Solve (1/20ax-4/15a-1/5b)-(5/2b-frac{5}{10}ax-frac{1}{3}a)+(frac{5}{5}a+frac{-5}{10}b-frac{1}{2}ax

$$( \frac { 1 } { 20 } a x - \frac { 4 } { 15 } a - \frac { 1 } { 5 } b ) - ( \frac { 5 } { 2 } b - \frac { 5 } { 10 } a x - \frac { 1 } { 3 } a ) + ( \frac { 5 } { 5 } a + \frac { - 5 } { 10 } b - \frac { 1 } { 2 } a x$$

Evaluate

$$\frac{ax}{20}+\frac{16a}{15}-\frac{16b}{5}$$

Solution Steps

Divide 5 by 5 to get 1.

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{1}{5}b-\left(\frac{5}{2}b-\frac{5}{10}ax-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

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

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{1}{5}b-\left(\frac{5}{2}b-\frac{1}{2}ax-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

To find the opposite of \frac{5}{2}b-\frac{1}{2}ax-\frac{1}{3}a, find the opposite of each term.

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{1}{5}b-\frac{5}{2}b-\left(-\frac{1}{2}ax\right)-\left(-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

Combine -\frac{1}{5}b and -\frac{5}{2}b to get -\frac{27}{10}b.

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{27}{10}b-\left(-\frac{1}{2}ax\right)-\left(-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

The opposite of -\frac{1}{2}ax is \frac{1}{2}ax.

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{27}{10}b+\frac{1}{2}ax-\left(-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

Combine \frac{1}{20}ax and \frac{1}{2}ax to get \frac{11}{20}ax.

$$\frac{11}{20}ax-\frac{4}{15}a-\frac{27}{10}b-\left(-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

The opposite of -\frac{1}{3}a is \frac{1}{3}a.

$$\frac{11}{20}ax-\frac{4}{15}a-\frac{27}{10}b+\frac{1}{3}a+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

Combine -\frac{4}{15}a and \frac{1}{3}a to get \frac{1}{15}a.

$$\frac{11}{20}ax+\frac{1}{15}a-\frac{27}{10}b+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

Combine \frac{1}{15}a and 1a to get \frac{16}{15}a.

$$\frac{11}{20}ax+\frac{16}{15}a-\frac{27}{10}b+\frac{-5}{10}b-\frac{1}{2}ax$$

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

$$\frac{11}{20}ax+\frac{16}{15}a-\frac{27}{10}b-\frac{1}{2}b-\frac{1}{2}ax$$

Combine -\frac{27}{10}b and -\frac{1}{2}b to get -\frac{16}{5}b.

$$\frac{11}{20}ax+\frac{16}{15}a-\frac{16}{5}b-\frac{1}{2}ax$$

Combine \frac{11}{20}ax and -\frac{1}{2}ax to get \frac{1}{20}ax.

$$\frac{1}{20}ax+\frac{16}{15}a-\frac{16}{5}b$$

Expand

$$\frac{ax}{20}+\frac{16a}{15}-\frac{16b}{5}$$

Solution Steps

Divide 5 by 5 to get 1.

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{1}{5}b-\left(\frac{5}{2}b-\frac{5}{10}ax-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

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

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{1}{5}b-\left(\frac{5}{2}b-\frac{1}{2}ax-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

To find the opposite of \frac{5}{2}b-\frac{1}{2}ax-\frac{1}{3}a, find the opposite of each term.

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{1}{5}b-\frac{5}{2}b-\left(-\frac{1}{2}ax\right)-\left(-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

Combine -\frac{1}{5}b and -\frac{5}{2}b to get -\frac{27}{10}b.

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{27}{10}b-\left(-\frac{1}{2}ax\right)-\left(-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

The opposite of -\frac{1}{2}ax is \frac{1}{2}ax.

$$\frac{1}{20}ax-\frac{4}{15}a-\frac{27}{10}b+\frac{1}{2}ax-\left(-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

Combine \frac{1}{20}ax and \frac{1}{2}ax to get \frac{11}{20}ax.

$$\frac{11}{20}ax-\frac{4}{15}a-\frac{27}{10}b-\left(-\frac{1}{3}a\right)+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

The opposite of -\frac{1}{3}a is \frac{1}{3}a.

$$\frac{11}{20}ax-\frac{4}{15}a-\frac{27}{10}b+\frac{1}{3}a+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

Combine -\frac{4}{15}a and \frac{1}{3}a to get \frac{1}{15}a.

$$\frac{11}{20}ax+\frac{1}{15}a-\frac{27}{10}b+1a+\frac{-5}{10}b-\frac{1}{2}ax$$

Combine \frac{1}{15}a and 1a to get \frac{16}{15}a.

$$\frac{11}{20}ax+\frac{16}{15}a-\frac{27}{10}b+\frac{-5}{10}b-\frac{1}{2}ax$$

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

$$\frac{11}{20}ax+\frac{16}{15}a-\frac{27}{10}b-\frac{1}{2}b-\frac{1}{2}ax$$

Combine -\frac{27}{10}b and -\frac{1}{2}b to get -\frac{16}{5}b.

$$\frac{11}{20}ax+\frac{16}{15}a-\frac{16}{5}b-\frac{1}{2}ax$$

Combine \frac{11}{20}ax and -\frac{1}{2}ax to get \frac{1}{20}ax.

$$\frac{1}{20}ax+\frac{16}{15}a-\frac{16}{5}b$$