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JAMB 2010 Mathematics · Question 46

Simplify (34\frac{3}{4} of 49\frac{4}{9} ÷\div 912\frac{1}{2}) ÷\div 1519\frac{5}{19}

Options

  1. A.15\frac{1}{5}
  2. B.14\frac{1}{4}
  3. C.136\frac{1}{36}
  4. D.125\frac{1}{25}

Answer: C. 136\frac{1}{36}

Explanation written with AI and checked against the answer key

Analyze the question: We simplify (3/4 of 4/9 ÷ 9½) ÷ 1 5/19. Following BODMAS, "of" is done first, then division. Step 1: "of" first 3/4 of 4/9 = 3/4 × 4/9 = 12/36 = 1/3 Step 2: Convert the mixed numbers 9½ = 19/2 1 5/19 = 24/19 Step 3: Divide inside the bracket 1/3 ÷ 19/2 = 1/3 × 2/19 = 2/57 Step 4: Divide by 1 5/19 2/57 ÷ 24/19 = 2/57 × 19/24 = 38/1368 = 1/36 (Check: 57 = 3 × 19, so the 19s cancel: 2/(3×24) = 2/72 = 1/36.) Answer: 1/36, which is option C. Tip: In BODMAS, "of" comes right after brackets. Convert mixed numbers to improper fractions early, and look for common factors (like 19 here) to cancel before multiplying.

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