

2. Multiply .25 by .13.

.25

.13

75

25

.0325

Study of Problem

Write the Hence, 6 x 5.8

a. What is the sum of the decimal places in the multiplier and multiplicand? in the product?

b. The product, then, must contain how many places?

c. How many significant figures are there in the product?

The number of decimal places in the product of the two numbers is the sum of the decimal places in both multiplier and multiplicand.

67. How many acres are there in three fields of 65.875 acres each?

68. There are 31.5 gallons in a barrel. How many gallons are there in 63 barrels ?

69. A merchant sold 75 yards of muslin at $.125 per yard. How much did he receive for it?

70. Find the cost of 15.3125 acres of land @ $50.

71. Find the product of .095 multiplied by 3.17.

72. Find the product of 909 multiplied by 9.99. 73. Find the product of .0725 multiplied by 480.

74. If a gallon of water weighs 8.338 pounds, find the weight of 24 gallons.

75. A franc equals $.193. How many cents are there in 125 francs?

76. A meter equals 1.093 yards. Find the number of yards in 64 meters.