Solve 31/8div21/4*44/5

$$3 \frac { 1 } { 8 } \div 2 \frac { 1 } { 4 } \times 4 \frac { 4 } { 5 }$$

Evaluate

$$\frac{20}{3}\approx 6.666666667$$

Solution Steps

Divide \frac{3\times 8+1}{8} by \frac{2\times 4+1}{4} by multiplying \frac{3\times 8+1}{8} by the reciprocal of \frac{2\times 4+1}{4}.

$$\frac{\left(3\times 8+1\right)\times 4}{8\left(2\times 4+1\right)}\times \frac{4\times 5+4}{5}$$

Cancel out 4 in both numerator and denominator.

$$\frac{1+3\times 8}{2\left(1+2\times 4\right)}\times \frac{4\times 5+4}{5}$$

Multiply 3 and 8 to get 24.

$$\frac{1+24}{2\left(1+2\times 4\right)}\times \frac{4\times 5+4}{5}$$

Add 1 and 24 to get 25.

$$\frac{25}{2\left(1+2\times 4\right)}\times \frac{4\times 5+4}{5}$$

Multiply 2 and 4 to get 8.

$$\frac{25}{2\left(1+8\right)}\times \frac{4\times 5+4}{5}$$

Add 1 and 8 to get 9.

$$\frac{25}{2\times 9}\times \frac{4\times 5+4}{5}$$

Multiply 2 and 9 to get 18.

$$\frac{25}{18}\times \frac{4\times 5+4}{5}$$

Multiply 4 and 5 to get 20.

$$\frac{25}{18}\times \frac{20+4}{5}$$

Add 20 and 4 to get 24.

$$\frac{25}{18}\times \frac{24}{5}$$

Multiply \frac{25}{18} times \frac{24}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 24}{18\times 5}$$

Do the multiplications in the fraction \frac{25\times 24}{18\times 5}.

$$\frac{600}{90}$$

Reduce the fraction \frac{600}{90} to lowest terms by extracting and canceling out 30.

$$\frac{20}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{3} = 6\frac{2}{3} = 6.666666666666667$$