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glass, and seven panes in each row, how many in the whole ?

12. If one lemon cost four cents, how much will twelve lemons cost?

EXERCISES IN FRACTIONAL MULTIPLICATION.

Multiplication of Fractions by Whole Numbers.

1. If you repeat one half four times what is the product?

2. If you multiply three fourths by seven, what is the product?

3. What is two thirds multiplied by eight?

4. If a man spend two twelfths of a dollar a day, how many twelfths does he spend in a week?

Ans. As there are seven days in a week, a man spends seven times as much in a week as in one day. Seven times two twelfths is fourteen twelfths. He spends fourteen twelfths of a dollar in a week.

5. If a man gives two eighths of a pound of meat to six persons, how many eighths does he give away?

6. If a boy gives two fourths of an orange to seven of his companions, how many fourths does he give away? 7. If a man drinks three fourths of a pint of brandy a day, how many fourths does he drink in a week?

8. What is three times three eighths? Six times six sevenths?

9. If a man lays by two eighths of a dollar a day, how much does he save in a week?

10. If there are two thirds of a pound of meat for each one in a family of seven, how much is there in the whole? 11. What is six times four tenths?

12. What is nine times two thirds?
13. What is seven times four ninths?
14. What is eight times six tenths?
15. What is twelve times two fourths?
16. What is nine times three tenths?
17. What is five times three sixteenths?
18. What is six times seven twentieths?

The multiplication of whole numbers by fractions, is deferred to the Second Part, because it involves the process of Division, which must first be explained.

DIVISION.

How many two cents are there in four cents?

How many two cents in six cents?

How many two cents in eight?

How many two cents in ten?

How many two cents in twelve?

How

three cents are there in six cents? many many in nine? How many in twelve?

How

How many four cents are there in eight? How many in twelve?

What part of six is
What part of ten is

How many five cents are there in ten? What part of two cents is one cent? What part of four cents is two? two? What part of eight is two? two? What part of twelve is two? Three cents is what part of six? nine? Of twelve?

What part of eight is four?

four?

Three is what part of

What part of twelve is

What part of five cents is one? What part of five is
What part of five is three?

two?

Six ? &c.

Four? Five?

How many two sixths are there in four sixths ?
How many three fourths are there in six fourths?
How many four twelfths in eight twelfths?
What part of two twelfths is one twelfth ?
What part of four twelfths is two twelfths?
What part of nine twelfths is three twelfths?

Division is finding how often one number is contained in another, and thus finding what part of one number is another number.

How many times is six contained in twelve? In eighteen? What part of eighteen is six?

twelve is six?

What part of

How many times is five contained in ten? In fifteen?

What is Division?

Five is what part of ten? Of fifteen ?

How many times is seven contained in fourteen? In twenty-one ?

What part of fourteen is seven? What part of twentyone is seven ?

How many times is nine contained in eighteen?

How many times is ten contained in twenty? In thirty? In forty?

What part of sixteen is four?

What part of eighteen is six?
What part of sixteen is eight?

One is what part of thirty? Two is what part of thir ty? Three is what part of thirty? Six? Eight? Eleven? Fourteen? Twenty is what part of thirty? &c.

How many two sevenths are there in ten sevenths?
How many three eighths are there in nine eighths?
How many six tenths in eighteen tenths?

How many seven ninths in twenty-one ninths?
How many five elevenths in twenty elevenths?
How many three eighteenths are there in twelve eight-
eenths?

Two sixths is what part part of four sixths?
Two sevenths is what part of ten sevenths?
Three eighths is what part of nine eighths?
What part of eighteen tenths is six tenths?
What part of fourteen ninths is seven ninths?
What part of fifteen elevenths is five elevenths?
What part of twelve eighteenths is three eighteenths?
The number which is divided is called the Dividend.
The number by which you divide is called the Divisor.
The answer is called the Quotient.

If you find how many times three there are in twelve, which is the Divisor? The Dividend? The Quotient?

If twelve is divided by six, which is the Dividend? The Divisor? The Quotient?

When whole numbers are divided by whole numbers, it is called Simple Division.

When either the divisor or dividend is a fraction, it is called Fractional Division.

What is the dividend and what the divisor? What is the answer called? What is simple division? What is fractional division?

Exercises in Simple Division.

1. If you divide 12 cents equally among three boys, how many will each one have?

Ans. Each one will have as many as there are threes in twelve; or four cents.

2. If there are forty-eight panes of glass in a window, and there are eight panes in each row, how many rows are there?

Ans. As many as there are eights in forty-eight; or

six rows.

3. How much broadcloth, at six dollars a yard, can you buy for twenty-four dollars?

4. How many hours would it take you to travel twentyone miles, if you travelled three miles an hour?

5. If you divided thirty-six apples equally among four boys, how many would you give them apiece?

6. How many pounds of raisins, at nine cents a pound, can you buy for sixty-three cents?

7. How many reams of paper, at seven dollars a ream, can you buy for forty-nine dollars?

8. A man agreed to work eight months, for seventy-two dollars, how much did he receive a month?

9. If you buy a bushel of pears for forty-eight cents, how much are they a peck?

10. If there are six shillings in a dollar, how many dollars in thirty-six shillings?

11. Four men bought a horse for forty-eight dollars, what did each man pay?

12. A man gave sixty-three cents for a horse to ride nine miles, how much was that for each mile?

13. A man agreed to pay eight cents a mile for a horse, and he paid sixty-four cents, how many miles did he go? 14. A man had forty-two dollars, which he paid for wood, at seven dollars a cord, how many cords did he buy?

15. Two boys are running, and are forty-eight rods apart. The hindermost boy gains upon the other, three rods a minute, in how many minutes will he overtake the foremost boy?

16. A vessel contains sixty-three gallons, and discharges seven gallons an hour, in how many hours will it be emptied ?

17. If you wish to put sixty-four pounds of butter in eight boxes, how many pounds would you put in each box?

EXERCISES in FRACTIONAL DIVISION.

Division of Whole Numbers by Fractions.

1. How many halves are there in six oranges? 2. How many thirds are there in four apples?

Ans. One apple has three thirds, four apples have four times as many, or twelve thirds.

3. How many fourths are there in three oranges ?
4. How many fifths are there in four apples?
5. How many sixths are there in two oranges?
6. How many half dollars are there in four dollars?
7. How many quarters of a dollar in five dollars?
8. How many half eagles in eight eagles?

9. In two dollars how many thirds of a dollar?

10. If there are six one thirds in two dollars, how many two thirds are there?

Ans. There are only half as many two thirds as there are one thirds, or three two thirds.

11. In two dollars, how many one sixths? How many two sixths?

12. A man divided two dollars among his workmen, and gave them a third of a dollar apiece, how many workmen had he?

13. A man divided four dollars equally among his chil. dren, and gave them each two thirds of a dollar, how many children had he?

Ans. As many children as there are two thirds in four dollars. In four dollars there are twelve one thirds. There are half as many two thirds, or six. He had six children.

14. If a man gave two sevenths of a dollar to each of his servants, and gave away in the whole four dollars, how many servants had he?

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