Solve 61/422/15-51/3div8/9

$$6 \frac{ 1 }{ 4 } 2 \frac{ 2 }{ 15 } - 5 \frac { 1 } { 3 } \div \frac{ 8 }{ 9 }$$

Evaluate

$$\frac{22}{3}\approx 7.333333333$$

Solution Steps

Multiply 6 and 4 to get 24.

$$\frac{24+1}{4}\times \frac{2\times 15+2}{15}-\frac{\frac{5\times 3+1}{3}}{\frac{8}{9}}$$

Add 24 and 1 to get 25.

$$\frac{25}{4}\times \frac{2\times 15+2}{15}-\frac{\frac{5\times 3+1}{3}}{\frac{8}{9}}$$

Multiply 2 and 15 to get 30.

$$\frac{25}{4}\times \frac{30+2}{15}-\frac{\frac{5\times 3+1}{3}}{\frac{8}{9}}$$

Add 30 and 2 to get 32.

$$\frac{25}{4}\times \frac{32}{15}-\frac{\frac{5\times 3+1}{3}}{\frac{8}{9}}$$

Multiply \frac{25}{4} times \frac{32}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 32}{4\times 15}-\frac{\frac{5\times 3+1}{3}}{\frac{8}{9}}$$

Do the multiplications in the fraction \frac{25\times 32}{4\times 15}.

$$\frac{800}{60}-\frac{\frac{5\times 3+1}{3}}{\frac{8}{9}}$$

Reduce the fraction \frac{800}{60} to lowest terms by extracting and canceling out 20.

$$\frac{40}{3}-\frac{\frac{5\times 3+1}{3}}{\frac{8}{9}}$$

Divide \frac{5\times 3+1}{3} by \frac{8}{9} by multiplying \frac{5\times 3+1}{3} by the reciprocal of \frac{8}{9}.

$$\frac{40}{3}-\frac{\left(5\times 3+1\right)\times 9}{3\times 8}$$

Cancel out 3 in both numerator and denominator.

$$\frac{40}{3}-\frac{3\left(1+3\times 5\right)}{8}$$

Multiply 3 and 5 to get 15.

$$\frac{40}{3}-\frac{3\left(1+15\right)}{8}$$

Add 1 and 15 to get 16.

$$\frac{40}{3}-\frac{3\times 16}{8}$$

Multiply 3 and 16 to get 48.

$$\frac{40}{3}-\frac{48}{8}$$

Divide 48 by 8 to get 6.

$$\frac{40}{3}-6$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{40}{3}-\frac{18}{3}$$

Since \frac{40}{3} and \frac{18}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40-18}{3}$$

Subtract 18 from 40 to get 22.

$$\frac{22}{3}$$

Factor

$$\frac{2 \cdot 11}{3} = 7\frac{1}{3} = 7.333333333333333$$