87. 1.78 x 1.024

95. 101.1 x 11.01 103. 5.00237 × 3.0701

104. If a man walks 4.75 miles in an hour, how far will he walk in 11.25 hours?

105. How many yards of cloth are there in 12.4 bales, each bale containing 56.375 yards?

106. A farmer averages 35.875 bushels of wheat from 12.95 How many bushels does he harvest?

acres.

107. Find the cost of 18.75 dozen eggs at $.125 a dozen.

Multiplying by moving the decimal point.

1. Multiply 5.25 by 10; by 100; by 1000.

10 × 5.25 = 52.50 100 × 5.25 = 525.00 1000 × 5.25 = 5250.00

Study of Problem

a. How may we multiply a decimal by 10? by 100? by 1000?

b. How is the value of a number affected by moving the decimal point one place to

the right? two places? three places?
c. How, then, may a number be multiplied by 10? by 100?

Multiply first by 10; then by 100; then by 1000.

DIVISION OF DECIMALS

Dividing a decimal or a mixed decimal by an integer. 1. Divide 48 hundredths by 4; by 6; by 8; by 12.

2. .484? .48+6= ? .48+12= ?

3. Compare 6).12 and .72+ 6.

.12

4. Divide 24 and 64 hundredths by 4; by 8. 5. Divide thus: 4)24.64 8)24.64 12)48.72

6.16

3.08

4.06

In each of the above problems the decimal or mixed decimal was simply separated or partitioned into equal parts.

Divide as in integers, placing the decimal point in the quotient directly above or below the point in the dividend, before you begin to divide.

HAM. INT. ARITH. - 13

39. If 8 yards of muslin are sold for $.80, what is the price per yard?

40. When 144 pens are sold for $.72, what is the price per pen?

41. If 10 sheets of paper are sold for $.05, what is the price per sheet?

42. If $.27 is paid for 1000 cubic feet of gas, what is the price per cubic foot?

43. Find the sum of the quotients:

Dividing any number by a decimal.

Divide 5.5 by 5.5.

1. 5.5 5.5 = 1 55 ÷ 55 = 1

Study of Problem

a. What is the first quotient? the second? b. What was done to the first problem to make the second?

c. Did moving the decimal point to the right, in both dividend and divisor, change the quotient?

Multiplying both dividend and divisor by the same number does not change the quotient.

Observe that .6).66 = 6)6.6; .02).004 = 2).4

2. Divide 6.25 by .5. 6.25.562.5 ÷ 5

5)62.5

12.5

+

a. Make the divisor an integer by moving the decimal point one place to the right in both dividend and divisor.

b. Show that this does not affect the quotient.

c. Solve, placing the decimal point in the quotient before beginning to divide.

3. Divide 62.5 by .025.

62.5÷.025= 62500 ÷ 25.

25)62500
2500

a. Make the divisor an integer by moving the decimal point three places to the right.

b. Solve, placing the decimal point in the quotient before beginning to divide.

Move the decimal point the required number of places to the right in both dividend and divisor so that the divisor will be a whole number. Divide as in the division of a decimal by an integer.

The use of the caret in division of decimals.

Another method is to mark off by a caret (^) as many decimal places from the right of the decimal point in the dividend as there are decimal places in the divisor, and then to divide as in integers, placing the decimal point directly below or above the caret in the dividend. Thus,

.5).005= .5).0^05

0.01

It is evident in the above problem that if both the dividend and the divisor were changed so as to make the divisor a whole number, the decimal point in the dividend would be in the place occupied by the caret. The decimal point must therefore be placed in the quotient directly above or below the caret.

The caret determines the position of the decimal point in the quotient and at the same time retains the identity of the problem.

Mark off by a caret the same number of decimal places from the right of the decimal point in the dividend as there are decimal places in the divisor. Divide as in integers, placing the decimal point in the quotient directly above or below the caret, before beginning to divide.