Question

4 5/8 + 5/12

Answer 1

To add \(4 \frac{5}{8}\) and \(\frac{5}{12}\), we first convert the mixed number \(4 \frac{5}{8}\) to an improper fraction.

1. Convert \(4 \frac{5}{8}\) to an improper fraction:
\[
4 \frac{5}{8} = \frac{4 \times 8 + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8}
\]

2. Now, we need to add \(\frac{37}{8}\) and \(\frac{5}{12}\). To do this, we need a common denominator. The least common multiple of \(8\) and \(12\) is \(24\).

3. Convert \(\frac{37}{8}\) and \(\frac{5}{12}\) to have a denominator of \(24\):
\[
\frac{37}{8} = \frac{37 \times 3}{8 \times 3} = \frac{111}{24}
\]
\[
\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}
\]

4. Now we can add the two fractions:
\[
\frac{111}{24} + \frac{10}{24} = \frac{111 + 10}{24} = \frac{121}{24}
\]

5. Finally, we can convert \(\frac{121}{24}\) back to a mixed number:
- Divide \(121\) by \(24\): \(121 \div 24 = 5\) (whole number),
- Remainder: \(121 - (24 \times 5) = 121 - 120 = 1\),
- Thus, \(\frac{121}{24} = 5 \frac{1}{24}\).

Therefore, \(4 \frac{5}{8} + \frac{5}{12} = 5 \frac{1}{24}\).