2.4

10

24.0

Ten times 4 tenths are 40 tenths, which equal 4 units and no tenths. Write 0 tenths. 10 times 2 units are 20 units, and 4 units are 24 units. Write the 24 units. Read your answer. Compare your answer with your multiplicand. What change has taken place in the position of the decimal point?

2.46

100 246.00

The explanation here is the same as that above. Observe the change in the position of the point. Multiply 3.2 by 10. Multiply 2.42 by 100.

In these examples do you observe the same change

in the position of the decimal point?

Formulate a rule for multiplying a decimal by 10, 100, etc.

DECIMAL FRACTIONS.

DIVISION.

79

NOTE. - If the quotient is placed below the dividend or above, the decimal points come under each other as in addition or subtraction.

To divide a decimal fraction by a whole number, or to find a part of a decimal.

3) 4.65

1.55

3 is contained in 4 units 1 unit times, and 1 unit remaining. 1 unit is equal to 10 tenths, and 6 tenths make 16 tenths. 3 is contained in 16 tenths 5 tenths times and 1 tenth remaining. 1 tenth is equal to 10 hundredths and 5 hundredths make 15 hundredths. 3 is contained in 15 hundredths 5 hundredths times.

80

DECIMAL FRACTIONS. DIVISION.

To find a part of a decimal, or to divide a decimal fraction by a whole number of 2 figures.

1.32 36) 47.86

36

118

108

106

The explanation here is the same as on page 79, and need not be repeated. Place the point when you write tenths. Notice also that the point in the quotient comes above the point in the dividend.

Divide:

1. 24)45.84 35)474.25 46) 17.48 26)58.50

72

34

2. 57) 68.97 68) 108.8

79)56.09 35)52.50

ORAL.

NOTE. If the pupils cannot read to thousandths, teach them to do so. To divide a decimal fraction by 10, 100, etc.

10) 2.40 .24

81

10 is not contained in 2 units. Change 2 units to tenths. 10 is contained in 24 tenths 2 tenths times and 4 tenths remaining. Change 4 tenths to hundredths. 10 is contained in 40 hundredths 4 hundredths times. Compare your answer, .24, with your dividend, 2.4. What change has been made? What short way then can you discover to divide any decimal by 10?

Divide the following numbers by 10:

Formulate a rule for dividing a decimal by 10, 100, etc.

82

DECIMAL FRACTIONS.

To find a decimal part of a decimal or to multiply a decimal fraction by a decimal fraction.

Multiply 2.4 by .4.

.2/4

14

.96

This example means find 4 tenths of 2.4. We first find, as in Lesson 67. We find this to be .24. If .24 is, will be 4 times .24 (page 77), which is .96.

NOTE. By this method the points before the 4 in both multiplicand and multiplier are removed, and the single point before the 2 takes their place.

To change these points, as in the illustration, takes only a second of time.

9. Formulate a rule for finding a decimal part of a decimal.