8 8/15-4 9/20

To subtract the mixed numbers \( 8 \frac{8}{15} \) and \( 4 \frac{9}{20} \), follow these steps:

1. Convert the mixed numbers to improper fractions:

   For \( 8 \frac{8}{15} \): \[ 8 \frac{8}{15} = \frac{8 \times 15 + 8}{15} = \frac{120 + 8}{15} = \frac{128}{15} \]

   For \( 4 \frac{9}{20} \): \[ 4 \frac{9}{20} = \frac{4 \times 20 + 9}{20} = \frac{80 + 9}{20} = \frac{89}{20} \]

2. Find a common denominator to subtract the fractions. The least common multiple (LCM) of 15 and 20 is 60.

   • Convert \( \frac{128}{15} \) to a fraction with a denominator of 60: \[ \frac{128}{15} = \frac{128 \times 4}{15 \times 4} = \frac{512}{60} \]

   • Convert \( \frac{89}{20} \) to a fraction with a denominator of 60: \[ \frac{89}{20} = \frac{89 \times 3}{20 \times 3} = \frac{267}{60} \]

3. Now, subtract the two fractions: \[ \frac{512}{60} - \frac{267}{60} = \frac{512 - 267}{60} = \frac{245}{60} \]

4. Simplify the fraction \( \frac{245}{60} \):

   • The greatest common divisor (GCD) of 245 and 60 is 5: \[ \frac{245 \div 5}{60 \div 5} = \frac{49}{12} \]

5. Convert back to a mixed number: \[ 49 \div 12 = 4 \quad \text{(whole number part)} \] \[ 49 - (4 \times 12) = 49 - 48 = 1 \quad \text{(remainder)} \] Thus, \( \frac{49}{12} = 4 \frac{1}{12} \).

The final result is: \[ 8 \frac{8}{15} - 4 \frac{9}{20} = 4 \frac{1}{12} \]