CHAPTER II

BREAKING UP WHOLE NUMBERS INTO FRACTIONS FOR FINE WORK

Fractions. Here is the finish of a quarter-mile run. There are 1760 yards in a mile. How many yards in a quarter mile?

This picture was taken in the Harvard Stadium during a Harvard-Princeton Dual Track Meet.

What part of a mile is the 220 yard dash?

A football game is divided into halves, and each half is again divided into two equal parts. What are these parts called?

Hockey is usually played in three twenty-minute periods. What part of the game is each period?

What part of a regular base-ball game is an inning?

Fractions are nothing new; they are a continuation of division which we have just studied. We have all used them since we first gave half our apple to a chum or a third of our marbles to each of our two brothers. The beauty of fractions is that they help us to do so many things easily, which without them would be hard.

Use of Fractions. When you motor over a highway that is being repaired you often see piles of rock and other materials gathered near a stone crusher. They are to be broken up into finer material to build the smooth road which makes driving swift and pleasant.

So in most industries large materials are broken into smaller parts for finer, quicker work.

In just this way in mathematics, the whole number one is broken into smaller parts, called fractions, to enable us to do finer and quicker work. Just as the skilled men, who do the finer work, are paid more than the workers on coarse raw materials, so it will pay us to learn the fine points in mathematics; this we cannot do without a knowledge of fractions.

Buying Goods

Here is some simple practice in fractions. See how many of these examples you can do-in-your-head. In buying things you should check each charge mentally.

1. Mary bought 10 pencils for a quarter. How much would one cost?

2. Henry bought 3 oranges for 10 cents. What was the cost of one?

3. John bought for his mother 4 pounds of meat at 301⁄2 cents a pound. How much did it cost him?

4. Everett purchased 6 pounds of sugar at 6 cents a pound. How much would the merchant charge him?

5. Anna's father bought 23 pounds of prunes at 24 cents a pound. How much did the prunes cost him?

6. How many cents will 63 yards of cloth cost Maud if she pays 4 dimes a yard for it?

7. One quarter dozen eggs at 6 dimes a dozen will cost

cents.

8. Charles bought a bicycle for $36 and sold it for of what it cost him. For how much less than its cost did he sell it?

9. Lula bought 87 yards of muslin at 20 cents a yard.

What did it cost her?

10. State the cost of

(a) 72 yds. at $ a yard.

(b) 32 yds. at $5 a yard.

11. How many yards can be bought for $1

Different Kinds of Fractions. There are several kinds of fractions, all of which we must learn to recognize and name.

Common fractions have two parts, the numerator (the number above the line) and the denominator (the number below the line), called the terms of the fraction.

The denominator shows into how many parts the number is divided and the numerator shows how many of these parts are taken. For example, in this figure AC is a figure one inch long divided into 4 equal parts. The shaded part AB shows 3 of those 4 equal parts.

A

B C

Thus AB is of AC.

The fraction may also be thought of as a short way of indicating 3 ÷ 4.

A proper fraction is a common fraction whose numerator is smaller than its denominator, as §, 1,

5

An improper fraction is one whose numerator is equal to or larger than its denominator, as §, .

9

A mixed number is a whole number (called integer) plus a fraction. Thus 6 + 1 = 61.

Changing the Forms of Fractions. - Fractions which have different numerators and different denominators may still be equivalent in value. For instance, = 1, for one half dollar has the same value as two quarters.

Fractions may be changed in form, but not in value, by either multiplying or dividing both numerator and denominator by the same number. The new form is still equivalent to the old.

Lowest Terms.

=

A fraction is said to be reduced to

its lowest terms when both numerator and denominator

are as small as they can be made without changing