Solve 23^2/4-43/4-10

$$2 \frac { 3 ^ { 2 } } { 4 } - 4 \frac { 3 } { 4 } - 10$$

Evaluate

$$-\frac{41}{4}=-10.25$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$2\times \frac{9}{4}-\frac{4\times 4+3}{4}-10$$

Express 2\times \frac{9}{4} as a single fraction.

$$\frac{2\times 9}{4}-\frac{4\times 4+3}{4}-10$$

Multiply 2 and 9 to get 18.

$$\frac{18}{4}-\frac{4\times 4+3}{4}-10$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{9}{2}-\frac{4\times 4+3}{4}-10$$

Multiply 4 and 4 to get 16.

$$\frac{9}{2}-\frac{16+3}{4}-10$$

Add 16 and 3 to get 19.

$$\frac{9}{2}-\frac{19}{4}-10$$

Least common multiple of 2 and 4 is 4. Convert \frac{9}{2} and \frac{19}{4} to fractions with denominator 4.

$$\frac{18}{4}-\frac{19}{4}-10$$

Since \frac{18}{4} and \frac{19}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-19}{4}-10$$

Subtract 19 from 18 to get -1.

$$-\frac{1}{4}-10$$

Convert 10 to fraction \frac{40}{4}.

$$-\frac{1}{4}-\frac{40}{4}$$

Since -\frac{1}{4} and \frac{40}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-40}{4}$$

Subtract 40 from -1 to get -41.

$$-\frac{41}{4}$$

Factor

$$-\frac{41}{4} = -10\frac{1}{4} = -10.25$$