6. Required the product of 6 by of 5. Ans. 20. 7. Required the product of 3 of f by k of 34. Ans. H. 8. Required the product of 34 by 4**. Ans. 1414+ 9. Required the product of 5, 1, $ of and 44. Ans. 231. 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. 26 We first multiply 26 by 3: 3 the product is 78. Afterwards 78 we multiply 26 by }; the pro 26 x 1=13 duct is 13: hence the entire 91 Ans. product is 91. Ex. 2. Multiply 48 by 84. 48 x8=384 Ans. 392 3. Multiply 67 by 9. Ans. 608 77 4. Multiply 842 by 7+. Ans. 59874 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 num. ber? § 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 $1 per yard? Ans. $57 2. What will 32 gallons of brandy cost, at $17 per gallon ? Ans. $36. 3. If 1lb. of tea cost $14, what will 6f1b. cost? Ans. $714 4. What will be the cost of 17} yards of cambric at 27 shillings per yard ? Ans. £2 3s 9d. 5. What will 1577 barrels of cider come to at $3 per barrel? Ans. $45% DIVISION OF VULGAR FRACTIONS. § 153. We have seen 41, that division of inte. ger 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 t; 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 I times: hence t's would be one of the equal parts of the pear. § 154. When we divide a fraction by a whole number, we are divide the fraction into as many equal parts as there are units in the divisor, and this may be done, as was shown in g 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 nuinber. Ex. 1. Divide by 2. Here 1+2="4=f: or 1+2=i==ş Ans. 2. Divide H by 9. Anus. Ef 3. Divide 48 by 15. Ans. Hi=1 CASE II. § 156. To divide one fraction by another. Et. 1. Divide if by $. The divisor =5xį. If the divisor were 5, the quotient would be als=,1% $ 117. But since the divisor is only 1 of 5, the true quotient will be rty x8=y=f: for it is evident that the fraction # antain 7 of 5,8 more times than it would con. But since the value of a fraction is equally affected by multiplying the denominator or dividing the nu. merator, 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. Ex. 1. Divide ff by s. Divisor 8+8= =+ Ans. Or +*+1=****=*=* Ans. 2. Divide f by it. I ty=+*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 ater 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 1 is 8 times greater than to: hence the quotient is right, being 8 times greater than unity 166 DIVISION OF VULGAR FRACTIONS. QUESTIONS. $ 153. What does dirision of whole numbers explain ? In fractions, may the divisor be larger than the dividend ? In such case will the quotient he 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 ? APPLICATIONS. 1. If 716. of sugar cost 4 of a dollar, what is the price per pound ? 41-7=344 of a dollar; or 4 of age cents =4490=8 cents. Ans. Bet cents. 2. If of a dollar will pay for 10476. of nails, ow inuch is the price per pound? Ans. dolls.=474 cts. |