Solve (61/2-83/4):1/8+113/7

$$( 6 \frac { 1 } { 2 } - 8 \frac { 3 } { 4 } ) : \frac { 1 } { 8 } + 11 \frac { 3 } { 7 }$$

Evaluate

$$-\frac{46}{7}\approx -6.571428571$$

Solution Steps

Multiply 6 and 2 to get 12.

$$\frac{\frac{12+1}{2}-\frac{8\times 4+3}{4}}{\frac{1}{8}}+\frac{11\times 7+3}{7}$$

Add 12 and 1 to get 13.

$$\frac{\frac{13}{2}-\frac{8\times 4+3}{4}}{\frac{1}{8}}+\frac{11\times 7+3}{7}$$

Multiply 8 and 4 to get 32.

$$\frac{\frac{13}{2}-\frac{32+3}{4}}{\frac{1}{8}}+\frac{11\times 7+3}{7}$$

Add 32 and 3 to get 35.

$$\frac{\frac{13}{2}-\frac{35}{4}}{\frac{1}{8}}+\frac{11\times 7+3}{7}$$

Least common multiple of 2 and 4 is 4. Convert \frac{13}{2} and \frac{35}{4} to fractions with denominator 4.

$$\frac{\frac{26}{4}-\frac{35}{4}}{\frac{1}{8}}+\frac{11\times 7+3}{7}$$

Since \frac{26}{4} and \frac{35}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{26-35}{4}}{\frac{1}{8}}+\frac{11\times 7+3}{7}$$

Subtract 35 from 26 to get -9.

$$\frac{-\frac{9}{4}}{\frac{1}{8}}+\frac{11\times 7+3}{7}$$

Divide -\frac{9}{4} by \frac{1}{8} by multiplying -\frac{9}{4} by the reciprocal of \frac{1}{8}.

$$-\frac{9}{4}\times 8+\frac{11\times 7+3}{7}$$

Express -\frac{9}{4}\times 8 as a single fraction.

$$\frac{-9\times 8}{4}+\frac{11\times 7+3}{7}$$

Multiply -9 and 8 to get -72.

$$\frac{-72}{4}+\frac{11\times 7+3}{7}$$

Divide -72 by 4 to get -18.

$$-18+\frac{11\times 7+3}{7}$$

Multiply 11 and 7 to get 77.

$$-18+\frac{77+3}{7}$$

Add 77 and 3 to get 80.

$$-18+\frac{80}{7}$$

Convert -18 to fraction -\frac{126}{7}.

$$-\frac{126}{7}+\frac{80}{7}$$

Since -\frac{126}{7} and \frac{80}{7} have the same denominator, add them by adding their numerators.

$$\frac{-126+80}{7}$$

Add -126 and 80 to get -46.

$$-\frac{46}{7}$$

Factor

$$-\frac{46}{7} = -6\frac{4}{7} = -6.571428571428571$$