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6. What is the sum of F#, 3 and #2 Ans. 24++. 7. A merchant purchased a lot of cotton yarn, and sold or of it to one man, and # of # to another: what part of the lot did he sell ?” Ans. #. 8. A man sells # of a lot of iron to one man, and # of £ to another: what part does he sell ? Ans. The whole. 9. If one gentleman own or of a common pasture: a 2d, #3: and a third, #, what part of the pasture is
Erplanation.—for of an hour equal ##r of a day. 11. What part of a pound is the sum of , of a
15. A merchant has 4 casks of rum which contain No. 1, 973 gal.; No. 2, 100; ; No. 3, 110; ; and No. 4, 11.5%. How many gallons in the 4 casks 2
2773(2 number of whole gal. contained 2520 in the fractions.
New num. 253
* The compound fraction must be reduced to a simpl the simple fraction used instead of the compound ...of e one, and
Eaplanation.—In the first place, we reduce the fractions to a common denominator. Each fraction reduced, expresses the same part of a gallon which it did before. (See Illustration, page 156.) Each mixed number in the right hand column, represents the same quantity as the number standing against it in the left. Next we add all the numerators of the fractions in the right hand column, and find their sum to be 2773. It requires 1260 of the fractional units to equal one gal., therefore, as many times as 1260 can be taken from 2773, so many whole gallons are expressed by the fractions, which we find to be two, and these two gal. we add to the unit column. .
In adding other mixed numbers, one must be added to the whole number for each time the common denominator can be taken from the sum of the numerators, for the common denominator will always show how many parts, like those expressed by the fractions, are required to equal an unit or 1, in a whole number.
r Multiply the numerator of the multiplicand by the numerator of the multiplier, and the denominator of the multiplicand by the denominator of the multiplier,-the former product written over the latter, will constitute the answer. If either or both of the given fractions be compounded, the continued product of the numerators and the continued product of the denominators will form the answer required.
Remark. The product will be as much less than the multiplicand as the multiplier is less than an unit. If the multiplier be more than an unit, the product will be as much greater than the multiplicand as the multiplier is greater than an unit.
Most of the questions belonging to this rule are similar to the first 30 questions in reduction of compound fractions, and are operated in a similar manner and for the same reasons. The student should re-examine the illustration on page 145, and the several explanations under the first part of that rule, for he should pass over no questions without endeavouring to understand the principles on which their operations are founded.
1. What is the product of multiplied by #2
Explanation.—The multiplier 4, being less than an unit, we can only take such a part of #, the multiplicand, as # is of an unit, and this we shall do by multiplying one fraction by the other, since the product of the denominators will be greater than that of the numerators. The question is the same as if it had been—what is # of #.
# X#=#; the answer.
3. Multiply $3 by #. - Prod. 3%. 3. What is the product of ##, multiplied by 3 of #2 Ans. P. 4. What is the product of # * into P, 2 Ans. ***, or 1 ##. JNote 5.—When a mixed number is given, it is most convenient to change it to an improper fraction, then the improper fraction may
be used instead of the mixed number, the same as the improper fraction in the last question.
10. If a barrel of mackerel cost $4}}, what will 3} bar. cost at the same rate 7 - Ans. $17.3%. 11. What is the product of 1204, multiplied by 100; ? Ans. 1212219;. 12. A man labours for 124 dollars per month, what will be his wages for 84 months 7 Ans. $1063.
13. At # of a dollar per yard, what will 4 yards of riband come to ?
Explanation.—If one yard cost 1 fifth of a dollar, 4 yards must cost 4 fifths; and this we shall obtain by multiplying the numerator of 4 by 4 the number of yards. Ans, # of a dollar. The numerator of any simple fraction always denotes how many parts of an unit, or single quantity, are expressed by the fraction, therefore by multiplying the numerator by a whole number, we place in the numerator of the product, the number of parts, or fractional units, contained in the given numerator, as many times as there are units in the whole number. In multiplying the numerator of a fraction by a whole number, we increase the real value of the fraction, because the denominator not being altered, the parts of a quantity express
ed by the numerator of the product, are just as large as the parts contained in the numerator of the multiplicand, and we have more of them.
Ans. 2. 16. At # of a shilling per pound, what will 7 lb. of copperas come to ? Ans. 1 S.
17. If a man work for #4 of a dollar per day, what will he receive for 101 days’ work 2. Ans. 791.
18. If a horse eat for of a bushel of oats in one day, how many bushels will he eat in 30 days?
20. The toll of a certain bridge is $825 a year, and is divided into 60 shares. A gentleman owning 7 shares, wishes to know what his part of the toll will be for one year.
Explanation.—He owns or of the whole. If we divide 825 by 60, the quotient will be the value of one share, and multiplying the value of one share by 7, will give the value of 7 shares. But if we multiply 825 by 7, and divide the product by 60, the dividend, 5775 is 7 times 825, consequently the quotient must be 7 times as large as when we divided 825 by 60. Ans. $964. From this explanation it appears, that we shall obtain the same result whether we multiply a whole number by the numerator of a fraction, and divide by the denominator, or divide the whole number by the denominator and multiply the quotient by the numerator.
21. What is the product of 1091, multiplied by 42 Ans. 848#.
22. A and B bought a lot of cotton in company for
1150 dollars, of which A paid 635 dollars, and B the