Question

1. grandma rose would like to sew matching outfits for 3 of her grandchildren. the oldest grandchild requires $2\frac{9}{16}$ yards of fabric, and the other 2 grandchildren require $\frac{7}{8}$ yards each. how much material should grandma rose buy?

\bigcirc $3\frac{37}{16}$ yards
\bigcirc $3\frac{5}{16}$ yards
\bigcirc $4\frac{25}{32}$ yards
\bigcirc $4\frac{5}{16}$ yards

Explanation:

Step1: Convert mixed number to improper fraction

The oldest grandchild requires \( 2\frac{9}{16} \) yards. Convert this to an improper fraction: \( 2\frac{9}{16}=\frac{2\times16 + 9}{16}=\frac{32+9}{16}=\frac{41}{16} \)

Step2: Calculate fabric for 2 younger grandchildren

Each of the other 2 grandchildren requires \( \frac{7}{8} \) yards. So total for them is \( 2\times\frac{7}{8}=\frac{14}{8}=\frac{7}{4} \). Convert \( \frac{7}{4} \) to sixteenths: \( \frac{7}{4}=\frac{28}{16} \)

Step3: Add fabric for all grandchildren

Add the fabric for the oldest (\( \frac{41}{16} \)) and the two younger (\( \frac{28}{16} \)): \( \frac{41}{16}+\frac{28}{16}=\frac{41 + 28}{16}=\frac{69}{16} \)

Step4: Convert back to mixed number

\( \frac{69}{16}=4\frac{5}{16} \) (since \( 16\times4 = 64 \), \( 69-64 = 5 \))

Answer:

\( 4\frac{5}{16} \) yards (the last option: \( 4\frac{5}{16} \) yards)