Solve 8.6*[7/8-(7/16-1/8)]

$$8.6 \times [ \frac { 7 } { 8 } - ( \frac { 7 } { 16 } - \frac { 1 } { 8 } ) ]$$

Evaluate

$$4.8375$$

Solution Steps

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

$$8.6\left(\frac{7}{8}-\left(\frac{7}{16}-\frac{2}{16}\right)\right)$$

Since \frac{7}{16} and \frac{2}{16} have the same denominator, subtract them by subtracting their numerators.

$$8.6\left(\frac{7}{8}-\frac{7-2}{16}\right)$$

Subtract 2 from 7 to get 5.

$$8.6\left(\frac{7}{8}-\frac{5}{16}\right)$$

Least common multiple of 8 and 16 is 16. Convert \frac{7}{8} and \frac{5}{16} to fractions with denominator 16.

$$8.6\left(\frac{14}{16}-\frac{5}{16}\right)$$

Since \frac{14}{16} and \frac{5}{16} have the same denominator, subtract them by subtracting their numerators.

$$8.6\times \frac{14-5}{16}$$

Subtract 5 from 14 to get 9.

$$8.6\times \frac{9}{16}$$

Convert decimal number 8.6 to fraction \frac{86}{10}. Reduce the fraction \frac{86}{10} to lowest terms by extracting and canceling out 2.

$$\frac{43}{5}\times \frac{9}{16}$$

Multiply \frac{43}{5} times \frac{9}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{43\times 9}{5\times 16}$$

Do the multiplications in the fraction \frac{43\times 9}{5\times 16}.

$$\frac{387}{80}$$

Factor

$$\frac{43 \cdot 3 ^ {2}}{5 \cdot 2 ^ {4}} = 4\frac{67}{80} = 4.8375$$