Question

add.
(1) $\frac{5}{8} + \frac{9}{20} =$
(2) $\frac{3}{10} + \frac{2}{25} =$
(3) $\frac{3}{14} + \frac{1}{28} =$
(4) $\frac{7}{15} + \frac{13}{30} =$
(5) $\frac{3}{11} + \frac{13}{33} =$

Explanation:

Step1: Find a common denominator for \(\frac{5}{8}\) and \(\frac{9}{20}\)

The least common multiple of 8 and 20 is 40. Convert the fractions: \(\frac{5}{8}=\frac{5\times5}{8\times5}=\frac{25}{40}\), \(\frac{9}{20}=\frac{9\times2}{20\times2}=\frac{18}{40}\)

Step2: Add the fractions

\(\frac{25}{40}+\frac{18}{40}=\frac{25 + 18}{40}=\frac{43}{40}\)

Step1: Find a common denominator for \(\frac{3}{10}\) and \(\frac{2}{25}\)

The least common multiple of 10 and 25 is 50. Convert the fractions: \(\frac{3}{10}=\frac{3\times5}{10\times5}=\frac{15}{50}\), \(\frac{2}{25}=\frac{2\times2}{25\times2}=\frac{4}{50}\)

Step2: Add the fractions

\(\frac{15}{50}+\frac{4}{50}=\frac{15 + 4}{50}=\frac{19}{50}\)

Step1: Find a common denominator for \(\frac{3}{14}\) and \(\frac{1}{28}\)

The least common multiple of 14 and 28 is 28. Convert the fraction: \(\frac{3}{14}=\frac{3\times2}{14\times2}=\frac{6}{28}\)

Step2: Add the fractions

\(\frac{6}{28}+\frac{1}{28}=\frac{6 + 1}{28}=\frac{7}{28}=\frac{1}{4}\)

Step1: Find a common denominator for \(\frac{7}{15}\) and \(\frac{13}{30}\)

The least common multiple of 15 and 30 is 30. Convert the fraction: \(\frac{7}{15}=\frac{7\times2}{15\times2}=\frac{14}{30}\)

Step2: Add the fractions

\(\frac{14}{30}+\frac{13}{30}=\frac{14 + 13}{30}=\frac{27}{30}=\frac{9}{10}\)

Step1: Find a common denominator for \(\frac{3}{11}\) and \(\frac{13}{33}\)

The least common multiple of 11 and 33 is 33. Convert the fraction: \(\frac{3}{11}=\frac{3\times3}{11\times3}=\frac{9}{33}\)

Step2: Add the fractions

\(\frac{9}{33}+\frac{13}{33}=\frac{9 + 13}{33}=\frac{22}{33}=\frac{2}{3}\)

Answer:

(1) \(\frac{43}{40}\)
(2) \(\frac{19}{50}\)
(3) \(\frac{1}{4}\)
(4) \(\frac{9}{10}\)
(5) \(\frac{2}{3}\)