JAMB 2016 Mathematics · Question 31

Simplify 1 - ( $\frac{1}{7}$ x 3 $\frac{1}{2}$ ) $\div$ $\frac{3}{4}$

Options

A.2
B. $\frac{1}{3}$
C.1
D. $\frac{2}{3}$

Answer: B. $\frac{1}{3}$

Explanation written with AI and checked against the answer key

Analyze the question: We need to simplify 1 − (1/7 × 3½) ÷ 3/4. By BODMAS, we work out the brackets first, then the division, then the subtraction. Concept: BODMAS says to do Brackets, Orders, Division/Multiplication, then Addition/Subtraction. Mixed numbers must be converted to improper fractions before multiplying. Solution: Step 1: Convert the mixed number. 3½ = 7/2 Step 2: Work the bracket. 1/7 × 7/2 = 7/14 = 1/2 Step 3: Divide by 3/4 (multiply by the reciprocal). 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3 Step 4: Subtract from 1. 1 − 2/3 = 1/3 Answer: 1/3, which is option B. (Note: if the division were done only on the 1 − ... part, you would get a different result, but BODMAS clearly puts division before subtraction.) Tip: Look for cancellations early. Here 1/7 × 7/2 cancels the 7s immediately. Always convert mixed numbers first, and remember that "÷ a fraction" means "× its reciprocal".

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Simplify 1 - (17\frac{1}{7}71​ x 3 12\frac{1}{2}21​) ÷\div÷ 34\frac{3}{4}43​

Options

Answer: B. 13\frac{1}{3}31​

Simplify 1 - ( $\frac{1}{7}$ x 3 $\frac{1}{2}$ ) $\div$ $\frac{3}{4}$

Answer: B. $\frac{1}{3}$