Precalculus Examples

$\frac{2}{3} \cdot | - \frac{5}{8} - \frac{1}{4} |$

Step 1

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

$\frac{2}{3} \cdot | - \frac{5}{8} - \frac{1}{4} \cdot \frac{2}{2} |$

Step 2

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

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Step 2.1

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

$\frac{2}{3} \cdot | - \frac{5}{8} - \frac{2}{4 \cdot 2} |$

Step 2.2

Multiply $4$ by $2$ .

$\frac{2}{3} \cdot | - \frac{5}{8} - \frac{2}{8} |$

Step 3

Combine the numerators over the common denominator.

$\frac{2}{3} \cdot | \frac{- 5 - 2}{8} |$

Step 4

Subtract $2$ from $- 5$ .

$\frac{2}{3} \cdot | \frac{- 7}{8} |$

Step 5

Remove non-negative terms from the absolute value.

$\frac{2}{3} \cdot \frac{7}{8}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $8$ .

$\frac{2}{3} \cdot \frac{7}{2 (4)}$

Step 6.2

Cancel the common factor.

$\frac{2}{3} \cdot \frac{7}{2 \cdot 4}$

Step 6.3

Rewrite the expression.

$\frac{1}{3} \cdot \frac{7}{4}$

Step 7

Multiply $\frac{1}{3}$ by $\frac{7}{4}$ .

$\frac{7}{3 \cdot 4}$

Step 8

Multiply $3$ by $4$ .

$\frac{7}{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{12}$

Decimal Form:

$0.58\overline{3}$