Solve 71/2-81/5*61/4+21/10

$$7 \frac { 1 } { 2 } - 8 \frac { 1 } { 5 } * 6 \frac { 1 } { 4 } + 2 \frac { 1 } { 10 }$$

Evaluate

$$-\frac{833}{20}=-41.65$$

Solution Steps

Multiply 7 and 2 to get 14.

$$\frac{14+1}{2}-\frac{8\times 5+1}{5}\times \frac{6\times 4+1}{4}+\frac{2\times 10+1}{10}$$

Add 14 and 1 to get 15.

$$\frac{15}{2}-\frac{8\times 5+1}{5}\times \frac{6\times 4+1}{4}+\frac{2\times 10+1}{10}$$

Multiply 8 and 5 to get 40.

$$\frac{15}{2}-\frac{40+1}{5}\times \frac{6\times 4+1}{4}+\frac{2\times 10+1}{10}$$

Add 40 and 1 to get 41.

$$\frac{15}{2}-\frac{41}{5}\times \frac{6\times 4+1}{4}+\frac{2\times 10+1}{10}$$

Multiply 6 and 4 to get 24.

$$\frac{15}{2}-\frac{41}{5}\times \frac{24+1}{4}+\frac{2\times 10+1}{10}$$

Add 24 and 1 to get 25.

$$\frac{15}{2}-\frac{41}{5}\times \frac{25}{4}+\frac{2\times 10+1}{10}$$

Multiply \frac{41}{5} times \frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{2}-\frac{41\times 25}{5\times 4}+\frac{2\times 10+1}{10}$$

Do the multiplications in the fraction \frac{41\times 25}{5\times 4}.

$$\frac{15}{2}-\frac{1025}{20}+\frac{2\times 10+1}{10}$$

Reduce the fraction \frac{1025}{20} to lowest terms by extracting and canceling out 5.

$$\frac{15}{2}-\frac{205}{4}+\frac{2\times 10+1}{10}$$

Least common multiple of 2 and 4 is 4. Convert \frac{15}{2} and \frac{205}{4} to fractions with denominator 4.

$$\frac{30}{4}-\frac{205}{4}+\frac{2\times 10+1}{10}$$

Since \frac{30}{4} and \frac{205}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-205}{4}+\frac{2\times 10+1}{10}$$

Subtract 205 from 30 to get -175.

$$-\frac{175}{4}+\frac{2\times 10+1}{10}$$

Multiply 2 and 10 to get 20.

$$-\frac{175}{4}+\frac{20+1}{10}$$

Add 20 and 1 to get 21.

$$-\frac{175}{4}+\frac{21}{10}$$

Least common multiple of 4 and 10 is 20. Convert -\frac{175}{4} and \frac{21}{10} to fractions with denominator 20.

$$-\frac{875}{20}+\frac{42}{20}$$

Since -\frac{875}{20} and \frac{42}{20} have the same denominator, add them by adding their numerators.

$$\frac{-875+42}{20}$$

Add -875 and 42 to get -833.

$$-\frac{833}{20}$$

Factor

$$-\frac{833}{20} = -41\frac{13}{20} = -41.65$$