Solve 4a-7b/8a-8a-8b/8a

$$\frac { 4 a - 7 b } { 8 a } - \frac { 8 a - 8 b } { 8 a }$$

Evaluate

$$\frac{b}{8a}-\frac{1}{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8a-8b}{8a}.

$$\frac{4a-7b}{8a}-\frac{8\left(a-b\right)}{8a}$$

Cancel out 8 in both numerator and denominator.

$$\frac{4a-7b}{8a}-\frac{a-b}{a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8a and a is 8a. Multiply \frac{a-b}{a} times \frac{8}{8}.

$$\frac{4a-7b}{8a}-\frac{8\left(a-b\right)}{8a}$$

Since \frac{4a-7b}{8a} and \frac{8\left(a-b\right)}{8a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a-7b-8\left(a-b\right)}{8a}$$

Do the multiplications in 4a-7b-8\left(a-b\right).

$$\frac{4a-7b-8a+8b}{8a}$$

Combine like terms in 4a-7b-8a+8b.

$$\frac{-4a+b}{8a}$$

Expand

$$\frac{b}{8a}-\frac{1}{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8a-8b}{8a}.

$$\frac{4a-7b}{8a}-\frac{8\left(a-b\right)}{8a}$$

Cancel out 8 in both numerator and denominator.

$$\frac{4a-7b}{8a}-\frac{a-b}{a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8a and a is 8a. Multiply \frac{a-b}{a} times \frac{8}{8}.

$$\frac{4a-7b}{8a}-\frac{8\left(a-b\right)}{8a}$$

Since \frac{4a-7b}{8a} and \frac{8\left(a-b\right)}{8a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a-7b-8\left(a-b\right)}{8a}$$

Do the multiplications in 4a-7b-8\left(a-b\right).

$$\frac{4a-7b-8a+8b}{8a}$$

Combine like terms in 4a-7b-8a+8b.

$$\frac{-4a+b}{8a}$$