Question

FIND THE DIFFERENCE
24 5/9-13 7/12

Answer 1

To find the difference between \( 24 \frac{5}{9} \) and \( 13 \frac{7}{12} \), we first need to convert both mixed numbers into improper fractions.

1. Convert \( 24 \frac{5}{9} \) to an improper fraction:
\[
24 \frac{5}{9} = \frac{(24 \times 9) + 5}{9} = \frac{216 + 5}{9} = \frac{221}{9}
\]

2. Convert \( 13 \frac{7}{12} \) to an improper fraction:
\[
13 \frac{7}{12} = \frac{(13 \times 12) + 7}{12} = \frac{156 + 7}{12} = \frac{163}{12}
\]

Now, we need to subtract \( \frac{163}{12} \) from \( \frac{221}{9} \). To do this, we need a common denominator. The least common multiple (LCM) of 9 and 12 is 36.

3. Convert \( \frac{221}{9} \) to have a denominator of 36:
\[
\frac{221}{9} = \frac{221 \times 4}{9 \times 4} = \frac{884}{36}
\]

4. Convert \( \frac{163}{12} \) to have a denominator of 36:
\[
\frac{163}{12} = \frac{163 \times 3}{12 \times 3} = \frac{489}{36}
\]

5. Now, subtract the two fractions:
\[
\frac{884}{36} - \frac{489}{36} = \frac{884 - 489}{36} = \frac{395}{36}
\]

6. Finally, we can convert \( \frac{395}{36} \) back to a mixed number:
- Divide 395 by 36. The quotient is 10 and the remainder is 35.
\[
\frac{395}{36} = 10 \frac{35}{36}
\]

Thus, the difference \( 24 \frac{5}{9} - 13 \frac{7}{12} \) is:
\[
\boxed{10 \frac{35}{36}}
\]