Solve 10-7/8+4{frac{3/4+frac{1{2}}}}

$$10- \frac{ 7 }{ 8+ \frac{ 4 }{ \frac{ 3 }{ 4+ \frac{ 1 }{ 2 } } } }$$

Evaluate

$$\frac{19}{2}=9.5$$

Solution Steps

Divide 4 by \frac{3}{4+\frac{1}{2}} by multiplying 4 by the reciprocal of \frac{3}{4+\frac{1}{2}}.

$$10-\frac{7}{8+\frac{4\left(4+\frac{1}{2}\right)}{3}}$$

Convert 4 to fraction \frac{8}{2}.

$$10-\frac{7}{8+\frac{4\left(\frac{8}{2}+\frac{1}{2}\right)}{3}}$$

Since \frac{8}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$10-\frac{7}{8+\frac{4\times \frac{8+1}{2}}{3}}$$

Add 8 and 1 to get 9.

$$10-\frac{7}{8+\frac{4\times \frac{9}{2}}{3}}$$

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

$$10-\frac{7}{8+\frac{\frac{4\times 9}{2}}{3}}$$

Multiply 4 and 9 to get 36.

$$10-\frac{7}{8+\frac{\frac{36}{2}}{3}}$$

Divide 36 by 2 to get 18.

$$10-\frac{7}{8+\frac{18}{3}}$$

Divide 18 by 3 to get 6.

$$10-\frac{7}{8+6}$$

Add 8 and 6 to get 14.

$$10-\frac{7}{14}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$10-\frac{1}{2}$$

Convert 10 to fraction \frac{20}{2}.

$$\frac{20}{2}-\frac{1}{2}$$

Since \frac{20}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-1}{2}$$

Subtract 1 from 20 to get 19.

$$\frac{19}{2}$$

Factor

$$\frac{19}{2} = 9\frac{1}{2} = 9.5$$