Question

5.
$\frac{3}{4} + \frac{5}{8}$ =

7.
$\frac{5}{6} + \frac{4}{5}$ =

9.
$\frac{3}{5} + \frac{1}{3}$ =

Explanation:

Problem 5: $\boldsymbol{\frac{3}{4} + \frac{5}{8}}$

Step1: Find a common denominator

The denominators are 4 and 8. The least common denominator (LCD) of 4 and 8 is 8.
Rewrite $\frac{3}{4}$ with denominator 8: $\frac{3}{4} = \frac{3\times2}{4\times2} = \frac{6}{8}$

Step2: Add the fractions

Now add $\frac{6}{8}$ and $\frac{5}{8}$: $\frac{6}{8} + \frac{5}{8} = \frac{6 + 5}{8} = \frac{11}{8}$ (or $1\frac{3}{8}$)

Step1: Find a common denominator

The denominators are 6 and 5. The LCD of 6 and 5 is 30.
Rewrite $\frac{5}{6}$: $\frac{5}{6} = \frac{5\times5}{6\times5} = \frac{25}{30}$
Rewrite $\frac{4}{5}$: $\frac{4}{5} = \frac{4\times6}{5\times6} = \frac{24}{30}$

Step2: Add the fractions

Add $\frac{25}{30}$ and $\frac{24}{30}$: $\frac{25}{30} + \frac{24}{30} = \frac{25 + 24}{30} = \frac{49}{30}$ (or $1\frac{19}{30}$)

Step1: Find a common denominator

The denominators are 5 and 3. The LCD of 5 and 3 is 15.
Rewrite $\frac{3}{5}$: $\frac{3}{5} = \frac{3\times3}{5\times3} = \frac{9}{15}$
Rewrite $\frac{1}{3}$: $\frac{1}{3} = \frac{1\times5}{3\times5} = \frac{5}{15}$

Step2: Add the fractions

Add $\frac{9}{15}$ and $\frac{5}{15}$: $\frac{9}{15} + \frac{5}{15} = \frac{9 + 5}{15} = \frac{14}{15}$

Answer:

$\frac{11}{8}$ (or $1\frac{3}{8}$)

Problem 7: $\boldsymbol{\frac{5}{6} + \frac{4}{5}}$