Question

(5) $3\frac{23}{24} + 8\frac{7}{36} =$
(6) $3\frac{9}{20} + 5\frac{17}{40} =$

Explanation:

Step1: Solve \( 3\frac{23}{24}+8\frac{7}{36} \)

First, add the whole numbers: \( 3 + 8 = 11 \)
Then, find a common denominator for the fractions. The least common multiple of 24 and 36 is 72.
Convert \( \frac{23}{24} \) to \( \frac{23\times3}{24\times3}=\frac{69}{72} \)
Convert \( \frac{7}{36} \) to \( \frac{7\times2}{36\times2}=\frac{14}{72} \)
Add the fractions: \( \frac{69}{72}+\frac{14}{72}=\frac{83}{72}=1\frac{11}{72} \)
Add the whole number and the fraction: \( 11 + 1\frac{11}{72}=12\frac{11}{72} \)

Step2: Solve \( 3\frac{9}{20}+5\frac{17}{40} \)

Add the whole numbers: \( 3 + 5 = 8 \)
Find a common denominator for the fractions. The least common multiple of 20 and 40 is 40.
Convert \( \frac{9}{20} \) to \( \frac{9\times2}{20\times2}=\frac{18}{40} \)
Add the fractions: \( \frac{18}{40}+\frac{17}{40}=\frac{35}{40}=\frac{7}{8} \)
Add the whole number and the fraction: \( 8+\frac{7}{8}=8\frac{7}{8} \)

Answer:

\( 3\frac{23}{24}+8\frac{7}{36}=12\frac{11}{72} \)
\( 3\frac{9}{20}+5\frac{17}{40}=8\frac{7}{8} \)