1 Gal.

CHAPTER III

FRACTIONS

How many pint cups of water must be emptied into a quart measure to fill it? If we pour a pint cup full of water into a quart measure, it will be only half filled. A pint is what part of a quart?

of a quart, how many halves are there in

A quart of water will fill the gallon measure to the lower line. How many quarts are there in a gallon? A quart is what part of a gallon?

of a gallon how many quarts?

=

of a gallon of a gallon?

How many pints are there in a gallon? A pint, then, is what part of a gallon?

How many pints are there in a quart? A quart, then, equals how many eighths of a gallon?

By comparing pints, quarts and a gallon find the following:

A gallon of a gallon? A gallon of a gallon?

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A dime is equal to how many cents? A cent is what part of the value of a dime? A nickel is equal to how many cents? A nickel is equal in value to what part of a dime?

of a dime = of a dime?

Unless a considerable amount of concrete material has been presented to the pupils in studying fractions in the primary book, the teacher should have the pupils use the pint, quart and gallon measures in comparing the above fractional parts.

4. The circle at the left is divided into 6 equal parts. What is each of these 6 parts called? The shaded portion of the circle is what part of the circle?

of the circle of the circle?

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5. This rectangle is divided into 8 equal parts.

What

is each of these parts called? The shaded portion is what part of the retangle?

of the rectangle = of the rectangle?

Take a sheet of paper and fold it so that it is divided into halves and crease. Then fold again and crease.

is now divided into fourths.

The sheet

Use the sheet of creased paper to answer the following:

of the sheet of the sheet?

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Fold the sheet of paper so that it is divided into 16 equal parts. Unfold and use the creased paper to find the following:

Draw a line a foot long on the board and divide it into 3 equal parts. Each of these parts is called of a foot.

Divide each of the three parts into 2 equal parts. The foot line is now divided into 6 equal parts and each part is called of a foot.

Comparisons between halves, fourths, eighths and sixteenths may also be made with dry measures: 1 peck-2 gallons=8 quarts=16 pints. Then 1 pint-quart gallon=1 peck.

This work can then be extended to such fractions as of a gallon, & of a gallon, etc.

A foot ruler is divided into how many inches? An inch is what part of a foot?

Draw a line a foot long and mark it off into inches. Draw a longer line through the middle of this ********* foot line dividing it into halves.

of a foot of a foot?

Draw another foot line and mark it off into inches. Draw two longer marks through the four and eight inch marks to divide the line into thirds.

Draw a foot line and mark it off into inches.

Divide it

into fourths.

of a foot

of a foot?

In the illustration at the left, the sheet of paper is shown divided into 4 equal parts. The shaded portion of the paper represents three-fourths of the whole sheet. Three-fourths may

be written in the shorter form. The number is called

a fraction.1

The number 4 (written below the short horizontal line) is called the denominator (namer) of the fraction. The denominator shows into how many equal parts the whole thing has been divided. The denominator 4 of the fraction shows that the whole was divided into 4 equal parts.

The denominator also indicates the size of the parts. If the sheet were divided into eight equal parts, how would each of the parts compare in size with one of the equal parts if the sheet were divided into fourths? Compare one of the 16 equal parts of the sheet with a fourth and an eighth. We see then that the larger we make the number (as 4, 8 or 16) in the denominator the smaller is the size of each of the equal parts into which the whole has been divided.

is

The number 3 (written above the line in the fraction called the numerator of the fraction and shows how many of the equal parts have been taken to form the fraction.

1A fraction is a number composed of one or more of the equal parts of a whole.

Exercise 1

Name the numerators and denominators of the following fractions, telling what each shows, as follows:

5 is the denominator. It shows that the whole thing has been divided into 5 equal parts. 4 is the numerator. It shows that 4 of the 5 equal parts have been taken to form the fraction.

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A proper fraction is one whose value is less than a whole. In a proper fraction the numerator is less than the denominator. is a proper fraction.

An improper fraction represents either a whole or more than a whole. The numerator of an improper fraction is equal to or greater than the denominator. is an improper fraction. A mixed number is a number composed of a whole number and a fraction. 14 is a mixed number.

An integer (or whole number) is made up of whole units. 5 is an integer because it is made up of 5 whole units.

Any improper fraction may be changed to either an integer or a mixed number. Likewise any integer or mixed number may be changed to an improper fraction.

1. Change to an integer.

A fraction is sometimes considered as an indicated division means 9 divided by 3.

Then = 3.