Solve 1/16+7/8-5(1/2)+3/4-sqrt{64}

$$\frac { 1 } { 16 } + \frac { 7 } { 8 } - 5 ( \frac { 1 } { 2 } ) + \frac { 3 } { 4 } - \sqrt { 64 }$$

Evaluate

$$-\frac{141}{16}=-8.8125$$

Solution Steps

Least common multiple of 16 and 8 is 16. Convert \frac{1}{16} and \frac{7}{8} to fractions with denominator 16.

$$\frac{1}{16}+\frac{14}{16}-5\times \frac{1}{2}+\frac{3}{4}-\sqrt{64}$$

Since \frac{1}{16} and \frac{14}{16} have the same denominator, add them by adding their numerators.

$$\frac{1+14}{16}-5\times \frac{1}{2}+\frac{3}{4}-\sqrt{64}$$

Add 1 and 14 to get 15.

$$\frac{15}{16}-5\times \frac{1}{2}+\frac{3}{4}-\sqrt{64}$$

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

$$\frac{15}{16}-\frac{5}{2}+\frac{3}{4}-\sqrt{64}$$

Least common multiple of 16 and 2 is 16. Convert \frac{15}{16} and \frac{5}{2} to fractions with denominator 16.

$$\frac{15}{16}-\frac{40}{16}+\frac{3}{4}-\sqrt{64}$$

Since \frac{15}{16} and \frac{40}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-40}{16}+\frac{3}{4}-\sqrt{64}$$

Subtract 40 from 15 to get -25.

$$-\frac{25}{16}+\frac{3}{4}-\sqrt{64}$$

Least common multiple of 16 and 4 is 16. Convert -\frac{25}{16} and \frac{3}{4} to fractions with denominator 16.

$$-\frac{25}{16}+\frac{12}{16}-\sqrt{64}$$

Since -\frac{25}{16} and \frac{12}{16} have the same denominator, add them by adding their numerators.

$$\frac{-25+12}{16}-\sqrt{64}$$

Add -25 and 12 to get -13.

$$-\frac{13}{16}-\sqrt{64}$$

Calculate the square root of 64 and get 8.

$$-\frac{13}{16}-8$$

Convert 8 to fraction \frac{128}{16}.

$$-\frac{13}{16}-\frac{128}{16}$$

Since -\frac{13}{16} and \frac{128}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-13-128}{16}$$

Subtract 128 from -13 to get -141.

$$-\frac{141}{16}$$

Factor

$$-\frac{141}{16} = -8\frac{13}{16} = -8.8125$$