This question is the same as the following:

In 183 bushels, how many 4 of a bushel? many 7ths of a bushel?

In 1 bushel there are 7, consequently in are 18 times 7 sevenths; that is, 126, and Answer 129 persons.

That is, how

18 bushels there more make 129,

Reduce 2817 to an improper fraction. That is, in 2817 how many 25

Since there are 2 in 1, in 28 there must be 28 times as many. 28 times 25 are 700, and 17 more are 717. Ans.

717

25.

Hence to reduce a whole number to an improper fraction with a given denominator, or a mixed number to an improper fraction multiply the whole number by the denominator, and if it is a mixed number add the numerator of the fraction, and write the result over the denominator.

XV. A man hired 7 labourers for 1 day and gave them of a dollar apiece; how many dollars did he pay the whole?

If we suppose each doliar to be divided into 5 equal parts, it would take 3 parts to pay I man, 6 parts to pay 2 men, &c. and 7 times 3 or 21 parts, that is, of a dollar to pay the whole. 2 of a dollar are 4 dollars. Ans. 4 dollars.

A man bought 13 bushels of grain, at bushel; how many dollars did it come to?

& of a dollar a

`g of a dollar are 5 shillings. 13 bushels at 5 shillings a bushel, would come to 65 shillings, which is 10 dollars and 5 shillings.

6.5

In the first form, 13 times of a dollar are 5 of a dollar; that is 10 dollars, as before.

A man found by experience, that one day with_another, his horse would consume of a bushel of oats in a day; hono many bushels would he consume in 5 weeks or 35 days?

If we suppose cach bushel to be divided into 37 equal parts, he would consume 13 parts each day. In 35 days he would consume 35 times 13 parts, which is 455 parts. But the parts are 37ths, therefore it is 455 12 bushels.

1 1

This process is called multiplying a fraction by a whole number.

1372

The fraction 253, signifies that 1 is divided into 1372 equal parts, and that 253 of those parts are used. To multiply it by 48, is to take 48 times as many parts, that is, to multiply the numerator 253 by 48.

1372

13

The product of 253 by 48 is 12144; this written over the denominator is 12144, which being reduced is 811. Ans. To multiply a fraction then, is to multiply the number of parts used; hence the rule: multiply the numerator and write the product over the denominator.

Note. It is generally most convenient, when the numerator becomes larger than the denominator, to reduce the fraction to a whole or mixed number.

It is sometimes necessary to multiply a mixed number.

Bought 13 tons of iron, at 9714 dollars a ton; what did it come to ?

In this example the whole number and the fraction must be multiplied separately. 13 times 97 are 1261. 13 times are equal to 434; this added to 1261 makes 12653 dollars.

182

379

Ans.

Hence, to multiply a mixed number: multiply the whole number and the fraction separately; then reduce the fraction to a whole or mixed number, and add it to the product of the whole number.

XVI. We have seen that single things may be divided into parts, and that numbers may be divided into as many parts as they contain units; that is, 4 may be divided into 4 parts, 7 into 7 parts, &c. It now remains to be shown, how every number may be divided into any number of equal parts.

If 3 yards of cloth cost 12 dollars, what is that a yard?

It is evident that the price of 3 yards must be divided into 3 equal parts, in order to have the price of 1 yard. That is, of 12 must be found.

We know by the table of Pythagoras, that 3 times 4 are 12, therefore of 12, or 4 dollars is the price of I yard.

If 5 yards of cloth cost 45 dollars, what is that a yard?

1 yard will cost of 45 dollars. 5 times 9 are 45, therefore 9 is of 45, or the price of 1 yard.

The two last examples are similar to the first example Art. 9. If we take 1 dollar for each yard, it will be 5 dollars, then one for each yard again, it will be 5 more, and so on, until the whole is divided. The question, therefore, is to see how many times 5 is contained in 45, and the result will be a number that is contained 5 times in 45. 5 is contained 9 times, therefore 9 is contained 5 times in 45. This is evident also from Art. III. When a number, therefore, is to be divided into parts, it is done by division. The number to be divided is the dividend, the number of parts the divisor, and the quotient is one of the parts.

A man owned a share in a bank worth 136 dollars, and sold of it; how many dollars did he sell it for?

136 (2

Ans. 68 dollars.

2 is contained 68 times in 136, therefore 2 times 68 are 136, consequently 68 is of 136.

A ticket drew a prize of 2,845 dollars, of which A owned }; what was his share?

2845 (5

Ans. 569 dollars.

Since 5 is contained 569 times in 2,845, 5 times 569 are equal to 2,845, therefore 569 is of 2,845. Division may be explained, as taking a part of a number. In the above example I say, of 28(00) is 5(00) and 3(00) over. Then supposing 3 at the left of 4, I say, of 34(0) is 6(0) and 4(0) over. Then of 45 is 9. Writing all together it makes 569, as before. The same explanation will apply when the divisor is a large number.

Bought 43 tons of iron for 4;171 dollars; how much was

it a ton?

1 ton is will be

part of 43 tons, therefore the price of 1 ton part of the price of 43 tons.

4171 (43

387

97 dollars.

301

301

Two men A and B traded in company and gained 456 dollars, of which A was to have and B3; what was the share of each?

The name of the fraction shows how to perform this example. of 456 signifies that 456 must be divided into 8 equal parts, and 5 of the parts taken.of 456 is 57, 5 times 57 are 285, and 3 times 57 are 171. A's share 285, and B's 171 dollars.

A man bought 68 barrels of pork for 1224 dollars, and sold 47 barrels, at the same rate that he gave for it. How much did the 47 barrels come to?

68

To answer this question it is necessary to find the price of 1 barrel, and then of 47. 1 barrel costs of 1224 dollars, and 47 barrels cost 7 of it. of 1224 is 18. 47 times are 18 are 846. Ans. 846 dollars.

68

To find any fractional part of a number, divide the number by the denominator of the fraction, and multiply the quotient by the numerator.

A man bought 5 yards of cloth for 28 dollars; what was that a yard?

of 25 is 5, and of 30 is 6. of 28 then must be between 5 and 6.

Cases of this kind frequently occur, in which a number cannot be divided into exactly the number of parts proposed, except by taking fractions. But it may easily be done by fractions.

of 25 dollars is 5 dollars. It now remains to find of 3 dollars. Suppose each dollar divided into 5 equal parts, and take 1 part from each. That will be 3 parts or of a dollar. Ans. 53 dollars. of a dollar is of 100 gents, which is 60 cents. Ans. $5.60.

A man had 853 lb. of butter, which he wished to divide into 7 equal parts; how many pounds would there be in each part?

of 847 lb. is 121 lb. Then suppose each of the 6 remaining pounds to be divided into 7 equal parts, and take 1 part from each; that will be 6 parts, or of a pound. Ans. 1214.

853 (7

121 lb. Ans.