Question

(6) \\(\frac{2}{15} + \frac{1}{18} =\\)
(7) \\(\frac{5}{14} + \frac{2}{21} =\\)
(8) \\(\frac{7}{15} + \frac{1}{30} =\\)
(9) \\(\frac{1}{16} + \frac{3}{32} =\\)
(10) \\(\frac{5}{12} + \frac{1}{36} =\\)
(11) \\(\frac{7}{18} + \frac{7}{36} =\\)

Explanation:

Step1: Solve \(\frac{2}{15}+\frac{1}{18}\)

Find the least common denominator (LCD) of 15 and 18. Prime factors of 15: \(3\times5\), prime factors of 18: \(2\times3^2\). LCD is \(2\times3^2\times5 = 90\).
Rewrite fractions: \(\frac{2\times6}{15\times6}=\frac{12}{90}\), \(\frac{1\times5}{18\times5}=\frac{5}{90}\).
Add: \(\frac{12 + 5}{90}=\frac{17}{90}\).

Step2: Solve \(\frac{5}{14}+\frac{2}{21}\)

LCD of 14 (\(2\times7\)) and 21 (\(3\times7\)) is \(2\times3\times7 = 42\).
Rewrite: \(\frac{5\times3}{14\times3}=\frac{15}{42}\), \(\frac{2\times2}{21\times2}=\frac{4}{42}\).
Add: \(\frac{15 + 4}{42}=\frac{19}{42}\).

Step3: Solve \(\frac{7}{15}+\frac{1}{30}\)

LCD of 15 and 30 is 30.
Rewrite: \(\frac{7\times2}{15\times2}=\frac{14}{30}\), \(\frac{1}{30}\) remains.
Add: \(\frac{14 + 1}{30}=\frac{15}{30}=\frac{1}{2}\).

Step4: Solve \(\frac{1}{16}+\frac{3}{32}\)

LCD of 16 and 32 is 32.
Rewrite: \(\frac{1\times2}{16\times2}=\frac{2}{32}\), \(\frac{3}{32}\) remains.
Add: \(\frac{2 + 3}{32}=\frac{5}{32}\).

Step5: Solve \(\frac{5}{12}+\frac{1}{36}\)

LCD of 12 and 36 is 36.
Rewrite: \(\frac{5\times3}{12\times3}=\frac{15}{36}\), \(\frac{1}{36}\) remains.
Add: \(\frac{15 + 1}{36}=\frac{16}{36}=\frac{4}{9}\).

Step6: Solve \(\frac{7}{18}+\frac{7}{36}\)

LCD of 18 and 36 is 36.
Rewrite: \(\frac{7\times2}{18\times2}=\frac{14}{36}\), \(\frac{7}{36}\) remains.
Add: \(\frac{14 + 7}{36}=\frac{21}{36}=\frac{7}{12}\).

Answer:

(6) \(\boldsymbol{\frac{17}{90}}\)
(7) \(\boldsymbol{\frac{19}{42}}\)
(8) \(\boldsymbol{\frac{1}{2}}\)
(9) \(\boldsymbol{\frac{5}{32}}\)
(10) \(\boldsymbol{\frac{4}{9}}\)
(11) \(\boldsymbol{\frac{7}{12}}\)