Martha is making a recipe that requires 2/5 of a cup of sugar. She only has 1/3 of a cup of sugar at home, though. What fraction of the recipe can Martha make with the amount of sugar she has?
Martha has 1/3 of a cup of sugar, which is less than the 2/5 of a cup required by the recipe. Thus, she can only make a fraction of the recipe that is 1/3 / 2/5 = 1/3 * 5/2 = 5/6. Answer: \boxed{\frac{5}{6}}.
To determine the fraction of the recipe Martha can make with the amount of sugar she has, we need to divide the amount she has by the required amount.
Martha has 1/3 of a cup of sugar, and the recipe requires 2/5 of a cup.
To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction.
So, we have (1/3) / (2/5).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Thus, (1/3) / (2/5) = (1/3) * (5/2).
Multiplying the numerators gives us 1 * 5 = 5, and multiplying the denominators gives us 3 * 2 = 6.
Therefore, (1/3) / (2/5) = 5/6.
So, Martha can make 5/6 of the recipe with the amount of sugar she has.
To find the fraction of the recipe that Martha can make with the amount of sugar she has, we need to compare the amount of sugar she has (1/3 cup) with the amount required for the recipe (2/5 cup).
To do this, we need to find a common denominator for 3 and 5, which is 15.
Now, let's convert 1/3 to a fraction with a denominator of 15:
1/3 = (1/3) * (5/5) = 5/15
So, Martha has 5/15 cup of sugar.
Now, we can compare this with the required amount of sugar (2/5 cup):
5/15 is equivalent to 2/5 because if we multiply the numerator and denominator of 2/5 by 3, we get 6/15, which is equal to 5/15.
Therefore, Martha has 2/5 of the required amount of sugar. So, she can make 2/5 or 40% of the recipe with the amount of sugar she has.