Question

find the sum. simplify your answer.
$5 \frac{13}{21} + 4 \frac{2}{7} = \square \frac{\square}{\square}$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(5\frac{13}{21}\) to an improper fraction: \(5\frac{13}{21}=\frac{5\times21 + 13}{21}=\frac{105+13}{21}=\frac{118}{21}\).
Then, convert \(4\frac{2}{7}\) to an improper fraction: \(4\frac{2}{7}=\frac{4\times7 + 2}{7}=\frac{28 + 2}{7}=\frac{30}{7}\).

Step2: Find a common denominator

The denominators are 21 and 7. The least common denominator is 21. Rewrite \(\frac{30}{7}\) with denominator 21: \(\frac{30}{7}=\frac{30\times3}{7\times3}=\frac{90}{21}\).

Step3: Add the fractions

Now add \(\frac{118}{21}+\frac{90}{21}=\frac{118 + 90}{21}=\frac{208}{21}\).

Step4: Convert back to a mixed number

Divide 208 by 21: \(21\times9 = 189\), \(208-189 = 19\). So \(\frac{208}{21}=9\frac{19}{21}\).

Answer:

\(9\frac{19}{21}\) (or in the boxed format as per the problem's layout: the whole number is 9, numerator 19, denominator 21)