Solve (1/2a-1/3b-1/4c)-(1/3a-frac{1}{4}b-frac{1}{5}c)

$$( \frac { 1 } { 2 } a - \frac { 1 } { 3 } b - \frac { 1 } { 4 } c ) - ( \frac { 1 } { 3 } a - \frac { 1 } { 4 } b - \frac { 1 } { 5 } c )$$

Evaluate

$$\frac{a}{6}-\frac{b}{12}-\frac{c}{20}$$

Solution Steps

To find the opposite of \frac{1}{3}a-\frac{1}{4}b-\frac{1}{5}c, find the opposite of each term.

$$\frac{1}{2}a-\frac{1}{3}b-\frac{1}{4}c-\frac{1}{3}a-\left(-\frac{1}{4}b\right)-\left(-\frac{1}{5}c\right)$$

The opposite of -\frac{1}{4}b is \frac{1}{4}b.

$$\frac{1}{2}a-\frac{1}{3}b-\frac{1}{4}c-\frac{1}{3}a+\frac{1}{4}b-\left(-\frac{1}{5}c\right)$$

The opposite of -\frac{1}{5}c is \frac{1}{5}c.

$$\frac{1}{2}a-\frac{1}{3}b-\frac{1}{4}c-\frac{1}{3}a+\frac{1}{4}b+\frac{1}{5}c$$

Combine \frac{1}{2}a and -\frac{1}{3}a to get \frac{1}{6}a.

$$\frac{1}{6}a-\frac{1}{3}b-\frac{1}{4}c+\frac{1}{4}b+\frac{1}{5}c$$

Combine -\frac{1}{3}b and \frac{1}{4}b to get -\frac{1}{12}b.

$$\frac{1}{6}a-\frac{1}{12}b-\frac{1}{4}c+\frac{1}{5}c$$

Combine -\frac{1}{4}c and \frac{1}{5}c to get -\frac{1}{20}c.

$$\frac{1}{6}a-\frac{1}{12}b-\frac{1}{20}c$$

Expand

$$\frac{a}{6}-\frac{b}{12}-\frac{c}{20}$$

Solution Steps

To find the opposite of \frac{1}{3}a-\frac{1}{4}b-\frac{1}{5}c, find the opposite of each term.

$$\frac{1}{2}a-\frac{1}{3}b-\frac{1}{4}c-\frac{1}{3}a-\left(-\frac{1}{4}b\right)-\left(-\frac{1}{5}c\right)$$

The opposite of -\frac{1}{4}b is \frac{1}{4}b.

$$\frac{1}{2}a-\frac{1}{3}b-\frac{1}{4}c-\frac{1}{3}a+\frac{1}{4}b-\left(-\frac{1}{5}c\right)$$

The opposite of -\frac{1}{5}c is \frac{1}{5}c.

$$\frac{1}{2}a-\frac{1}{3}b-\frac{1}{4}c-\frac{1}{3}a+\frac{1}{4}b+\frac{1}{5}c$$

Combine \frac{1}{2}a and -\frac{1}{3}a to get \frac{1}{6}a.

$$\frac{1}{6}a-\frac{1}{3}b-\frac{1}{4}c+\frac{1}{4}b+\frac{1}{5}c$$

Combine -\frac{1}{3}b and \frac{1}{4}b to get -\frac{1}{12}b.

$$\frac{1}{6}a-\frac{1}{12}b-\frac{1}{4}c+\frac{1}{5}c$$

Combine -\frac{1}{4}c and \frac{1}{5}c to get -\frac{1}{20}c.

$$\frac{1}{6}a-\frac{1}{12}b-\frac{1}{20}c$$