JAMB 2011 Mathematics · Question 34

Simplify $\frac{3\frac{2}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}$

Options

A. $5\frac{2}{3}$
B.30
C. $4\frac{1}{3}$
D.50

Answer: D. 50

Explanation written with AI and checked against the answer key

Step 1: Analyze the question We need to simplify a fraction made up of products of fractions. First, convert the mixed number to an improper fraction. 3⅔ = 11/3 Step 2: Numerator (11/3) × (5/6) × (2/3) = (11 × 5 × 2) / (3 × 6 × 3) = 110/54 = 55/27 Step 3: Denominator (11/15) × (3/4) × (2/27) = (11 × 3 × 2) / (15 × 4 × 27) = 66/1620 = 11/270 Step 4: Divide (55/27) ÷ (11/270) = (55/27) × (270/11) Cancel 55 with 11, which gives 5, and 270 with 27, which gives 10: = 5 × 10 = 50 Answer: 50, which is option D. **Tip: In a big fraction of fractions, don't multiply everything out first. Flip the denominator and cancel common factors across the numerators and denominators. Here 11 and 55 cancel, and 27 and 270 cancel, which makes the arithmetic quick.

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Simplify 323×56×231115×34×227\frac{3\frac{2}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}1511​×43​×272​332​×65​×32​​

Options

Answer: D. 50

Simplify $\frac{3\frac{2}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}$