Pre-Algebra Examples

$(\frac{2}{3} - \frac{1}{4}) \div \frac{5}{7}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(\frac{2}{3} - \frac{1}{4}) \frac{7}{5}$

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{2}{3} \cdot \frac{4}{4} - \frac{1}{4}) \frac{7}{5}$

Step 3

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{2}{3} \cdot \frac{4}{4} - \frac{1}{4} \cdot \frac{3}{3}) \frac{7}{5}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$(\frac{2 \cdot 4}{3 \cdot 4} - \frac{1}{4} \cdot \frac{3}{3}) \frac{7}{5}$

Step 4.2

Multiply $3$ by $4$ .

$(\frac{2 \cdot 4}{12} - \frac{1}{4} \cdot \frac{3}{3}) \frac{7}{5}$

Step 4.3

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

$(\frac{2 \cdot 4}{12} - \frac{3}{4 \cdot 3}) \frac{7}{5}$

Step 4.4

Multiply $4$ by $3$ .

$(\frac{2 \cdot 4}{12} - \frac{3}{12}) \frac{7}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 - 3}{12} \cdot \frac{7}{5}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $4$ .

$\frac{8 - 3}{12} \cdot \frac{7}{5}$

Step 6.2

Subtract $3$ from $8$ .

$\frac{5}{12} \cdot \frac{7}{5}$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Cancel the common factor.

$\frac{5}{12} \cdot \frac{7}{5}$

Step 7.2

Rewrite the expression.

$\frac{1}{12} \cdot 7$

Step 8

Combine $\frac{1}{12}$ and $7$ .

$\frac{7}{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{12}$

Decimal Form:

$0.58\overline{3}$