Solve (51/4div3/5*1/7)div5/8

$$( 5 \frac { 1 } { 4 } \div \frac{ 3 }{ 5 } \times \frac{ 1 }{ 7 } ) \div \frac{ 5 }{ 8 }$$

Evaluate

$$2$$

Solution Steps

Divide \frac{5\times 4+1}{4} by \frac{3}{5} by multiplying \frac{5\times 4+1}{4} by the reciprocal of \frac{3}{5}.

$$\frac{\frac{\left(5\times 4+1\right)\times 5}{4\times 3}\times \frac{1}{7}}{\frac{5}{8}}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{\left(20+1\right)\times 5}{4\times 3}\times \frac{1}{7}}{\frac{5}{8}}$$

Add 20 and 1 to get 21.

$$\frac{\frac{21\times 5}{4\times 3}\times \frac{1}{7}}{\frac{5}{8}}$$

Multiply 21 and 5 to get 105.

$$\frac{\frac{105}{4\times 3}\times \frac{1}{7}}{\frac{5}{8}}$$

Multiply 4 and 3 to get 12.

$$\frac{\frac{105}{12}\times \frac{1}{7}}{\frac{5}{8}}$$

Reduce the fraction \frac{105}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{35}{4}\times \frac{1}{7}}{\frac{5}{8}}$$

Multiply \frac{35}{4} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{35\times 1}{4\times 7}}{\frac{5}{8}}$$

Do the multiplications in the fraction \frac{35\times 1}{4\times 7}.

$$\frac{\frac{35}{28}}{\frac{5}{8}}$$

Reduce the fraction \frac{35}{28} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{5}{4}}{\frac{5}{8}}$$

Divide \frac{5}{4} by \frac{5}{8} by multiplying \frac{5}{4} by the reciprocal of \frac{5}{8}.

$$\frac{5}{4}\times \frac{8}{5}$$

Multiply \frac{5}{4} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 8}{4\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$2$$

Factor

$$2$$