Solve (81/5+41/5)-(66/8-62/4)

$$( 8 \frac { 1 } { 5 } + 4 \frac { 1 } { 5 } ) - ( 6 \frac { 6 } { 8 } - 6 \frac { 2 } { 4 } )$$

Evaluate

$$\frac{243}{20}=12.15$$

Solution Steps

Multiply 8 and 5 to get 40.

$$\frac{40+1}{5}+\frac{4\times 5+1}{5}-\left(\frac{6\times 8+6}{8}-\frac{6\times 4+2}{4}\right)$$

Add 40 and 1 to get 41.

$$\frac{41}{5}+\frac{4\times 5+1}{5}-\left(\frac{6\times 8+6}{8}-\frac{6\times 4+2}{4}\right)$$

Multiply 4 and 5 to get 20.

$$\frac{41}{5}+\frac{20+1}{5}-\left(\frac{6\times 8+6}{8}-\frac{6\times 4+2}{4}\right)$$

Add 20 and 1 to get 21.

$$\frac{41}{5}+\frac{21}{5}-\left(\frac{6\times 8+6}{8}-\frac{6\times 4+2}{4}\right)$$

Since \frac{41}{5} and \frac{21}{5} have the same denominator, add them by adding their numerators.

$$\frac{41+21}{5}-\left(\frac{6\times 8+6}{8}-\frac{6\times 4+2}{4}\right)$$

Add 41 and 21 to get 62.

$$\frac{62}{5}-\left(\frac{6\times 8+6}{8}-\frac{6\times 4+2}{4}\right)$$

Multiply 6 and 8 to get 48.

$$\frac{62}{5}-\left(\frac{48+6}{8}-\frac{6\times 4+2}{4}\right)$$

Add 48 and 6 to get 54.

$$\frac{62}{5}-\left(\frac{54}{8}-\frac{6\times 4+2}{4}\right)$$

Reduce the fraction \frac{54}{8} to lowest terms by extracting and canceling out 2.

$$\frac{62}{5}-\left(\frac{27}{4}-\frac{6\times 4+2}{4}\right)$$

Multiply 6 and 4 to get 24.

$$\frac{62}{5}-\left(\frac{27}{4}-\frac{24+2}{4}\right)$$

Add 24 and 2 to get 26.

$$\frac{62}{5}-\left(\frac{27}{4}-\frac{26}{4}\right)$$

Since \frac{27}{4} and \frac{26}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{62}{5}-\frac{27-26}{4}$$

Subtract 26 from 27 to get 1.

$$\frac{62}{5}-\frac{1}{4}$$

Least common multiple of 5 and 4 is 20. Convert \frac{62}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{248}{20}-\frac{5}{20}$$

Since \frac{248}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{248-5}{20}$$

Subtract 5 from 248 to get 243.

$$\frac{243}{20}$$

Factor

$$\frac{3 ^ {5}}{2 ^ {2} \cdot 5} = 12\frac{3}{20} = 12.15$$