Solve (2/3+4/5)div(4/4+2/3)

$$( \frac{ 2 }{ 3 } + \frac{ 4 }{ 5 } ) \div ( \frac{ 4 }{ 4 } + \frac{ 2 }{ 3 } )$$

Evaluate

$$\frac{22}{25}=0.88$$

Solution Steps

Divide 4 by 4 to get 1.

$$\frac{\frac{2}{3}+\frac{4}{5}}{1+\frac{2}{3}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{\frac{10}{15}+\frac{12}{15}}{1+\frac{2}{3}}$$

Since \frac{10}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+12}{15}}{1+\frac{2}{3}}$$

Add 10 and 12 to get 22.

$$\frac{\frac{22}{15}}{1+\frac{2}{3}}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{22}{15}}{\frac{3}{3}+\frac{2}{3}}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{22}{15}}{\frac{3+2}{3}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{22}{15}}{\frac{5}{3}}$$

Divide \frac{22}{15} by \frac{5}{3} by multiplying \frac{22}{15} by the reciprocal of \frac{5}{3}.

$$\frac{22}{15}\times \frac{3}{5}$$

Multiply \frac{22}{15} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 3}{15\times 5}$$

Do the multiplications in the fraction \frac{22\times 3}{15\times 5}.

$$\frac{66}{75}$$

Reduce the fraction \frac{66}{75} to lowest terms by extracting and canceling out 3.

$$\frac{22}{25}$$

Factor

$$\frac{2 \cdot 11}{5 ^ {2}} = 0.88$$