FRACTIONS.

INTRODUCTORY LESSON.

Definitions and Illustrations.

WHEN any whole thing or number is divided into any number of equal parts, the parts are called fractions of the thing or number.

If an orange be divided into two equal parts, the parts are called halves. If it be divided into three equal parts, the parts are called thirds. If it be divided into four equal parts, the parts are called fourths. If it be divided into five equal parts, the parts are called fifths. If it be divided into six equal parts, the parts are called sixths. If it be divided into seven equal parts, the parts are called sevenths. If it be divided into eight equal parts, the parts are called eighths. If it be divided into nine equal parts, the parts are called ninths. If it be divided into ten equal parts, the parts are called tenths. If it be divided into eleven equal parts, the parts are called elevenths. If it be divided into twelve equal parts, the parts are called twelfths. The number of equal parts into which any whole thing or number is divided always indicates the name of the parts.

Fractions are usually expressed by two numbers written one above the other, with a short line between them

two

7 seven

1 one 3 three 4 four thus: 5 five six 6 Ž half, thirds, fourths, 5 fifths, 6 sixths, sevenths, eighths, I &ffus, 8 eight 9 nine 10 ten 11 eleven 9 ninths, 10 tenths, TTelevenths, 12 twelfths.

The number below the line expresses the number of equal parts into which the whole thing or number is supposed to be divided; and it is called the denominator, because it indicates the name of the parts, as thirds, fourths, fifths, &c.

The number above the line is called the numerator, because it shows the number of equal parts expressed by the fraction.

LESSON I.

1. In a unit, or 1, there are 2 halves.

How many halves are there in 2? In 2? In 4? In 44 In 6? In 61? In 8? In 8? In 10? In 101? The 2 halves of any whole thing or unit are equal to the whole thing or unit; hence, in any number of halves, there must be 1 half as many whole ones or units as there are halves.

2. How many whole ones are there in 4 halves? In 5 halves? In 8 halves? In 9 halves? In 12 halves? In 13 halves? In 16 halves? In 17 halves? In 20 halves? In 21 halves? In 24 halves ? 3. In a unit, or 1, there are 3 thirds. How many

thirds are there in 2? In 24? In 4? In 43? In 6? Since the 3 thirds of any whole thing or unit are equal to the whole thing or unit, there must be 1 third as many whole ones or units as there are thirds. 4. How many whole ones are there in 6 thirds?

In 14 thirds?
In 24 thirds?

In 7

In 18

thirds? In 12 thirds? thirds? In 19 thirds? 5. In a unit, or 1, there are 4 fourths. How many fourths are there in 3? In 54? In 7? In 92? Since 4 fourths are equal to a whole one, there must be 1 fourth as many whole ones as there are fourths. 6. How many whole ones in 12 fourths? In 21 fourths? In 28 fourths? In 38 fourths? *7. In a unit, or 1, there are 5 fifths. How many fifths are there in 2? · In 3? In 4?

In 5? In 6?

Since 5 fifths are equal to a whole one, there must be 1 fifth as many whole ones as there are fifths.

8. How many whole ones are there in 10 fifths? In 16 fifths? In 20 fifths? In 27 fifths? In 30 fifths? How many sixths

9. In a unit, or 1, there are 6 sixths. are there in 3? In 4? In 5?

In 6g? In 7?

Since 6 sixths are equal to a whole one, there must be 1 sixth as many whole ones as there are sixths.

10. How many whole ones are there in 18 sixths? In 25

LESSON II

1. In a unit, or 1, there are 7 sevenths.

sevenths are there in 4?
In 8? In 94? In 10?

How many

In 54? In 6? In 74 ?
In 12?

Since I sevenths are equal to a whole one, there must be 1 seventh as many whole ones as there are sevenths.

2. How many whole ones are there in 28 sevenths? In 36 sevenths? In 42 sevenths? In 51

sevenths? In 56 sevenths?

In 84 sevenths?

In 66 sevenths?

3. In a unit, or 1, there are 8 eighths? How many eighths are there in 5? In 63? In 7? In 8g? In 9? In 10g? In 11? In 12?

Since 8 eighths are equal to a whole one, there must be 1 eighth as many whole ones as there are eighths. 4. How many whole ones are there in 40 eighths? In 51 eighths? In 56 eighths? In 69 eighths? In 72 eighths? In 86 eighths? In 88 eighths? In 96 eighths?

5. In a unit, or 1, there are 9 ninths. are there in 6? In 74? In 8? In 10ğ? In 11? In 12?

How many ninths

In 98? In 10?

