Solve 25-p/3-2p/9-5/3

$$25 - \frac { p } { 3 } - \frac { 2 p } { 9 } - \frac { 5 } { 3 }$$

Evaluate

$$-\frac{5p}{9}+\frac{70}{3}$$

Short Solution Steps

Convert 25 to fraction \frac{75}{3}.

$$\frac{75}{3}-\frac{p}{3}-\frac{2p}{9}-\frac{5}{3}$$

Since \frac{75}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-5}{3}-\frac{p}{3}-\frac{2p}{9}$$

Subtract 5 from 75 to get 70.

$$\frac{70}{3}-\frac{p}{3}-\frac{2p}{9}$$

Since \frac{70}{3} and \frac{p}{3} have the same denominator, add them by adding their numerators.

$$\frac{70+p}{3}-\frac{2p}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 9 is 9. Multiply \frac{70+p}{3} times \frac{3}{3}.

$$\frac{3\left(70+p\right)}{9}-\frac{2p}{9}$$

Since \frac{3\left(70+p\right)}{9} and \frac{2p}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(70+p\right)-2p}{9}$$

Do the multiplications in 3\left(70+p\right)-2p.

$$\frac{210+3p-2p}{9}$$

Combine like terms in 210+3p-2p.

$$\frac{210+p}{9}$$

Factor

$$\frac{5\left(42-p\right)}{9}$$

Solution Steps

Factor out \frac{1}{9}.

$$\frac{210-5p}{9}$$

Consider 225-3p-2p-15. Multiply and combine like terms.

$$-5p+210$$

Consider -5p+210. Factor out 5.

$$5\left(-p+42\right)$$

Rewrite the complete factored expression.

$$\frac{5\left(-p+42\right)}{9}$$