II. DIVISION OF A DECIMAL BY TEN OR A MULTIPLE OF TEN

What is of 752 5 pounds? 1 of the same weight? To?

1. How many places to the left is the decimal point moved in dividing the number above by 10? By 100? By 1000?

2. Divide by 10: 2.5; 3.75; 425.8; 83.75; 2.425; .625.

In dividing one quantity by another of the same name or denomination, the quotient is an integer when, as in the problems above, the division comes out even.

1 A popular but less simple method of explaining the placing of the decimal point in the quotient is called "Clearing the Divisor" - .625 .25 = ? If there were no decimal place in the divisor (.25), this problem should be solved in the way that all problems are solved when the divisor is a whole number. The question then arises as to the possibility of making the divisor a whole number. Since multiply

DIVISION OF DECIMALS

(2)

167

How many times is .25 miles contained in .625 miles?

Notice, in dividing .62 by .25, that the terms have the same denominator, and that the quotient is the whole number 2; also, that further division gives the decimal, 5 tenths.

.8.0V21

In dividing a number by a decimal, point off with a carat (v) a number of decimal places in the dividend equal to those in the divisor; then place the decimal point in the quotient directly above the carat.

[With pencil.]

First place the decimal point in the quotients and then perform the following divisions:

ing both dividend and divisor by the same number does not alter the value of a quotient, it is possible to make the divisor .25 a whole number by multiplying it by 100, provided we also multiply the dividend .625 by 100. .25 X 100 = 25, ,625 X 100 62.5. .625 ÷ .25 62.5 25. The rule for this method is: In

=

=

dividing a number by a decimal, clear the divisor of its decimal by moving the decimal point in both dividend and divisor the necessary places to the right, and then proceed as in the division of a decimal by a whole number.

This method may be used if the teacher prefers it.

IV. EXERCISES FOR SKILL

[With pencil.] Practice on each set of problems below until you can get the right figures in the quotients and the decimal points correctly placed.

G. Divide: 945 by 42; 152 by 32; 1518 by 300; 1494 by 2000.

II. Test and Graded Practice

With the help of this test find out and overcome your difficulties with decimals. If you fail to get the right answer to a problem in the test, practice solving the problems in the set having the same letter, then try the problem again.

125

A. Write as decimals: 316, 21000, 10000, 1800, 10000, 710000

12. Owning an Automobile

[Use pencil only when needed.]

1. The following articles are bought for an automobile: 2 new tires at $24.50 each; 2 inner tubes at $3.50 each; 1 spark plug at $1.00. What is their cost?

2. I have put into my car 10 gallons of gasoline at 28¢ a gallon and 2 quarts of oil at 25¢ a quart. In paying for them, what change should I receive from a five-dollar bill?

3. The small mileage register on my car reads 15.7 miles when I start on a trip and 98.0 miles when I return. How long was the trip?

4. I travel 77.5 miles in 4 hours. This is approximately how many miles an hour?

5. Traveling at an average rate of 16 miles an hour, at what time in the morning must I start on a trip 120 miles long in order to reach my destination at half past four o'clock in the afternoon?

6. My car makes 20 miles to a gallon of gasoline. The cost is how much per mile with gasoline selling at 28¢ a gallon?

7. I find that the cost per mile of my car is as follows: for tires, $.019; for gasoline, $.014; for oil and other lubricants, $.001, for repairs, $.011; for insurance, interest, depreciation, and other expenses, $.025. What is the total cost per mile?

8. What is the cost per mile for tires when a set of tires costing $120 are good for 6000 miles?

9. Find the total cost per mile when in one season the expenses for a car come to $742 and the distance covered is 8000 miles.

10. Find the differences in the cost per mile between a small car covering 6000 miles at a cost of $450 and that of a larger car covering 6500 miles at a total cost of $988.

*11. Make and solve 3 problems of your own from facts that you know about automobiles.