To find out how many hours Maria has left to complete her community service program, we need to subtract the time she has already spent from the total time required.
-
Convert the mixed numbers to improper fractions:
- For \(5 \frac{1}{2}\): \[ 5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \]
- For \(3 \frac{3}{4}\): \[ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \]
-
Next, we need to subtract \( \frac{15}{4} \) from \( \frac{11}{2} \). First, we convert \( \frac{11}{2} \) to a fraction with a denominator of 4: \[ \frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4} \]
-
Now perform the subtraction: \[ \frac{22}{4} - \frac{15}{4} = \frac{22 - 15}{4} = \frac{7}{4} \]
-
Finally, convert \( \frac{7}{4} \) back to a mixed number:
- \( \frac{7}{4} = 1 \frac{3}{4} \)
Thus, Maria has \( 1 \frac{3}{4} \) hours left to complete her community service program.