Question

Simplify answer if necessary. 5 5/8 + 2 5/6 + 1 1 1/4

Answer 1

To simplify the expression \( 5 \frac{5}{8} + 2 \frac{5}{6} + 1 \frac{1}{4} \), we will first convert each mixed number into an improper fraction.

1. **Convert mixed numbers to improper fractions**:
- For \( 5 \frac{5}{8} \):
\[
5 \frac{5}{8} = \frac{5 \times 8 + 5}{8} = \frac{40 + 5}{8} = \frac{45}{8}
\]

- For \( 2 \frac{5}{6} \):
\[
2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}
\]

- For \( 1 \frac{1}{4} \):
\[
1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4}
\]

2. **Add the improper fractions**:
We need a common denominator to add these fractions. The denominators are 8, 6, and 4. The least common multiple (LCM) of these numbers is 24.

- Convert \( \frac{45}{8} \) to have a denominator of 24:
\[
\frac{45}{8} \times \frac{3}{3} = \frac{135}{24}
\]

- Convert \( \frac{17}{6} \) to have a denominator of 24:
\[
\frac{17}{6} \times \frac{4}{4} = \frac{68}{24}
\]

- Convert \( \frac{5}{4} \) to have a denominator of 24:
\[
\frac{5}{4} \times \frac{6}{6} = \frac{30}{24}
\]

3. **Now add the fractions**:
\[
\frac{135}{24} + \frac{68}{24} + \frac{30}{24} = \frac{135 + 68 + 30}{24} = \frac{233}{24}
\]

4. **Convert the improper fraction back to a mixed number**:
To convert \( \frac{233}{24} \) back into a mixed number, divide 233 by 24:
- \( 233 \div 24 = 9 \) (since \( 24 \times 9 = 216 \))
- The remainder is \( 233 - 216 = 17 \).

Thus, \( \frac{233}{24} = 9 \frac{17}{24} \).

So the final simplified answer is:
\[
\boxed{9 \frac{17}{24}}
\]