Answer to Question #107378 in Algebra for Anu

Question

Identify the possible logic used by a child who gave the following answer.
2/3 x 3/2 = 13/6
How would you help her clear her misunderstanding.

Answer 1

The possible logic used by a child is

$2/3 × 3/2 = \frac{2×2 + 3×3}{2×3} = 13/6.$

The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator. Simplifying before multiplying helps avoid dealing with large numbers.

The correct answer is

$2/3 × 3/2 = \frac{2×3}{3×2} = \frac{6}{6} = \frac{1}{1} = 1.$