Question

Malcolm is making blueberry muffins and blueberry pancakes. He needs 3/4 cup of blueberries for the muffins and 5/6 cup of blueberries for the pancakes. How many cups of blueberries will Malcolm need to make both the muffins and the pancakes?

A.
1/12
B.
8/10
C. 1 5/12

D.
1 7/12

Answer 1

To find out how many cups of blueberries Malcolm needs for both the muffins and the pancakes, we will add the two quantities together: \( \frac{3}{4} \) cup for muffins and \( \frac{5}{6} \) cup for pancakes.

First, we need a common denominator to add these fractions. The denominators are 4 and 6. The least common multiple (LCM) of 4 and 6 is 12.

Now we will convert both fractions to have a denominator of 12:

1. Convert \( \frac{3}{4} \):
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]

2. Convert \( \frac{5}{6} \):
\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\]

Now we can add the two fractions:
\[
\frac{9}{12} + \frac{10}{12} = \frac{19}{12}
\]

Next, we can convert \( \frac{19}{12} \) to a mixed number:
\[
\frac{19}{12} = 1 \frac{7}{12}
\]

So, Malcolm needs a total of \( 1 \frac{7}{12} \) cups of blueberries to make both the muffins and the pancakes.

The correct answer is:
**D. \( 1 \frac{7}{12} \)**