Solve 51/4-21/2frac{1{2}}

$$\frac { 5 \frac { 1 } { 4 } - 21 } { 2 \frac { 1 } { 2 } }$$

Evaluate

$$-\frac{63}{10}=-6.3$$

Solution Steps

Multiply 5 and 4 to get 20.

$$\frac{\frac{20+1}{4}-21}{\frac{2\times 2+1}{2}}$$

Add 20 and 1 to get 21.

$$\frac{\frac{21}{4}-21}{\frac{2\times 2+1}{2}}$$

Convert 21 to fraction \frac{84}{4}.

$$\frac{\frac{21}{4}-\frac{84}{4}}{\frac{2\times 2+1}{2}}$$

Since \frac{21}{4} and \frac{84}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21-84}{4}}{\frac{2\times 2+1}{2}}$$

Subtract 84 from 21 to get -63.

$$\frac{-\frac{63}{4}}{\frac{2\times 2+1}{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{-\frac{63}{4}}{\frac{4+1}{2}}$$

Add 4 and 1 to get 5.

$$\frac{-\frac{63}{4}}{\frac{5}{2}}$$

Divide -\frac{63}{4} by \frac{5}{2} by multiplying -\frac{63}{4} by the reciprocal of \frac{5}{2}.

$$-\frac{63}{4}\times \frac{2}{5}$$

Multiply -\frac{63}{4} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-63\times 2}{4\times 5}$$

Do the multiplications in the fraction \frac{-63\times 2}{4\times 5}.

$$\frac{-126}{20}$$

Reduce the fraction \frac{-126}{20} to lowest terms by extracting and canceling out 2.

$$-\frac{63}{10}$$

Factor

$$-\frac{63}{10} = -6\frac{3}{10} = -6.3$$