Question

add.
(1) $\frac{3}{10} + \frac{2}{15} =$
(2) $\frac{1}{12} + \frac{1}{18} =$
(3) $\frac{3}{10} + \frac{7}{20} =$
(4) $\frac{1}{12} + \frac{1}{20} =$
(5) $\frac{1}{13} + \frac{3}{26} =$

Explanation:

Step1: Find a common denominator for \(\frac{3}{10}\) and \(\frac{2}{15}\). The least common multiple of 10 and 15 is 30.

\(\frac{3}{10}=\frac{3\times3}{10\times3}=\frac{9}{30}\), \(\frac{2}{15}=\frac{2\times2}{15\times2}=\frac{4}{30}\)

Step2: Add the fractions.

\(\frac{9}{30}+\frac{4}{30}=\frac{9 + 4}{30}=\frac{13}{30}\)

Step3: Find a common denominator for \(\frac{1}{12}\) and \(\frac{1}{18}\). The least common multiple of 12 and 18 is 36.

\(\frac{1}{12}=\frac{1\times3}{12\times3}=\frac{3}{36}\), \(\frac{1}{18}=\frac{1\times2}{18\times2}=\frac{2}{36}\)

Step4: Add the fractions.

\(\frac{3}{36}+\frac{2}{36}=\frac{3+2}{36}=\frac{5}{36}\)

Step5: Find a common denominator for \(\frac{3}{10}\) and \(\frac{7}{20}\). The least common multiple of 10 and 20 is 20.

\(\frac{3}{10}=\frac{3\times2}{10\times2}=\frac{6}{20}\)

Step6: Add the fractions.

\(\frac{6}{20}+\frac{7}{20}=\frac{6 + 7}{20}=\frac{13}{20}\)

Step7: Find a common denominator for \(\frac{1}{12}\) and \(\frac{1}{20}\). The least common multiple of 12 and 20 is 60.

\(\frac{1}{12}=\frac{1\times5}{12\times5}=\frac{5}{60}\), \(\frac{1}{20}=\frac{1\times3}{20\times3}=\frac{3}{60}\)

Step8: Add the fractions.

\(\frac{5}{60}+\frac{3}{60}=\frac{5+3}{60}=\frac{8}{60}=\frac{2}{15}\) (simplified)

Step9: Find a common denominator for \(\frac{1}{13}\) and \(\frac{3}{26}\). The least common multiple of 13 and 26 is 26.

\(\frac{1}{13}=\frac{1\times2}{13\times2}=\frac{2}{26}\)

Step10: Add the fractions.

\(\frac{2}{26}+\frac{3}{26}=\frac{2 + 3}{26}=\frac{5}{26}\)

Answer:

(1) \(\boldsymbol{\frac{13}{30}}\)
(2) \(\boldsymbol{\frac{5}{36}}\)
(3) \(\boldsymbol{\frac{13}{20}}\)
(4) \(\boldsymbol{\frac{2}{15}}\)
(5) \(\boldsymbol{\frac{5}{26}}\)