Solve 2/5-1/15θ-1/20-7/60=

$$\frac { 2 } { 5 } - \frac { 1 } { 15 } \theta - \frac { 1 } { 20 } - \frac { 7 } { 60 } =$$

Evaluate

$$-\frac{\theta }{15}+\frac{7}{30}$$

Solution Steps

Least common multiple of 5 and 20 is 20. Convert \frac{2}{5} and \frac{1}{20} to fractions with denominator 20.

$$\frac{8}{20}-\frac{1}{15}\theta -\frac{1}{20}-\frac{7}{60}$$

Since \frac{8}{20} and \frac{1}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-1}{20}-\frac{1}{15}\theta -\frac{7}{60}$$

Subtract 1 from 8 to get 7.

$$\frac{7}{20}-\frac{1}{15}\theta -\frac{7}{60}$$

Least common multiple of 20 and 60 is 60. Convert \frac{7}{20} and \frac{7}{60} to fractions with denominator 60.

$$\frac{21}{60}-\frac{1}{15}\theta -\frac{7}{60}$$

Since \frac{21}{60} and \frac{7}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-7}{60}-\frac{1}{15}\theta$$

Subtract 7 from 21 to get 14.

$$\frac{14}{60}-\frac{1}{15}\theta$$

Reduce the fraction \frac{14}{60} to lowest terms by extracting and canceling out 2.

$$\frac{7}{30}-\frac{1}{15}\theta$$

Factor

$$\frac{7-2\theta }{30}$$

Solution Steps

Factor out \frac{1}{60}.

$$\frac{14-4\theta }{60}$$

Consider 24-4\theta -3-7. Multiply and combine like terms.

$$-4\theta +14$$

Consider -4\theta +14. Factor out 2.

$$2\left(-2\theta +7\right)$$

Rewrite the complete factored expression.

$$\frac{-2\theta +7}{30}$$