APPLICATIONS

ORAL AND SLATE EXERCISES.

154. Dry Measure is used in measuring grain, fruits, etc.

1. In 1 peck how many pints? In 2 pecks? In 8 pecks? In 24 quarts? In 3 bushels? In 10 bushels ?

2. In 448 pints how many pecks?

SOLUTION. Since 2 pints make 1 quart, 448 pints must make as many quarts as 2 quarts are contained times in 448 quarts, which are 224. Again, since 8 quarts make 1 peck, 224 quarts must make as many pecks as 8 quarts are contained times in 224 quarts, which are 28. Hence in 448 pints there are 28 pecks.

In 2080 qt. ?

In

3. How many bushels in 540 pk.? 1088 pt.? In 22272 pt.? In 15104 qt. ? 4. At 8 cents a quart, how many bushels of peaches can be bought for $15.36? For $20.48? For $23.04 ?

SOLUTION.-Since $15.36 are equal 1536 cents, as many quarts of peaches can be bought for $15.36 as 8 cents are contained times in 1536 cents, which are 192 and 192 quarts make 6 bushels.

Observe, the dividend is changed to cents to be of the same name as the divisor.

5. At 12 cents a peck, how many pecks of potatoes can be bought for 36 ct.? For 96 ct.? For $8.76? For $64.56? yard, how many yards of cloth can be For 75 ct.? For $1? For $8?

6. At 25 cents a bought for 50 cents?

ORAL AND SLATE EXERCISES.

155. Liquid Measure is used to measure all kinds of

1. How many pints in 12 qt.? In 25 qt.? In 10 gal.?

In 30 gal.?

2. How many gallons in 16 qt.? In 28 qt.? In 64 pt.? In 96 pt.? In 160 pt.?

3. Express 48 pints in gallons; 72 gills in quarts.

4. In a cistern there are 2835 gal. of water; how many hogsheads does it contain?

5. If one quart of molasses cost $.23, what will be the cost of 4 gal.? 1.? 18 gal.? 2 hhd.?

6. In 5 hhd. how many qt.? How many gills?

7. At 4 cents a pint, how many gallons of milk can be bought for $4.48? For $8.64? For $9.60?

SOLUTION.-1. Since 1 gallon makes 8 pints, at 4 cents a pint 1 gallon can be bought for 32 cents.

2. Since 1 gallon can be bought for 32 cents, as many gallons can be bought for $4.48, or 448 cents, as 32 cents are contained times in 448 cents, which are 14.

8. At 5 cents a pint for vinegar, how many gal. can be bought for $4.40? For $5.60? For $7.60 ?

9. When maple syrup costs 16 cents a quart, how many gallons can be bought for $1.28? For $7.68? For $47.36?

10. At 9 cents a quart, how many gallons of kerosene can be bought for $1.44? For $2.52? For $3.24? For $26.64?

EXERCISES ON EXACT DIVISORS.

156. 1. What numbers will divide 12 without a remainder? A number that will divide another without a remainder is called an Exact Divisor.

Find all the exact divisors of each of the following numbers:

17. What number is an exact divisor of each of the numbers 4, 6, and 10? Of each of the numbers 9, 15, and 27 ?

A number which is an exact divisor of each of two or more numbers is called a Common Divisor.

18. Find the common divisors of each of the following sets of numbers:

19. What is the Greatest Common Divisor of 8 and 12? Of 18 and 30?

The greatest number that is an exact divisor of each of two or more numbers is called the Greatest Common Divisor.

20. Find the greatest common divisor of each of the following sets:

EXERCISES ON MULTIPLES.

157. 1. Twenty-four is how many times eight? How many times six? How many times twelve? How many times twenty-four?

A number which is one or more times another number is called a Multiple of that number.

2. What is a multiple of 3? Of 6? Of 4? Of 8? Of 10? Of 7? Of 11? Of 9? Of 12 ?

3. Name three multiples of 9; of 5; of 8; of 12.

4. Find the first three multiples of 17; of 23; of 29.

Thus, 1st multiple is 17, 2d multiple 17 × 2 17 × 3 = 51.

34, 3d multiple

5. Find the first 4 multiples of 25; of 37; of 63; of 95; of 84; of 235; of 347; of 836; of 793; of 965.

6. How many multiples can you find for 19? For 35? for 69? For any given number?

7. Find a number which is a multiple of 4 and of 6.

Thus, 4×6=24, hence 24 is a multiple of both 4 and 6.

8. Find a number which is a multiple of 7 and of 9; of 5 and of 8; of 6 and of 11; of 3 and of 9; of 9 and of 12.

A number which is a multiple of two or more numbers is called a Common Multiple of these numbers.

9. Of what numbers is 12 a common Is 45? Is 63? Is 48? Is 72 ? Is 64? Find a common multiple:

multiple?

Is 21?

Is 88? Is 108?

19. Of how many cents is 20 cents a multiple? 30 cents? 25 cents? 56 cents? 72 cents?

FRACTIONS

ORAL EXERCISES.

158. 1. One of the two equal parts of a whole thing is called one-half, thus:

One of the two

equal parts of a

peach is called

one-half of a

peach.

2. How many halves are there in one peach? In one apple? In one dollar? In one cake? In one of anything?

3. One of the three equal parts of a whole thing is called one-third, thus:

One of the three equal parts of a pear is called one-third of a pear.

4. How many thirds are there in one pear? In one inch? In one pound of sugar? In one of anything?

5. One of the four equal parts of a whole thing is called one-fourth, thus:

One of the four equal parts of an orange is called one-fourth of

an orange.

6. How many fourths are there in one orange? In one pie? 7. What is meant by one-half of anything? One-third? One-fourth? Two-thirds? Three-fourths? Three-thirds? 8. One or more of the equal parts of a unit is called a Fraction.