Solve (5/6)^2-2*5/6+7

$$( \frac { 5 } { 6 } ) ^ { 2 } - \frac { 2 \times 5 } { 6 } + 7$$

Evaluate

$$\frac{217}{36}\approx 6.027777778$$

Solution Steps

Calculate \frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$\frac{25}{36}-\frac{2\times 5}{6}+7$$

Multiply 2 and 5 to get 10.

$$\frac{25}{36}-\frac{10}{6}+7$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{25}{36}-\frac{5}{3}+7$$

Least common multiple of 36 and 3 is 36. Convert \frac{25}{36} and \frac{5}{3} to fractions with denominator 36.

$$\frac{25}{36}-\frac{60}{36}+7$$

Since \frac{25}{36} and \frac{60}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-60}{36}+7$$

Subtract 60 from 25 to get -35.

$$-\frac{35}{36}+7$$

Convert 7 to fraction \frac{252}{36}.

$$-\frac{35}{36}+\frac{252}{36}$$

Since -\frac{35}{36} and \frac{252}{36} have the same denominator, add them by adding their numerators.

$$\frac{-35+252}{36}$$

Add -35 and 252 to get 217.

$$\frac{217}{36}$$

Factor

$$\frac{7 \cdot 31}{2 ^ {2} \cdot 3 ^ {2}} = 6\frac{1}{36} = 6.027777777777778$$