12. Subtract 13. Subtract Ans. Ans. 144 25 from 1598. 1728* 14. Subtract 332 from 89. 4272 1068 Ans. 637 15. What is the difference between 91 and 23. OPERATION. 91 = 94 23 = 212 6,7, Ans. from 84 120. = SOLUTION. We first reduce the fractional parts, and, to a common denominator, 12. Since we cannot take from, we add 1: 1 to, which makes 11⁄2, and from 11⁄2 leaves. We now add 1 to the 2 in the subtrahend (50). Three from 9 leaves 6. We thus obtain 62, the difference required. RULE. To subtract mixed numbers, reduce the fractional parts to a common denominator, and then subtract the fractional and integral parts separately. Or, Reduce the mixed numbers to improper fractions, and subtract the less from the greater by the usual method. 16. From 8 take 33. 17. From 25 take 9. 18. From 4 take 1. 19. Subtract 14 from 6. 20. Subtract 120 from 450. 21. Subtract 43 from 37. 125 Ans. 418. Ans. 16. Ans. 330 22 Find the difference between 49 and 751. 23. Find the difference between 2275 and 1962. 24. From a cask of oil containing 31 gallons, 17 gallons were drawn. How many gallons remained? Ans. 137. 25. A farmer, having 450 acres of land, sold 3043 How many acres had he left? Ans. 14518. 26. If flour is bought for $64 per barrel, and sold for $73, what will be the gain per barrel? acres. 27. From the sum of and 31, take the difference between 4 and 51. Ans. 3 28. What number added to 25 will make 74? Ans. 435. 29. What fraction added to will make ? Ans. 30 MULTIPLICATION. EXAMPLES. 135. To multiply a fraction by an integer. 1. If 1 yard of cloth costs of a dollar, how much will 5 yards cost? OPERATION. 3 × 5 = 15 = 33, Ans. fourths, equal to 33 dollars. ing its numerator (124). 2. If 1 gallon of molasses costs of a dollar, how much will 5 gallons cost? OPERATION. SOLUTION. Since 5, the multiplier, is a factor of 20, the denominator of the multiplicand, we perform the multiplication by dividing the denominator, 20, by the multiplier, 5, and we have, equal to 12 dollars. A fraction is multiplied by dividing its denominator (124). = 4 = 13, Ans. RULE. To multiply a fraction multiply its numerator, or divide its denominator. 3. Multiply 4. Multiply by 7. 5. Multiply by 12. by 63. 6. Multiply SOLUTION. Since 1 yard costs 3 fourths of a dollar, 5 yards will cost 5 times 3 fourths of a dollar, or 15 A fraction is multiplied by multiply OPERATION. Always divide the denominator when it is exactly divisible by the multiplier. Ans. 15 = 34. Ans. 15. by 5. Or, 41 51 = . 45 11× 9 = 99=491. 491, Ans. 8. Multiply 7 by 12. 9. Multiply by 8. 10. Multiply by 51. 11. Multiply 15g by 16. 102 12. Multiply 181 by 22. 13. If a man earns $8 a week, how will he earn in 12 weeks? 14. What will 9 yards of silk cost at of a dollar per yard? 15. What will 27 bushels of barley cost at 7 of a dollar per bushel? Ans. $23. OPERATION. 5)75 price of an acre. 15 cost of of an acre. 3 Ans. 45 cost of 3 of an acre. 136. To multiply an integer by a fraction. 1. At $75 an acre, how much will of an acre of land cost? 24 63 Multiplying by a fraction consists in multiplying by the numerator and dividing by the denominator of the multiplier. 2. Multiply 3 by 4. OPERATION. Or, 6g=53. 24 × SOLUTION. One fifth of an acre will cost of $75, which is $ 15; and will cost 3 times as much as, or $45. Ans. 911. Ans. 521 Ans. 2. Ans. 250. Ans. 165. many dollars 7. Multiply 42 by 93. Ans. 108. 9. Multiply 156 by 7. 10. At $8 a bushel, what will of a bushel of clover seed cost? 11. If a man travels 36 miles a day, how many miles will he travel in 10 days? Ans. 384 miles. 12. If a village lot is worth 450 dollars, what is of it worth? Ans. 262 dollars. 13. At 16 dollars a ton, what is the cost of 23 tons of hay? 1st step, 2d step, 137. To multiply a fraction by a fraction. 1. At of a dollar per bushel, how much will of a bushel of corn cost? Ans. 4091. Ans. 1165. OPERATION. ÷ 4 = 12, cost of of a bushel. 6 = 12 6 1 SOLUTION. - Dividing of a dollar by 4, we have, the cost of of a bushel. A fraction is divided by multiplying its denominator (124). Multiplying the cost of of a bushel by 3, we have of a dollar, the cost of of a bushel. It will readily be seen that we have found the product of the two numerators, 2 and 3, for a new numerator, and of the two denominators, 3 and 4, for a new denominator. RULE. I. Reduce all integers and mixed numbers to improper fractions. II. Find the product of the numerators for a new numerator, and of the denominators for a new denominator. Cancel all factors common to numerators and denominators. 2. Multiply by 4. 3. Multiply by . by 8. Ans. Ans. Fo Ans. 10 Ans. 3. 6. What is the product of, 4, 5, and 1? 8. What is the product of of times Ans. 28. Ans. 111. of of }, Ans. SOLUTION.Canceling like factors in the numerators and denominators, we have left in the numerator 7, and in the denominator 5 × 6 = 30, making for the product. 8 Fractions with the word of between them are sometimes called compound fractions. The word of is simply an equivalent for the sign of multiplication, x. 9. Multiply of 21 by 1 of 71⁄2. Ans. 1. 10. Multiply of 16 by 7 of 263. Ans. 851. 11. What is the sum of the products of 3, of 4, and of 31? Ans. 31. Ans. 2. 12. What is the value of 2 times of of 11? 13. What is the value of of of 12 times & of 8? 공 14. What is the value of 11 of of of 33 times of 9? Ans. 24 15. What is the product of 121 multiplied by 5 times Ans. 464 63 ? gop 16. At of a dollar per yard, what will of a yard of cloth cost? Ans. of a dollar. of his 17. If a man owns of a vessel, and sells share, what part of the whole vessel will he sell? 18. When oats are worth of a dollar per bushel, what is of a bushel worth? 19. What will 7 pounds of tea cost, at of a dollar per pound? Ans. $418. 20. What will 5 yards of cloth cost at of a dollar a yard? Ans. $3. 21. If a man owns of a plot of ground and sells of his share, what part of the plot does he sell? |