A baker is preparing a recipe that calls for 2 times the sum of \frac{1}{4} cup of milk an… — ACT

A baker is preparing a recipe that calls for $2$ times the sum of $\frac{1}{4}$ cup of milk and $\frac{2}{5}$ cup of water. What is the total volume, in cups, of these two liquid ingredients combined?

A
$\frac{2}{3}$
B
$\frac{9}{10}$
$\frac{13}{10}$ Answer
D
$\frac{34}{35}$
E
$\frac{13}{20}$

Answer

The correct answer is

\frac{13}{10}

cups.

To find the total volume, first determine the sum of the two fractions by finding a common denominator:

\frac{1}{4} + \frac{2}{5} = \frac{5}{20} + \frac{8}{20} = \frac{13}{20}

cups. Then, multiply this sum by

2

as required by the recipe:

2 \times \frac{13}{20} = \frac{26}{20} = \frac{13}{10}

cups.

Step-by-Step Solution

Find a common denominator for the two fractions to be added.

The common denominator for 4 and 5 is 20, converting the fractions to

\frac{5}{20}

and

\frac{8}{20}

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

Add the two converted fractions.

\frac{5}{20} + \frac{8}{20} = \frac{13}{20}

To find the sum of the ingredients inside the parentheses.

Multiply the sum of the fractions by 2.

2 \times \frac{13}{20} = \frac{26}{20} = \frac{13}{10}

The recipe calls for 2 times the sum of the two liquid ingredients.

Key Concept

Adding fractions with unlike denominators and performing operations in the correct order.

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