7. A storekeeper spent $190 in 6 days. His total receipts during that time were $350. Find his average profit for one day.

8. A boat sails 215 miles the first day, 235 miles the second day, 184 miles the third day, and 240 miles the fourth day. Find the average distance sailed each day.

9. 72 chairs are bought for $108. They are sold for $2.25. How much profit is made on each chair?

10. A grocer bought 36 barrels of flour for $216. He sold the flour at 7 ct. a pound. Find his gain.

11. 14 doz. umbrellas are bought for $504. Find the cost of 1 umbrella.

12. 24 doz. lead pencils are sold for $13.96. Find the cost of 1 pencil.

13. A manufacturer packs 10,800 pencils in boxes. There are 144 pencils in each box. Find the cost of all the pencils if each box costs $4.85.

14. A book costs $1.75. It is sold at $2.25. At that rate of profit, how many books must be sold to gain $80?

15. 730 books are to be placed on 45 shelves. 20 shelves hold 14 books each. How many books must be placed on each of the remaining shelves?

FRACTIONS

Terms of a Fraction

You have done many examples with numbers like, 4, §. ,, and . Such numbers are called fractions.

Numbers like 1, 4, 65, 128 are called whole numbers or integers.

Numbers like 12, 21, 10% are called mixed numbers.

In any fraction the number written below the line denotes the name of the parts. It is called the denominator. The number written above the line denotes the number of the parts. It is called the numerator.

For example, the shaded part of the circle may be represented by ; the number "4," or "denominator," tells the number of parts into which the circle is divided, and gives the name to the parts-"fourths"; while the numerator 3 tells how many "fourths are spoken of.

The denominator and numerator

are together called the terms of a

fraction; 4 and 3 are the terms of the fraction . Every fraction has two terms.

17

Name the denominators and the numerators of the following fractions:,,, To, 12, 16, 18, 105, 187.

61

1. How many fourths in 1 unit? In 2 units? In 3 units? In 4 units?

2. How many fourths in 11? In 12? In 12?

Fractions like 4, 4, 4 are called proper fractions, because their value is less than 1 (unit).

The numerator of a proper fraction is smaller than the denominator. Why?

Fractions like 4, 4, 4, 4, 4, etc., are called improper fractions, because their value is equal to 1 or greater than 1.

The numerator of an improper fraction is equal to or larger than the denominator. Why?

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3. Consider the answers to question 1 above. Are these answers proper or improper fractions? Why?

4. Are the answers to question 2 proper or improper fractions? Why?

ORAL EXERCISE

1. Name all the proper fractions whose denominators are 4.

2. Name proper fractions having 3 as a numerator; having 5; having 6; having 8; having 12.

3. Name 3 improper fractions with 2 as denominator; with 4; with 3; with 5; with 6; with 10.

WRITTEN EXERCISE

Put into separate columns the proper and the improper fractions among the following:,,, 4, 3, 1%, 11, 18, 12, 4, 18, 3, 13, 13, 3.

2

10

18
2

Changing a Whole Number to an Improper Fraction 1. How many quarter apples in 2 apples?

2. How many fourths in 2?

3. How many fourths in 3? In 4? In 5? In 7? In 10?

4. How many half melons in 1 melon? In 2 melons? In 5 melons? In 6 melons? In 9 melons? 5. How many thirds in 1? In 2? In 3? In 5? In 8? In 10?

6. How many fifths in 1? In 2? In 3? In 5? In 10? In 8? In 20?

7. How many eighths in 1? In 3? In 5? In 7? In 10? In 12? In 6?

8. How many tenths in 1? In 2? In 5? In 6? In 9? In 10? In 12? In 15?

The answer is 50o.

The short way is 4 x 125=500.

2. How many thirds in 225?

3. How many thirds in 56? In 110? In 200? In 275?

4. How many fourths in 25? In 65? In 75? In 225 ?

5.

How many eighths in 40? In 72? In 120? In 250 ?