Question

Martha is making a recipe that requires 2 fifths of a cup of sugar. She only has 1 third of a cup of sugar at home, though. What fraction of the recipe can Martha make with the amount of sugar she has?
A.
5 sixths

B.
5 ninths

C.
6 fifths

D.
3 eights

Answer 1

To find out what fraction of the recipe Martha can make with the amount of sugar she has, we need to compare the amount of sugar she has (1/3 cup) to the amount the recipe requires (2/5 cup).

We can do this by dividing the amount of sugar she has by the amount required by the recipe:

\[
\text{Fraction of the recipe} = \frac{\text{Amount of sugar she has}}{\text{Amount required by the recipe}} = \frac{\frac{1}{3}}{\frac{2}{5}}
\]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{1}{3} \div \frac{2}{5} = \frac{1}{3} \times \frac{5}{2} = \frac{1 \times 5}{3 \times 2} = \frac{5}{6}
\]

Therefore, the fraction of the recipe that Martha can make with the amount of sugar she has is \(\frac{5}{6}\), which corresponds to option:

**A. \( \frac{5}{6} \)**