Solve 2/3+1/5*2/3frac{6/7}{frac{4}{3}}

$$\frac{ 2 }{ 3 } + \frac{ 1 }{ 5 } \times \frac{ \frac{ 2 }{ 3 } \frac{ 6 }{ 7 } }{ \frac{ 4 }{ 3 } }$$

Evaluate

$$\frac{79}{105}\approx 0.752380952$$

Solution Steps

Multiply \frac{2}{3} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}+\frac{1}{5}\times \frac{\frac{2\times 6}{3\times 7}}{\frac{4}{3}}$$

Do the multiplications in the fraction \frac{2\times 6}{3\times 7}.

$$\frac{2}{3}+\frac{1}{5}\times \frac{\frac{12}{21}}{\frac{4}{3}}$$

Reduce the fraction \frac{12}{21} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}+\frac{1}{5}\times \frac{\frac{4}{7}}{\frac{4}{3}}$$

Divide \frac{4}{7} by \frac{4}{3} by multiplying \frac{4}{7} by the reciprocal of \frac{4}{3}.

$$\frac{2}{3}+\frac{1}{5}\times \frac{4}{7}\times \frac{3}{4}$$

Multiply \frac{4}{7} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}+\frac{1}{5}\times \frac{4\times 3}{7\times 4}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2}{3}+\frac{1}{5}\times \frac{3}{7}$$

Multiply \frac{1}{5} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}+\frac{1\times 3}{5\times 7}$$

Do the multiplications in the fraction \frac{1\times 3}{5\times 7}.

$$\frac{2}{3}+\frac{3}{35}$$

Least common multiple of 3 and 35 is 105. Convert \frac{2}{3} and \frac{3}{35} to fractions with denominator 105.

$$\frac{70}{105}+\frac{9}{105}$$

Since \frac{70}{105} and \frac{9}{105} have the same denominator, add them by adding their numerators.

$$\frac{70+9}{105}$$

Add 70 and 9 to get 79.

$$\frac{79}{105}$$

Factor

$$\frac{79}{3 \cdot 5 \cdot 7} = 0.7523809523809524$$