2,4/7,7 - 2,8/12,1

To subtract the two mixed numbers \( 2\frac{4}{7} \) and \( 2\frac{8}{12} \), we can follow these steps: 1. Convert the mixed numbers to improper fractions. 2. Make sure the fractions have a common denominator. 3. Subtract the fractions. 4. Convert back to a mixed number if necessary. ### Step 1: Convert to improper fractions For \( 2\frac{4}{7} \): \[ 2\frac{4}{7} = 2 \times 7 + 4 = 14 + 4 = 18 \] So, \[ 2\frac{4}{7} = \frac{18}{7} \] For \( 2\frac{8}{12} \): \[ 2\frac{8}{12} = 2 \times 12 + 8 = 24 + 8 = 32 \] So, \[ 2\frac{8}{12} = \frac{32}{12} \] ### Step 2: Simplify \( \frac{32}{12} \) To simplify \( \frac{32}{12} \), find the greatest common divisor (GCD) of 32 and 12, which is 4. Thus, \[ \frac{32 \div 4}{12 \div 4} = \frac{8}{3} \] ### Step 3: Find a common denominator The denominators are 7 and 3. The least common multiple (LCM) of 7 and 3 is 21. Now, convert the fractions to have the common denominator of 21: - For \( \frac{18}{7} \): \[ \frac{18}{7} = \frac{18 \times 3}{7 \times 3} = \frac{54}{21} \] - For \( \frac{8}{3} \): \[ \frac{8}{3} = \frac{8 \times 7}{3 \times 7} = \frac{56}{21} \] ### Step 4: Perform the subtraction Now we can subtract: \[ \frac{54}{21} - \frac{56}{21} = \frac{54 - 56}{21} = \frac{-2}{21} \] ### Conclusion Thus, \[ 2\frac{4}{7} - 2\frac{8}{12} = -\frac{2}{21} \] This result indicates the answer is negative, meaning that \( 2\frac{4}{7} \) is less than \( 2\frac{8}{12} \).