Solve 3(1/4+1/2)-2(1/4)^2=

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

Evaluate

$$\frac{17}{8}=2.125$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

$$3\left(\frac{1}{4}+\frac{2}{4}\right)-2\times \left(\frac{1}{4}\right)^{2}$$

Since \frac{1}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$3\times \frac{1+2}{4}-2\times \left(\frac{1}{4}\right)^{2}$$

Add 1 and 2 to get 3.

$$3\times \frac{3}{4}-2\times \left(\frac{1}{4}\right)^{2}$$

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

$$\frac{3\times 3}{4}-2\times \left(\frac{1}{4}\right)^{2}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{4}-2\times \left(\frac{1}{4}\right)^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{9}{4}-2\times \frac{1}{16}$$

Multiply 2 and \frac{1}{16} to get \frac{2}{16}.

$$\frac{9}{4}-\frac{2}{16}$$

Reduce the fraction \frac{2}{16} to lowest terms by extracting and canceling out 2.

$$\frac{9}{4}-\frac{1}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{9}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{18}{8}-\frac{1}{8}$$

Since \frac{18}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-1}{8}$$

Subtract 1 from 18 to get 17.

$$\frac{17}{8}$$

Factor

$$\frac{17}{2 ^ {3}} = 2\frac{1}{8} = 2.125$$