Since 9 ninths are equal to a whole one, there must be 1 ninth as many whole ones as there are ninths. 6. How many whole ones are there in 54 ninths? In

64 ninths? In 72 ninths? In 84 ninths? In 90 ninths? In 95 ninths? In 99 ninths? In 108 ninths?

7. In a unit, or 1, there are 10 tenths.

How many

tenths are there in 5? In 6? In 8? In 96? In 10? In 11? In 12?

10

Since 10 tenths are equal to a whole one, there must be 1 tenth as many whole ones as there are tenths.

8. How many whole ones are there in 50 tenths? In

63 tenths? In 80 tenths? In 96 tenths? In 100 tenths? In 119 tenths? In 120 tenths?

LESSON III.

1. If 1 half of a yard of cloth cost 5 cents, what will 2 halves, or a whole yard, cost?

2. If 1 third of a yard of cloth cost 4 cents, what will 2 thirds of a yard cost? What will 3 thirds, or a whole yard, cost?

3. If 1 fourth of a gallon of milk is worth 5 cents, what are 2 fourths of a gallon worth? 3 fourths? What is a gallon worth?

4. If 1 fifth of a bushel of apples is worth 10 cents, what are 2 fifths of a bushel worth? 3 fifths? 4 fifths? What is a bushel worth?

5. If 1 sixth of a bushel of wheat is worth 12 cents, what are 2 sixths of a bushel worth? 3 sixths? 4 sixths? 5 sixths? 5 sixths? What is a bushel worth? 6. If 1 seventh of a yard of silk cost 10 cents, what will 2 sevenths of a yard cost? 3 sevenths? 4 sevenths? 5 sevenths? 6 sevenths? What will

a yard cost

7. If 1 eighth of a pound of tea cost 7 cents, what will 2 eighths of a pound cost? 3 eighths? 4 eighths?

5 eighths? 6 eighths? 7 eighths? What will a pound cost?

4

8. If 1 ninth of an acre of land is worth 12 dollars, what are 2 ninths of an acre worth? 3 ninths? ninths? 5 ninths? 6 ninths? 7 ninths? 8 ninths? What is an acre worth?

9. If 1 tenth of a bushel of apples cost 10 cents, what will 2 tenths of a bushel cost? 3 tenths? 4 tenths? 5 tenths? 6 tenths? 7 tenths? 8 tenths? 9 tenths? What will a bushel cost?

10. If 1 twelfth of a pound of gold dust is worth 16 dollars, what are 2 twelfths of a pound worth? 3 twelfths? 4 twelfths? 5 twelfths? 6 twelfths? 7 twelfths? 8 twelfths? 9 twelfths? 10 twelfths? 11 twelfths? What is a pound worth?

11. If a yard of silk is worth 80 cents, what are 104 yards

LESSON IV.

1. When corn is worth 3 fourths of a dollar a bushel, how many dollars will 8 bushels cost? How many dollars will 12 bushels cost?

2 If a boy can earn 3 fifths of a dollar in a day, how many dollars can he earn in 5 days? How many dollars can he earn in 10 days?

3. A man worked 10 days for 6 fifths of a dollar a day; how many dollars did he earn in the 10 days?

4. William paid 3 eighths of a dollar for a pair of gloves, and 8 times as much for a hat; how many dollars did he pay for his hat?

5. A lady paid 7 eighths of a dollar for a pair of shoes, and 8 times as much for a bonnet; how many dollars did she pay for her bonnet?

6. A man paid 5 eighths of a dollar for a bushel of corn; how many dollars must he pay for 8 bushels?

7. Mary is 10 years old, and her age is just 2 thirds the age of Susan; how old is Susan ?

8. A boy paid 10 cents for 5 sixths of a pound of raisins; what would a pound cost, at the same rate? 9. A trader purchased a quantity of oats and corn; he paid 35 cents per bushel for the oats, which was 7 tenths as much as he paid per bushel for the corn. What was the price of the corn per bushel?

10. A farmer paid 27 dollars for a cow, which was 3 eighths of what he paid for a horse; how many dollars did he pay for his horse?

11. A trader sold a gold watch for 96 dollars, which was 8 sevenths of what the watch cost him; what was the cost of the watch?

12. Mary is 12 years old, and 5 sixths of Mary's age is 2 thirds of Caroline's age; how old is Caroline? 13. A piece of cloth containing 12 yards was sold for 60 dollars, which was 5 fourths of what it cost; what did it cost? What was the gain on each yard? 14. A man sold a horse for 63 dollars, which was 7 eighths of what the horse cost him; what was the cost of the horse? How much did he lose?