Solve 2(1/4)+1/3(frac{1{4})-1}

$$\frac { 2 ( \frac { 1 } { 4 } ) + 1 } { 3 ( \frac { 1 } { 4 } ) - 1 }$$

Evaluate

$$-6$$

Solution Steps

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Add 1 and 2 to get 3.

$$\frac{\frac{3}{2}}{3\times \frac{1}{4}-1}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{\frac{3}{2}}{\frac{3}{4}-1}$$

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

$$\frac{\frac{3}{2}}{\frac{3}{4}-\frac{4}{4}}$$

Since \frac{3}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{2}}{\frac{3-4}{4}}$$

Subtract 4 from 3 to get -1.

$$\frac{\frac{3}{2}}{-\frac{1}{4}}$$

Divide \frac{3}{2} by -\frac{1}{4} by multiplying \frac{3}{2} by the reciprocal of -\frac{1}{4}.

$$\frac{3}{2}\left(-4\right)$$

Express \frac{3}{2}\left(-4\right) as a single fraction.

$$\frac{3\left(-4\right)}{2}$$

Multiply 3 and -4 to get -12.

$$\frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$-6$$

Factor

$$-6$$