SUBTRACTION OF MIXED NUMBERS Subtraction of Mixed Numbers involving Reduction of a Unit in the Minuend for the fraction of the minuend. 5. From 24 subtract 163. and what are 6? 0 and what are 1? The one unit which we reduce in the minuend is equal to 4, which united with the given makes 4 6 what are 14, as the 4 is tenths of the next number, and 10 and 4 are 14. In subtracting in the 5th example given above, we think, 4 and what are 9, as the 1 is 8ths of the next number, and 8 and 1 are 9. The form of arrangement shown expresses the parts of the next number in a very convenient way, and suggests the guide to the reduction of the unit. 6. From 16 subtract 43. 7. From 1853 subtract 677. 8. From 120 subtract 565. 9. From 181 subtract 127. 10. From 75% subtract 621. 11. From 250 subtract 654. 12. From the sum of 161 and 123, subtract 258. 13. A man owned 150 acres of land. He sold 65 acres to one man and 165 acres to another man. How many acres had he left? 14. From a bin containing 75 bushels of grain, 243 bushels were sold and 16g bushels used for seed. How many bushels remained in the bin? 15. From a pole 28 ft. long a piece 143 ft. long was cut. How long was the part of the pole that remained? 16. The distance between two places is 1501 miles. What distance remains to go, after one has traveled 1307 miles of the route? 17. After selling 35 acres of land, a farmer had 1233 acres. How much more must he buy to have 150 acres? 18. Mary is 12,5 years old and her sister Sarah is 9 years old. How much older is one sister than 93 the other? 19. A pail filled with candy weighs 141 pounds. When empty, the pail weighs 23 pounds. How many pounds of candy were there in the pail? MULTIPLICATION AND DIVISION OF FRACTIONS 89. PRINCIPLE. In the multiplication of fractions, the product of the numerators gives the number of parts, and the product of the denominators gives the size of the parts of the required result. The operations are shortened by cancellation. The factors 4 and 5 are canceled from both numerator and denominator. This does not change the value of the product, but it shortens the work. Cancellation should be used as often as possible. 8. Multiply by J. 341 = 3 of 1÷ 11 or 4. 34 = 3 ofor 8. Ans. 4. Divide by 7. Ans. 4. Analysis: 1 contains, times. of 1 contains, of times, or . Ans. 3 4 Written form: ÷ 7 = 1 × 4 = 4. Note. If further study of the principle of inverting the divisor in division of fractions be desired, the facts are very clearly shown by use of folded paper in measuring. To prove that ÷ = 3 × 14, cut two pieces of paper of the same size, one to represent the unit and the other folded to represent of the unit. |