Solve 16|1/4-1|/frac{1{4}}

$$\frac { 16 | \frac { 1 } { 4 } - 1 | } { \frac { 1 } { 4 } }$$

Evaluate

$$48$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$\frac{16|\frac{1}{4}-\frac{4}{4}|}{\frac{1}{4}}$$

Since \frac{1}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16|\frac{1-4}{4}|}{\frac{1}{4}}$$

Subtract 4 from 1 to get -3.

$$\frac{16|-\frac{3}{4}|}{\frac{1}{4}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{3}{4} is \frac{3}{4}.

$$\frac{16\times \frac{3}{4}}{\frac{1}{4}}$$

Express 16\times \frac{3}{4} as a single fraction.

$$\frac{\frac{16\times 3}{4}}{\frac{1}{4}}$$

Multiply 16 and 3 to get 48.

$$\frac{\frac{48}{4}}{\frac{1}{4}}$$

Divide 48 by 4 to get 12.

$$\frac{12}{\frac{1}{4}}$$

Divide 12 by \frac{1}{4} by multiplying 12 by the reciprocal of \frac{1}{4}.

$$12\times 4$$

Multiply 12 and 4 to get 48.

$$48$$

Factor

$$2^{4}\times 3$$