Which multiplication expression can be used to check this division problem: StartFraction 2 Over 5 EndFraction divided by StartFraction 4 Over 15 EndFraction = StartFraction 3 Over 2 EndFraction

Question

Two-fifths times StartFraction 4 Over 15 EndFraction
Three-halves times StartFraction 4 Over 15 EndFraction
Three-halves times StartFraction 15 Over 4 EndFraction
Five-halves times StartFraction 15 Over 4 EndFraction

Answer 1

To check the division problem \( \frac{2}{5} \div \frac{4}{15} = \frac{3}{2} \), you can rewrite the division as a multiplication by the reciprocal. The original expression can be rewritten as:

\[ \frac{2}{5} \div \frac{4}{15} = \frac{2}{5} \times \frac{15}{4} \]

To verify that \( \frac{2}{5} \div \frac{4}{15} = \frac{3}{2} \), you can also check that:

\[ \frac{3}{2} \times \frac{4}{15} = \frac{2}{5} \]

So, the correct multiplication expression that can be used to check the division problem is:

\[ \frac{3}{2} \times \frac{4}{15} \]

Looking through the provided options, this corresponds to:

Three-halves times \( \frac{4}{15} \).