Evaluate (3/5) ÷ (9/10).

Evaluate (3/5) ÷ (9/10).

• A. 3/5
• B. 9/10
• C. 2/3
• D. 1

Answer: (C)

Dividing by a fraction is the same as multiplying by its reciprocal. So (3/5) ÷ (9/10) becomes (3/5) × (10/9). Multiplying gives 30/45, which simplifies to 2/3. You can also see this by canceling first: cancel 5 with 10 to get (3/1) × (2/9) = 6/9 = 2/3, or cancel 3 with 9 to get (1/5) × (10/3) = 10/15 = 2/3. In every path, the result is 2/3.

Dividing by a fraction is the same as multiplying by its reciprocal. So (3/5) ÷ (9/10) becomes (3/5) × (10/9). Multiplying gives 30/45, which simplifies to 2/3. You can also see this by canceling first: cancel 5 with 10 to get (3/1) × (2/9) = 6/9 = 2/3, or cancel 3 with 9 to get (1/5) × (10/3) = 10/15 = 2/3. In every path, the result is 2/3.