Solve 33/4+(-417/20)+8

$$3 \frac { 3 } { 4 } + ( - 4 \frac { 17 } { 20 } ) + 8$$

Evaluate

$$\frac{69}{10}=6.9$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{12+3}{4}-\frac{4\times 20+17}{20}+8$$

Add 12 and 3 to get 15.

$$\frac{15}{4}-\frac{4\times 20+17}{20}+8$$

Multiply 4 and 20 to get 80.

$$\frac{15}{4}-\frac{80+17}{20}+8$$

Add 80 and 17 to get 97.

$$\frac{15}{4}-\frac{97}{20}+8$$

Least common multiple of 4 and 20 is 20. Convert \frac{15}{4} and \frac{97}{20} to fractions with denominator 20.

$$\frac{75}{20}-\frac{97}{20}+8$$

Since \frac{75}{20} and \frac{97}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-97}{20}+8$$

Subtract 97 from 75 to get -22.

$$\frac{-22}{20}+8$$

Reduce the fraction \frac{-22}{20} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{10}+8$$

Convert 8 to fraction \frac{80}{10}.

$$-\frac{11}{10}+\frac{80}{10}$$

Since -\frac{11}{10} and \frac{80}{10} have the same denominator, add them by adding their numerators.

$$\frac{-11+80}{10}$$

Add -11 and 80 to get 69.

$$\frac{69}{10}$$

Factor

$$\frac{3 \cdot 23}{2 \cdot 5} = 6\frac{9}{10} = 6.9$$