Here we say, 294-119113, and Thus, $11 17 34-25, then place the numerators on the right of the line, and denominators on the left. 5 Ans. 85 How do you multiply one fraction by another? Ans. Place the numerators on the right, and the denominators on the left of a vertical line, and divide the product of the numbers on the right, by the product of those on the left, or when a number on either side of the line will measure one on the other side, divide first. 70. Multiply 191 by 92 Ans. 1805. 71. What is the product of of of 3 of 3 of 8? Ans. 11. Here observe we place all the numerators, viz., 3, 4, 2, 7, and 8, on the right of the line, and all the denominators, viz., 4, 5, 3, 8, and 9, on the left, there being a 4, 3, and an 8, on each side of the line, we cancel these, and Ans have 2 and 7 to multiply together, B4R7 14 numerator. 45 denominator. for a numerator, and 5 and 9, on the left of the line for a denominator. 75. Multiply 63 by of 7 of 2% of 5 of 71. 10 Ans. 105-261. 76. What will 93 yards of muslin cost at 93 cents a yard? Ans. 91 cents. 77. What will 74 cords of wood cost at 41 dollars a cord? Ans. $30. 78. What will 7 pounds of sugar cost at 83 cts. a pound? Ans. 63 cents. DIVISION OF FRACTIONS. We will now presume the learner to understand division to be the converse of multiplication, and he will need but little explanation to enable him to divide numbers involving fractions, with the same facility as to perform the like operation on numbers in their most simple form. Suppose you be required to multiply 23 by 13, you will proceed thus, 51119 13 That is, you change the 23 to an improper fraction=112, and place the numerator (119) on the right of a vertical line, and the denominator (5) on the left, the multiplier (13) you also place on the right Ans. 3093 of this line, &c. 1547 Now suppose you are required to divide 309 by 13, here as in multiplication the 309 must be changed to an improper fraction-1547, the numerator of which we place on the right of a vertical line, and the denominator on the left, as in multiplication, but the divisor (13) we place on the left of this line, and then proceed as in multiplication of fractions. Compare this Thus, 514 with the preceding question, and you will perceive that the operation has destroyed the result of multiplication; this then is division. Result 119 23 How do you divide a fraction? Ans. Place the numerator of the dividend on the right of a vertical line, and its denominator on the left, then place the divisor on the left of this line, and proceed as in multiplication. If the divisor be a fraction, place its numerator on the left side of the line. NOTE.-Observe that the denominator must never occupy the same side of the line as its numerator, hence, if you recollect on which side of the line to place the numerator, you will readily dispose of the denominator, as it must occupy the opposite side. 1. Divide 18 by 64 Here we say, 183=25, this being the dividend, we place its numerator, 75, on the right of the line, (and of course the denominator (4) on the opposite side,) the 64-25 being the divisor, its numerator must be placed on the left of this line. 17. Divide 113 by 18. Divide 9 by 31 19. Divide of 3 of 5 by 3 of ៖ 20. Divide of of 3 by of 3 of 8 of 5 Observe that we place all the numerators of the dividend on the right of the line, and all those of the divisor on the left. of 8 of 37 by 3 of 2 of 137. 21. Divide 22. Divide of 43. Ans. 49. 83 of 31 by of of 23. Ans. 117. 28 12 11 of 8 of 221 24. Divide of 4 of 7 of by of of 3 of 71. 23 25. If 4 yards of cotton cloth cost 63 cents, what will one yard cost? Ans. 14 cents. Why? 4-9 half yards, and since 9 half yards cost 63 cents, I half yard will cost one-ninth of 63 cents, and 2 half yards will cost of 63 cents. Here 4, being the divisor, we place its numerator on the left of the line. 26. If 6 pounds of beef cost 39 cents, how much is that a pound? Ans. 6 cts. Why?-6 lbs. 13 half pounds, and since 13 half pounds cost 39 cents, 2 half pounds or one pound will cost 2 thirteenths of 39 cents, 27. If 8 yards of cloth cost 37 dollars, how much is that a yard? Ans. 42 dollars, or 4 dollars and 50 cents. Why?-8= 25, and since 25 parts cost 371⁄2 dollars, one part will cost one twentyfifth of 37 dollars, and 3 parts will cost 3 twenty-fifths of 371⁄2, or. 75 dollars, |