Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση
[blocks in formation]

Ans. 20.

6. Required the product of 6 by of 5.

7. Required the product of of by { of 34.

8. Required the product of 34 by 414.

Ans. .

Ans. 14111. 9. Required the product of 5, 3, 4 of 3 and 4. Ans. 2.

NOTE. 152. In multiplying by a mixed number, we may first multiply by the integer, then multiply by the fraction, and then add the two products to gether. This is the best method when the numera tor of the fraction is 1.

Ex. 1. Multiply 26 by 31. We first multiply 26 by 3: the product is 78. Afterwards we multiply 26 by ; the product is 13: hence the entire product is 91.

Ex. 2. Multiply 48 by 8.

3. Multiply 67 by 971⁄2.

4. Multiply 842 by 74.

26

26x=13

3

78

91 Ans.

48×8=384

48×1 8

Ans. 392

Ans. 608

Ans. 5987f.

QUESTIONS.

§ 148. If we multiply by a whole number, how many times do we repeat the multiplicand? If we multiply a fraction by a whole number, how many times do we increase the frac tion?

§ 149. How do you multiply a fraction by a whole number?

§ 150. When you multiply by a fraction what is required? When the multiplier is less than 1, how much of the multiplicand do you take?

§ 151. How do you multiply one fraction by another? 152. How may you multiply by a mixed number? When is this the best method?

APPLICATIONS.

1. What will 7 yards of cloth cost at $ per yard?

Ans. $51. 2. What will 32 gallons of brandy cost, at $1} per gallon?

Ans. $36.

3. If 1lb. of tea cost $14, what will 6. cost? Ans. $71.

4. What will be the cost of 17 yards of cambric

at 24 shillings per yard?

Ans. £2 3s 9d.

5. What will 15 barrels of cider come to at $3 per barrel?

Ans. $45,

DIVISION OF VULGAR FRACTIONS.

§ 153. We have seen § 41, that division of integer numbers explains the manner of finding how many times a less number is contained in a greater.

In division of fractions, the divisor may be larger than the dividend, in which case the quotient be less than 1.

For example, divide 1 apple into 4 equal parts. Here it is plain, that each part will be; or that the dividend will contain the divisor but times.

Again, divide of a pear into 6 equal parts. It is plain, that 1 will contain 6, & times; therefore will contain 6 but times: hence would be one

of the equal parts of the pear.

§ 154. When we divide a fraction by a whole number, we are to divide the fraction into as many equal parts as there are units in the divisor, and this may be done, as was shown in § 115, and § 117, either by dividing the numerator, or multiplying the denominator by the whole number.

CASE I.

§ 155. To divide a fraction by a whole number. RULE.

Divide the numerator or multiply the denominator by the whole number.

Ex. 1. Divide by 2.

Here ÷2="43: or 1÷2=== Ans.

[merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small]

The divisor

by f

5×1. If the divisor were 5, the quotient would be 117. But since the =10 15 120 divisor is only of 5, the true quotient will be ×8 for it is evident that the fraction will contain of 5, 8 more times than it would con

[ocr errors][merged small]

But since the value of a fraction is equally affected by multiplying the denominator or dividing the numerator, it follows, that we might have divided the numerator 10 by 5, and the denominator 24 by 8, and obtained the same result. Hence we have the following

RULE.

Reduce compound fractions to simple ones, and whole numbers to improper fractions; then divide the numerator by the numerator, and the denominator by the denominator, if they will exactly divide ; but if not, invert the terms of the divisor, and then multiply the divisor and dividend together.

[blocks in formation]

Or ff÷}=ff×&=&=} Ans.

2. Divide by 1.

==×Y=y=8 Ans.

157. When the dividend is just equal to the divisor the quotient is 1. But when the dividend is greater than the divisor, the quotient will be greater than 1; and when the dividend is less than the divisor, the quotient will be less than 1. When the dividend is greater than the divisor, the quotient will be just as many times greater than unity as the dividend is greater than the divisor; and when the dividend is less than the divisor, the quotient will be just as many times less than unity as the dividend is less than the divisor. In the example above, the dividend is 8 times greater than her the quotient is right, being 8 times greater unity.

166

DIVISION OF VULGAR FRACTIONS.

QUESTIONS.

§ 153. What does division of whole numbers explain? In fractions, may the divisor be larger than the dividend? In such case will the quotient be greater or less than 1 ?

§ 154. What is required when a fraction is to be divided by a whole number? How may the division be made?

§ 155. How do you divide a fraction by a whole number? § 156. How d■ you divide one fraction by another?

§ 157. When the divisor and dividend are equal, what is the value of the quotient? When the dividend exceeds the divisor, will the quotient be greater or less than 1? How many times? When the dividend is less than the divisor will the quotient be less than 1? How many times?

[blocks in formation]

1. If 716. of sugar cost 4 of a dollar, what is the price per pound?

#7 of a dollar; or of 12 cents

525

==8 cents.

525

Ans. 8 cents.

2. If of a dollar will pay for 10126. of nails, ich is the price per pound?

Ans. dolls.4&cts.

« ΠροηγούμενηΣυνέχεια »