Solve a/8-15/4+b/2-2

$$\frac { a } { 8 } - \frac { 15 } { 4 } + \frac { b } { 2 } - 2$$

Evaluate

$$\frac{a+4b-46}{8}$$

Short Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\frac{a}{8}-\frac{15}{4}+\frac{b}{2}-\frac{8}{4}$$

Since -\frac{15}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a}{8}+\frac{-15-8}{4}+\frac{b}{2}$$

Subtract 8 from -15 to get -23.

$$\frac{a}{8}-\frac{23}{4}+\frac{b}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 4 is 8. Multiply \frac{23}{4} times \frac{2}{2}.

$$\frac{a}{8}-\frac{23\times 2}{8}+\frac{b}{2}$$

Since \frac{a}{8} and \frac{23\times 2}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a-23\times 2}{8}+\frac{b}{2}$$

Do the multiplications in a-23\times 2.

$$\frac{a-46}{8}+\frac{b}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 2 is 8. Multiply \frac{b}{2} times \frac{4}{4}.

$$\frac{a-46}{8}+\frac{4b}{8}$$

Since \frac{a-46}{8} and \frac{4b}{8} have the same denominator, add them by adding their numerators.

$$\frac{a-46+4b}{8}$$

Factor

$$\frac{a+4b-46}{8}$$

Solution Steps

Factor out \frac{1}{8}.

$$\frac{a-46+4b}{8}$$

Consider a-30+4b-16. Multiply and combine like terms.

$$a+4b-46$$

Rewrite the complete factored expression.

$$\frac{a+4b-46}{8}$$