Solve -2(9/4)^2+9(9/4)-7

$$- 2 ( \frac { 9 } { 4 } ) ^ { 2 } + 9 ( \frac { 9 } { 4 } ) - 7$$

Evaluate

$$\frac{25}{8}=3.125$$

Solution Steps

Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.

$$-2\times \frac{81}{16}+9\times \frac{9}{4}-7$$

Express -2\times \frac{81}{16} as a single fraction.

$$\frac{-2\times 81}{16}+9\times \frac{9}{4}-7$$

Multiply -2 and 81 to get -162.

$$\frac{-162}{16}+9\times \frac{9}{4}-7$$

Reduce the fraction \frac{-162}{16} to lowest terms by extracting and canceling out 2.

$$-\frac{81}{8}+9\times \frac{9}{4}-7$$

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

$$-\frac{81}{8}+\frac{9\times 9}{4}-7$$

Multiply 9 and 9 to get 81.

$$-\frac{81}{8}+\frac{81}{4}-7$$

Least common multiple of 8 and 4 is 8. Convert -\frac{81}{8} and \frac{81}{4} to fractions with denominator 8.

$$-\frac{81}{8}+\frac{162}{8}-7$$

Since -\frac{81}{8} and \frac{162}{8} have the same denominator, add them by adding their numerators.

$$\frac{-81+162}{8}-7$$

Add -81 and 162 to get 81.

$$\frac{81}{8}-7$$

Convert 7 to fraction \frac{56}{8}.

$$\frac{81}{8}-\frac{56}{8}$$

Since \frac{81}{8} and \frac{56}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81-56}{8}$$

Subtract 56 from 81 to get 25.

$$\frac{25}{8}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {3}} = 3\frac{1}{8} = 3.125$$