Question

8）\\(\frac{4}{5} + \frac{1}{10} =\\)\
9）\\(\frac{1}{15} + \frac{8}{10} =\\)\
10）\\(\frac{3}{7} + \frac{4}{14} =\\)

Explanation:

Problem 8: $\boldsymbol{\frac{4}{5} + \frac{1}{10}}$

Step1: Find a common denominator

The denominators are 5 and 10. The least common denominator (LCD) of 5 and 10 is 10. Rewrite $\frac{4}{5}$ with denominator 10: $\frac{4\times2}{5\times2}=\frac{8}{10}$.

Step2: Add the fractions

Now add $\frac{8}{10}$ and $\frac{1}{10}$: $\frac{8 + 1}{10}=\frac{9}{10}$.

Step1: Find a common denominator

The denominators are 15 and 10. The LCD of 15 and 10 is 30. Rewrite the fractions: $\frac{1\times2}{15\times2}=\frac{2}{30}$ and $\frac{8\times3}{10\times3}=\frac{24}{30}$.

Step2: Add the fractions

Add $\frac{2}{30}$ and $\frac{24}{30}$: $\frac{2 + 24}{30}=\frac{26}{30}$. Simplify by dividing numerator and denominator by 2: $\frac{13}{15}$.

Step1: Find a common denominator

The denominators are 7 and 14. The LCD of 7 and 14 is 14. Rewrite $\frac{3}{7}$ with denominator 14: $\frac{3\times2}{7\times2}=\frac{6}{14}$.

Step2: Add the fractions

Add $\frac{6}{14}$ and $\frac{4}{14}$: $\frac{6 + 4}{14}=\frac{10}{14}$. Simplify by dividing numerator and denominator by 2: $\frac{5}{7}$.

Answer:

$\frac{9}{10}$

Problem 9: $\boldsymbol{\frac{1}{15} + \frac{8}{10}}$