Answer:
67. 5 19/24
69. 22/27
70. 11
71. 3
Explanation:
67. The least common denominator for the two fractions is 8·3 = 24, so the sum can be written ...
4 3/24 + 1 16/24 = (4 +1) +(3 +16)/24 = 5 19/24
69. The dividend is best expressed as an improper fraction. Division by 9 is the same as multiplication by 1/9. Multiplying fractions requires you form the product of the numerators over the product of the denominators.
7 1/3 ÷ 9 = 22/3 × 1/9 = (22·1)/(3·9) = 22/27
70. The distributive property works well for this one.
4 × 2 3/4 = 4×2 + 4×3/4 = 8 + 3 = 11
71. You will get closer to the right answer if you write the operands correctly. The divisor is 5.25, not 15.25. You can also divide the numbers by rewriting them as improper fractions.
15 3/4 ÷ 5 1/4 = 63/4 ÷ 21/4 = 63/21 = 3
(When the fractions you're dividing have the same denominator, the quotient is the ratio of the numerators.)
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Comment on fraction math
You're taught to rewrite fractions for addition and subtraction so that they have the "least common denominator." Actually, any common denominator will do. It can often be simplest just to use the denominator that is the product of the denominators of the fractions you have. The result may need to be reduced, but that is true in any event.
a/b ± c/d = (ad ± bc)/(bd) . . . . always true.
The product "bd" is a suitable denominator that is easily found. The trouble of finding the "least" common denominator is only really necessary if your teacher insists.