Question

Perform the indicated operation. \(5 \frac{7}{12}+8 \frac{13}{16}\)

Short answer

Answer: The sum of the mixed numbers is \(14 \frac{19}{48}\).

Step-by-step solution

Decompose the mixed numbers

Write the mixed numbers as a sum of a whole number and a fraction: \(5 \frac{7}{12} = 5 + \frac{7}{12}\) \(8 \frac{13}{16} = 8 + \frac{13}{16}\)

Find a common denominator

In order to add the fractions, we need to find a common denominator. The least common multiple (LCM) of 12 and 16 is 48.

Rewrite the fractions with the common denominator

Write the fractions with the common denominator of 48: \(\frac{7}{12} = \frac{7 \cdot 4}{12 \cdot 4} = \frac{28}{48}\) \(\frac{13}{16} = \frac{13 \cdot 3}{16 \cdot 3} = \frac{39}{48}\)

Add the fractions

Now, add the fractions with the common denominator: \(\frac{28}{48} + \frac{39}{48} = \frac{28+39}{48} = \frac{67}{48}\)

Simplify the fraction

Observe that \(\frac{67}{48}\) is an improper fraction as the numerator is greater than the denominator. Convert it to a mixed number: \(\frac{67}{48} = 1 \frac{19}{48}\), since \(67 = (1 \cdot 48) + 19\)

Add the whole numbers

Add the whole numbers from the original mixed numbers: \(5+8 = 13\)

Combine the results

Finally, combine the whole numbers and the fractions to get the final answer: \(13 + 1 \frac{19}{48} = 14 \frac{19}{48}\) The result of the operation is \(14 \frac{19}{48}\).