ARITHMETIC—FIFTH GRADE
Aim:—
To teach division of decimals.
The following is assumed as class knowledge upon which the process should be based.
1. Ability to read and write decimals.
2. Vivid knowledge of the relations of one hundred to ten, ten to one unit, one unit to one tenth, one tenth to one hundredth, etc.
3. Knowledge of the process of division of whole numbers.
4. The principle: multiplying or dividing both dividend and divisor by the same number does not change the quotient.
Preparation:—
1. Division by an integer.
a. Find the value of 1 acre of land if 15 acres cost $77115.
$ 5141
15 ) $ 77115
75
21
15
61
60
15
15
b. Find the value of 1 acre of land if 15 acres cost $771.15.
$ 51.41
15 ) $ 771.15
75
21
15
6.1
6.0
.15
.15
Compare the steps in (b) with the corresponding steps in (a). The pupil will experience no difficulty in telling the unit that each quotient figure represents, for he knows that dividing any number into parts does not change its unit.
Presentation:—
a. 12 is contained in 36 how many times?
12 ) 36
3
b. Multiply both dividend and divisor in (a) by 2.
24 is contained in 72 how many times?
24 ) 72
3
c. Multiply both dividend and divisor in (a) by 10.
120 is contained in 360 how many times?
120 ) 360
3
Compare the quotients. Recall the principle: Multiplying both dividend and divisor by the same number does not change the quotient.
d. .2 is contained in 2.4 how many times?
Multiplying both numbers by 10, to what is the divisor
changed? To a whole number.
2 is contained in 24 how many times?
2 ) 24
12
e. .22 is contained in 2.42 how many times?
Change .22 to a whole number, by multiplying both the
numbers by 100.
22 is contained in 242 how many times?
11
22 ) 242
22
22
22
f. .005 is contained in .125 how many times?
By what shall both numbers be multiplied so that .005 may
become the whole number 5?
5 is contained in 125 how many times?
5 ) 125
25
g. 2.88 is contained in 3.456 how many times?
By what shall both numbers be multiplied so that 2.88
may become the whole number 288?
288 is contained in 345.6 how many times?
1.2
288 ) 345.6
288
57.6
57.6
Many such examples will enable the pupils to formulate the generalization: “To divide a decimal by a decimal, multiply the dividend and divisor by the power of ten that will change the divisor to an integer, then divide as in simple division.”