Pre-Algebra Examples

$\frac{1}{2} \div \frac{4}{7} - \frac{1}{4}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{2} \cdot \frac{7}{4} - \frac{1}{4}$

Step 1.2

Multiply $\frac{1}{2} \cdot \frac{7}{4}$ .

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Step 1.2.1

Multiply $\frac{1}{2}$ by $\frac{7}{4}$ .

$\frac{7}{2 \cdot 4} - \frac{1}{4}$

Step 1.2.2

Multiply $2$ by $4$ .

$\frac{7}{8} - \frac{1}{4}$

Step 2

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

$\frac{7}{8} - \frac{1}{4} \cdot \frac{2}{2}$

Step 3

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

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Step 3.1

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

$\frac{7}{8} - \frac{2}{4 \cdot 2}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{7}{8} - \frac{2}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 - 2}{8}$

Step 5

Subtract $2$ from $7$ .

$\frac{5}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{8}$

Decimal Form:

$0.625$