Questions: Find the sum. Write your answer in mixed number form, and reduce if possible. 31 1/5 + 18 1/7

Transcript text: Find the sum. Write your answer in mixed number form, and reduce if possible. \[ 31 \frac{1}{5}+18 \frac{1}{7} \]

Solution

Solution Steps

Step 1: Convert Mixed Numbers to Improper Fractions

Convert the mixed numbers to improper fractions: \[ 3 \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5} \] \[ 1 \frac{3}{8} = \frac{1 \times 8 + 3}{8} = \frac{11}{8} \] \[ 2 \frac{5}{7} = \frac{2 \times 7 + 5}{7} = \frac{19}{7} \]

Step 2: Find a Common Denominator

Find the least common multiple (LCM) of the denominators 5, 8, and 7. The LCM of 5, 8, and 7 is 280.

Step 3: Convert Fractions to Have a Common Denominator

Convert each fraction to have the common denominator of 280: \[ \frac{16}{5} = \frac{16 \times 56}{5 \times 56} = \frac{896}{280} \] \[ \frac{11}{8} = \frac{11 \times 35}{8 \times 35} = \frac{385}{280} \] \[ \frac{19}{7} = \frac{19 \times 40}{7 \times 40} = \frac{760}{280} \]

Step 4: Add the Fractions

Add the fractions: \[ \frac{896}{280} + \frac{385}{280} + \frac{760}{280} = \frac{896 + 385 + 760}{280} = \frac{2041}{280} \]

Step 5: Simplify the Fraction

Simplify the fraction if possible. In this case, \(\frac{2041}{280}\) cannot be simplified further.

Step 6: Convert Back to a Mixed Number

Convert the improper fraction back to a mixed number: \[ \frac{2041}{280} = 7 \frac{41}{280} \]