Questions: Multiplying Fractions

Question 1

What is 3/4 × 2/5?

• A. 5/9
• B. 6/20
• C. 15/8
• D. 6/9

Answer: (B)

Multiply numerators: 3 × 2 = 6. Multiply denominators: 4 × 5 = 20. The result is 6/20, which simplifies to 3/10. Option A (5/9) is the error of adding numerators and denominators instead of multiplying. Option C (15/8) is the error of multiplying diagonally instead of straight across.

Question 2

When multiplying 1/2 × 1/3, you need to find a common denominator before multiplying.

• T. True
• F. False

Answer: False

Finding a common denominator is only necessary for adding and subtracting fractions, not multiplying. For multiplication, you simply multiply numerator × numerator and denominator × denominator: (1 × 1)/(2 × 3) = 1/6. Applying the addition procedure to multiplication is one of the most common fraction errors.

Question 3

Why is the product of two proper fractions always smaller than either of the original fractions?

Model answer: Multiplying by a fraction less than 1 takes a part of the other fraction, making the result smaller. For example, 1/2 × 3/4 means 'half of three-fourths,' which is only 3/8 — smaller than both 1/2 and 3/4. The denominator grows while the numerator grows proportionally less, so the resulting fraction is smaller.

This is the key conceptual insight of fraction multiplication. Whole-number multiplication scales things up; fraction multiplication scales things down. The area model makes this visible: the product is a smaller sub-region of a unit square, always contained within both original fractions.