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MATHEMATICS FOR AIR CREW TRAINEES 10 reduced to a denominator = 110. The first is multiplied by 10 (both numerator and denominator), the second by 11, and the third by 22. Then 9 x 10 / 11 x 10 = 90/110; 7 X 11 / 10 x 11 = 77/110; and 4 x 22 / 5 x 22 = 88/110 therefore 9/11 + 7/10 + 4/5 = 90/110 + 77/110 + 88/110 = 90 + 77 + 88 / 110 = 255/110 but 255/110 = 255/5 / 110/5 = 51/22 Answer. (2) The easiest way to find the common denominator is to multiply all the different denominators together. This will frequently give a common denominator which is larger than necessary, but if the answer is then reduced to lowest terms this method will always work. (3) Example: 19/25 - 16/33 = ? Solution: 25 x 33 = 825 Then 19/25 - 16/33 = 627/825 - 400/825 = 627 - 400/825= 227/825 Answer. d. Exercises: (1) 2/3 - 1/3 = ? (2) 7/8 - 3/4 = 1/8 Answer. (3) 11/16 - 1/2 = ? (4) 2/3 + 3/4 + 5/6 + 7/8 + 11/12 + 13/12 = 5 1/8 Answer. (5) 9 1/6 + 8 5/3 + 7 = ? Hint: Add 1/6 and 5/3 first. (6) 7 2/3 + 9 3/4 + 11 1/2 = 28 11/12 Answer. (7) 14 3/4 + 30 1/2 + 4 = ? (8) A dealer had 16 gallons of oil to sell. He sold 1 1/2 gallons to one customer, 2 3/4 gallons to another, 7 1/4 gallons to another, and the remainder to a fourth customer. How much did he sell to the fourth customer? 4 1/2 gal. Answer. (9) A man can do a piece of work in 13 7/8 days. A boy can do the same piece of work in 19 1/2 days. How much longer does it take the boy to do the work? (10) The distance from outside to outside between two holes in a 21