148. Mary paid ADDITION. ORAL EXERCISES. of a dollar for a book, of a dollar for a hat, and of a dollar for a handkerchief. How many eighths of a dollar did she spend for all? 149. Smith owns of a vessel and Keen 3. How many sixteenths does Keen own? What part of the vessel do both own? Give the sum of the following fractions: of a dollar and of a dollar; also, and are like = Solution. = = Reducing the given fractions to fractions having the least common denominator, we have 4, 4, and 24, which added give § 224, or 21. 156. What is the sum of, 1, and 18? 157. What is the sum of 14, 1}, and %? = 124. Rule for Addition of Fractions. Change the fractions, if necessary, to fractions having a common denominator, add the numerators, write the sum over the common denominator, and simplify the result, if needful. 125. When there are mixed numbers, the fractions and the integers may be added separately, and the results united. 167. What is the sum of 153 and 24ğ? 168. What is the value of 37 + 1094 + 341? 169. A man paid $42 for a hat, $16 for a coat, and $57. How much did he pay for the whole? for a pair of boots. 170. A has in his farm 160 acres, B has 67 acres, and What is the number of acres in the three SUBTRACTION. ORAL EXERCISES. 171. A man owned 1 of a ship and sold . What part of Only like fractions can be subtracted the one from the having the least common denominator, we have 8 and 28. 28 sub tracted from leaves 11. 182. Find the difference between 21 and 31. 183. From take 33. 184. From take 14 127. Rule for Subtraction of Fractions. Change the fractions, if necessary, to fractions having a common denominator, find the difference of the numerators, and write it over the common denominator. What is the 194. I copied by mistake instead of. amount of error I made? 195. How much is 494 less 313? 4924932485 31 = 31 172 Solution. - Changing the fractions to fractions having a common denominator, we have 491 and 31. As we cannot take from 18, we take 1, or 3, from 49, leaving 48; and adding the 3 to 1, we have 481. Subtracting from, and 31 froin 48, we have, as the result required, 173. 202. A boy paid for a sled $7g, and for skates $18. How much more did he pay for the sled than for the skates? 203. The greater of two numbers is 150, and the smaller is 14743. What is their difference? 204. Two men start from the same place and travel in the same direction. When one has gone 17 miles and the other 19 miles, how far are they apart? MULTIPLICATION. A Fraction multiplied by an Integer. ORAL EXERCISES. 205. Multiply by 4. 日 3 X 4 16 Multiplying the numerator of Solution. by 4 gives 12, equal to ; or, dividing the denominator of by 4, gives . In either case, is multiplied by 4. For it will be seen by the illustration that multiplying the numerator by 4 increases the number of fractional units 4 times, while their size remains unchanged; and that dividing the denominator by 4 increases the size of the fractional units 4 times, while their number is unchanged. The effect of either process, therefore, is to increase the value of the fraction 4 times. 206. At each, how many dollars will 12 arithmetics cost? 207. At the rate of of a bushel of grain a week, how many bushels of grain will a horse consume in 6 weeks? 208. If 1 hat costs $34, what will 8 hats cost? 209. Multiply the fractions in Exercises 27 to 32 by 3; by 4; by 5; by 6; by 7; by 8; by 9; by 10; by 12. 210. Multiply the mixed numbers in Exercises 74 to 78 by the preceding integers. 128. Principle. A fraction is multiplied either by multiplying its numerator or by dividing its denominator. |