Pre-Algebra Examples

$\frac{1}{4} \div 2 \frac{1}{4} \div \frac{3}{4}$

Step 1

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.2

Add $2$ and $\frac{1}{4}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{1}{4} \div \frac{2 \cdot 4 + 1}{4} \div \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$\frac{1}{4} \div \frac{8 + 1}{4} \div \frac{3}{4}$

Step 1.2.4.2

Add $8$ and $1$ .

$\frac{1}{4} \div \frac{9}{4} \div \frac{3}{4}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{4} \div \frac{9}{4} \cdot \frac{4}{3}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{4} \cdot \frac{4}{9} \frac{4}{3}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Cancel the common factor.

$\frac{1}{4} \cdot \frac{4}{9} \frac{4}{3}$

Step 4.2

Rewrite the expression.

$\frac{1}{9} \cdot \frac{4}{3}$

Step 5

Multiply $\frac{1}{9} \cdot \frac{4}{3}$ .

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Step 5.1

Multiply $\frac{1}{9}$ by $\frac{4}{3}$ .

$\frac{4}{9 \cdot 3}$

Step 5.2

Multiply $9$ by $3$ .

$\frac{4}{27}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{27}$

Decimal Form:

$0.\overline{148}$