Solve 1/10(5p-1)-5/2p-p-3/5

$$\frac { 1 } { 10 } ( 5 p - 1 ) - \frac { 5 } { 2 } p - \frac { p - 3 } { 5 }$$

Evaluate

$$-\frac{11p}{5}+\frac{1}{2}$$

Short Solution Steps

Use the distributive property to multiply \frac{1}{10} by 5p-1.

$$\frac{1}{10}\times 5p+\frac{1}{10}\left(-1\right)-\frac{5}{2}p-\frac{p-3}{5}$$

Multiply \frac{1}{10} and 5 to get \frac{5}{10}.

$$\frac{5}{10}p+\frac{1}{10}\left(-1\right)-\frac{5}{2}p-\frac{p-3}{5}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}p+\frac{1}{10}\left(-1\right)-\frac{5}{2}p-\frac{p-3}{5}$$

Multiply \frac{1}{10} and -1 to get -\frac{1}{10}.

$$\frac{1}{2}p-\frac{1}{10}-\frac{5}{2}p-\frac{p-3}{5}$$

Combine \frac{1}{2}p and -\frac{5}{2}p to get -2p.

$$-2p-\frac{1}{10}-\frac{p-3}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 5 is 10. Multiply \frac{p-3}{5} times \frac{2}{2}.

$$-2p-\frac{1}{10}-\frac{2\left(p-3\right)}{10}$$

Since -\frac{1}{10} and \frac{2\left(p-3\right)}{10} have the same denominator, subtract them by subtracting their numerators.

$$-2p+\frac{-1-2\left(p-3\right)}{10}$$

Do the multiplications in -1-2\left(p-3\right).

$$-2p+\frac{-1-2p+6}{10}$$

Combine like terms in -1-2p+6.

$$-2p+\frac{5-2p}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2p times \frac{10}{10}.

$$\frac{10\left(-2\right)p}{10}+\frac{5-2p}{10}$$

Since \frac{10\left(-2\right)p}{10} and \frac{5-2p}{10} have the same denominator, add them by adding their numerators.

$$\frac{10\left(-2\right)p+5-2p}{10}$$

Do the multiplications in 10\left(-2\right)p+5-2p.

$$\frac{-20p+5-2p}{10}$$

Combine like terms in -20p+5-2p.

$$\frac{-22p+5}{10}$$

Expand

$$-\frac{11p}{5}+\frac{1}{2}$$

Short Solution Steps

Use the distributive property to multiply \frac{1}{10} by 5p-1.

$$\frac{1}{10}\times 5p+\frac{1}{10}\left(-1\right)-\frac{5}{2}p-\frac{p-3}{5}$$

Multiply \frac{1}{10} and 5 to get \frac{5}{10}.

$$\frac{5}{10}p+\frac{1}{10}\left(-1\right)-\frac{5}{2}p-\frac{p-3}{5}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}p+\frac{1}{10}\left(-1\right)-\frac{5}{2}p-\frac{p-3}{5}$$

Multiply \frac{1}{10} and -1 to get -\frac{1}{10}.

$$\frac{1}{2}p-\frac{1}{10}-\frac{5}{2}p-\frac{p-3}{5}$$

Combine \frac{1}{2}p and -\frac{5}{2}p to get -2p.

$$-2p-\frac{1}{10}-\frac{p-3}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 5 is 10. Multiply \frac{p-3}{5} times \frac{2}{2}.

$$-2p-\frac{1}{10}-\frac{2\left(p-3\right)}{10}$$

Since -\frac{1}{10} and \frac{2\left(p-3\right)}{10} have the same denominator, subtract them by subtracting their numerators.

$$-2p+\frac{-1-2\left(p-3\right)}{10}$$

Do the multiplications in -1-2\left(p-3\right).

$$-2p+\frac{-1-2p+6}{10}$$

Combine like terms in -1-2p+6.

$$-2p+\frac{5-2p}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2p times \frac{10}{10}.

$$\frac{10\left(-2\right)p}{10}+\frac{5-2p}{10}$$

Since \frac{10\left(-2\right)p}{10} and \frac{5-2p}{10} have the same denominator, add them by adding their numerators.

$$\frac{10\left(-2\right)p+5-2p}{10}$$

Do the multiplications in 10\left(-2\right)p+5-2p.

$$\frac{-20p+5-2p}{10}$$

Combine like terms in -20p+5-2p.

$$\frac{-22p+5}{10}$$