A chef uses \frac{1}{3} cup of milk and \frac{1}{4} cup of water for a recipe. What fracti… — ACT

A chef uses $\frac{1}{3}$ cup of milk and $\frac{1}{4}$ cup of water for a recipe. What fraction of a cup is the total liquid used in the recipe?

A
$\frac{2}{7}$
B
$\frac{1}{12}$
$\frac{7}{12}$ Answer
D
$\frac{1}{7}$
E
$\frac{1}{6}$

Answer

The correct fraction of a cup of liquid is

\frac{7}{12}

The correct answer is found by finding a common denominator for the two fractions. The least common multiple of 3 and 4 is 12. Converting the fractions gives

\frac{4}{12}

and

\frac{3}{12}

. Adding these fractions yields

\frac{7}{12}

Step-by-Step Solution

Identify the mathematical operation needed to find the total liquid.

The total amount of liquid is the sum of the two fractions:

\frac{1}{3} + \frac{1}{4}

To find the combined total of two separate quantities, addition is required.

Find a common denominator for the two fractions.

The least common multiple of 3 and 4 is 12. Convert the fractions:

\frac{1}{3} = \frac{4}{12}

and

\frac{1}{4} = \frac{3}{12}

Fractions must have the same denominator before they can be added.

Add the converted fractions.

\frac{4}{12} + \frac{3}{12} = \frac{7}{12}

Add the numerators together and keep the common denominator.

Key Concept

Adding fractions with unlike denominators.

Estimated Time:45s

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