Evaluate (1/4-1)(1/8+1/2)

$(\frac{1}{4} - 1) (\frac{1}{8} + \frac{1}{2})$

Step 1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{1}{4} - 1 \cdot \frac{4}{4}) (\frac{1}{8} + \frac{1}{2})$

Step 2

Combine $- 1$ and $\frac{4}{4}$ .

$(\frac{1}{4} + \frac{- 1 \cdot 4}{4}) (\frac{1}{8} + \frac{1}{2})$

Step 3

Combine the numerators over the common denominator.

$\frac{1 - 1 \cdot 4}{4} (\frac{1}{8} + \frac{1}{2})$

Step 4

Simplify the numerator.

Multiply $- 1$ by $4$ .

$\frac{1 - 4}{4} (\frac{1}{8} + \frac{1}{2})$

Subtract $4$ from $1$ .

$\frac{- 3}{4} (\frac{1}{8} + \frac{1}{2})$

Step 5

Move the negative in front of the fraction.

$- \frac{3}{4} (\frac{1}{8} + \frac{1}{2})$

Step 6

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{3}{4} (\frac{1}{8} + \frac{1}{2} \cdot \frac{4}{4})$

Step 7

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$- \frac{3}{4} (\frac{1}{8} + \frac{4}{2 \cdot 4})$

Multiply $2$ by $4$ .

$- \frac{3}{4} (\frac{1}{8} + \frac{4}{8})$

Step 8

Combine the numerators over the common denominator.

$- \frac{3}{4} \cdot \frac{1 + 4}{8}$

Step 9

Add $1$ and $4$ .

$- \frac{3}{4} \cdot \frac{5}{8}$

Step 10

Multiply $- \frac{3}{4} \cdot \frac{5}{8}$ .

Multiply $\frac{5}{8}$ by $\frac{3}{4}$ .

$- \frac{5 \cdot 3}{8 \cdot 4}$

Multiply $5$ by $3$ .

$- \frac{15}{8 \cdot 4}$

Multiply $8$ by $4$ .

$- \frac{15}{32}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{15}{32}$

Decimal Form:

$- 0.46875$

Evaluate (1/4-1)(1/8+1/2)

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