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WAEC 2015 Mathematics · Question 20

If m = 4, n = 9 and r = 16., evaluate mn\frac{m}{n} - 179\frac{7}{9} + nr\frac{n}{r}

Options

  1. A.1516\frac{5}{16}
  2. B.1116\frac{1}{16}
  3. C.516\frac{5}{16}
  4. D.- 3748\frac{37}{48}

Answer: D. - 3748\frac{37}{48}

Explanation written with AI and checked against the answer key

Analyze the question: We substitute m = 4, n = 9, r = 16 into m/n − 1 7/9 + n/r. Substitute: m/n = 4/9 n/r = 9/16 Expression: 4/9 − 1 7/9 + 9/16 Convert the mixed number: 1 7/9 = 16/9 Combine the first two terms: 4/9 − 16/9 = −12/9 = −4/3 Add 9/16: LCD of 3 and 16 is 48. −4/3 = −64/48 9/16 = 27/48 −64/48 + 27/48 = −37/48 Answer: −37/48, which matches option D. Tip: Always convert mixed numbers to improper fractions before adding or subtracting. Combine fractions with the same denominator first (here the two ninths) to keep the arithmetic simple. Also watch the signs: a negative result is possible, so don't dismiss option D just because the others are positive.

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