Solve (22/3div5/8)+(22/5*5/6)

$$( 2 \frac { 2 } { 3 } \div \frac{ 5 }{ 8 } )+( 2 \frac { 2 } { 5 } \times \frac{ 5 }{ 6 } )$$

Evaluate

$$\frac{94}{15}\approx 6.266666667$$

Solution Steps

Divide \frac{2\times 3+2}{3} by \frac{5}{8} by multiplying \frac{2\times 3+2}{3} by the reciprocal of \frac{5}{8}.

$$\frac{\left(2\times 3+2\right)\times 8}{3\times 5}+\frac{2\times 5+2}{5}\times \frac{5}{6}$$

Multiply 2 and 3 to get 6.

$$\frac{\left(6+2\right)\times 8}{3\times 5}+\frac{2\times 5+2}{5}\times \frac{5}{6}$$

Add 6 and 2 to get 8.

$$\frac{8\times 8}{3\times 5}+\frac{2\times 5+2}{5}\times \frac{5}{6}$$

Multiply 8 and 8 to get 64.

$$\frac{64}{3\times 5}+\frac{2\times 5+2}{5}\times \frac{5}{6}$$

Multiply 3 and 5 to get 15.

$$\frac{64}{15}+\frac{2\times 5+2}{5}\times \frac{5}{6}$$

Multiply 2 and 5 to get 10.

$$\frac{64}{15}+\frac{10+2}{5}\times \frac{5}{6}$$

Add 10 and 2 to get 12.

$$\frac{64}{15}+\frac{12}{5}\times \frac{5}{6}$$

Multiply \frac{12}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{64}{15}+\frac{12\times 5}{5\times 6}$$

Cancel out 5 in both numerator and denominator.

$$\frac{64}{15}+\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$\frac{64}{15}+2$$

Convert 2 to fraction \frac{30}{15}.

$$\frac{64}{15}+\frac{30}{15}$$

Since \frac{64}{15} and \frac{30}{15} have the same denominator, add them by adding their numerators.

$$\frac{64+30}{15}$$

Add 64 and 30 to get 94.

$$\frac{94}{15}$$

Factor

$$\frac{2 \cdot 47}{3 \cdot 5} = 6\frac{4}{15} = 6.266666666666667$$