Algebra Examples

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

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.

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

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 $\frac{4}{4}$ .

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 1}{4} \div 1 \frac{1}{2}$

Step 1.2.4.2

Add $8$ and $1$ .

$\frac{9}{4} \div 1 \frac{1}{2}$

Step 2

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

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Step 2.1

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

$\frac{9}{4} \div (1 + \frac{1}{2})$

Step 2.2

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

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{9}{4} \div (\frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{9}{4} \div \frac{2 + 1}{2}$

Step 2.2.3

Add $2$ and $1$ .

$\frac{9}{4} \div \frac{3}{2}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{9}{4} \cdot \frac{2}{3}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Factor $3$ out of $9$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $4$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$\frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$