Question

add.
(1) $\frac{3}{8} + \frac{5}{18} =$
(2) $\frac{4}{15} + \frac{3}{20} =$
(3) $\frac{5}{11} + \frac{3}{22} =$
(4) $\frac{1}{18} + \frac{1}{24} =$
(5) $\frac{1}{10} + \frac{7}{30} =$

Explanation:

Step1: Find a common denominator for \(\frac{3}{8}\) and \(\frac{5}{18}\)

The least common multiple of 8 and 18 is 72. Rewrite the fractions: \(\frac{3}{8}=\frac{3\times9}{8\times9}=\frac{27}{72}\), \(\frac{5}{18}=\frac{5\times4}{18\times4}=\frac{20}{72}\)

Step2: Add the fractions

\(\frac{27}{72}+\frac{20}{72}=\frac{27 + 20}{72}=\frac{47}{72}\)

Step1: Find a common denominator for \(\frac{4}{15}\) and \(\frac{3}{20}\)

The least common multiple of 15 and 20 is 60. Rewrite the fractions: \(\frac{4}{15}=\frac{4\times4}{15\times4}=\frac{16}{60}\), \(\frac{3}{20}=\frac{3\times3}{20\times3}=\frac{9}{60}\)

Step2: Add the fractions

\(\frac{16}{60}+\frac{9}{60}=\frac{16+9}{60}=\frac{25}{60}=\frac{5}{12}\)

Step1: Find a common denominator for \(\frac{5}{11}\) and \(\frac{3}{22}\)

The least common multiple of 11 and 22 is 22. Rewrite the fraction: \(\frac{5}{11}=\frac{5\times2}{11\times2}=\frac{10}{22}\)

Step2: Add the fractions

\(\frac{10}{22}+\frac{3}{22}=\frac{10 + 3}{22}=\frac{13}{22}\)

Step1: Find a common denominator for \(\frac{1}{18}\) and \(\frac{1}{24}\)

The least common multiple of 18 and 24 is 72. Rewrite the fractions: \(\frac{1}{18}=\frac{1\times4}{18\times4}=\frac{4}{72}\), \(\frac{1}{24}=\frac{1\times3}{24\times3}=\frac{3}{72}\)

Step2: Add the fractions

\(\frac{4}{72}+\frac{3}{72}=\frac{4+3}{72}=\frac{7}{72}\)

Step1: Find a common denominator for \(\frac{1}{10}\) and \(\frac{7}{30}\)

The least common multiple of 10 and 30 is 30. Rewrite the fraction: \(\frac{1}{10}=\frac{1\times3}{10\times3}=\frac{3}{30}\)

Step2: Add the fractions

\(\frac{3}{30}+\frac{7}{30}=\frac{3 + 7}{30}=\frac{10}{30}=\frac{1}{3}\)

Answer:

(1) \(\frac{47}{72}\)
(2) \(\frac{5}{12}\)
(3) \(\frac{13}{22}\)
(4) \(\frac{7}{72}\)
(5) \(\frac{1}{3}\)