Solve (75/1-53/4):21/2

$$( 7 \frac { 5 } { 1 } - 5 \frac { 3 } { 4 } ) : 2 \frac { 1 } { 2 }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Multiply 7 and 1 to get 7.

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

Add 7 and 5 to get 12.

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

Anything divided by one gives itself.

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

Multiply 5 and 4 to get 20.

$$\frac{12-\frac{20+3}{4}}{\frac{2\times 2+1}{2}}$$

Add 20 and 3 to get 23.

$$\frac{12-\frac{23}{4}}{\frac{2\times 2+1}{2}}$$

Convert 12 to fraction \frac{48}{4}.

$$\frac{\frac{48}{4}-\frac{23}{4}}{\frac{2\times 2+1}{2}}$$

Since \frac{48}{4} and \frac{23}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{48-23}{4}}{\frac{2\times 2+1}{2}}$$

Subtract 23 from 48 to get 25.

$$\frac{\frac{25}{4}}{\frac{2\times 2+1}{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{25}{4}}{\frac{4+1}{2}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{25}{4}}{\frac{5}{2}}$$

Divide \frac{25}{4} by \frac{5}{2} by multiplying \frac{25}{4} by the reciprocal of \frac{5}{2}.

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

Multiply \frac{25}{4} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{25\times 2}{4\times 5}.

$$\frac{50}{20}$$

Reduce the fraction \frac{50}{20} to lowest terms by extracting and canceling out 10.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$