Basic Math Examples

$2 \frac{1}{2} \div \frac{5}{6}$

Step 1

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

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Step 1.1

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

$(2 + \frac{1}{2}) \div \frac{5}{6}$

Step 1.2

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

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Step 1.2.1

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

$(2 \cdot \frac{2}{2} + \frac{1}{2}) \div \frac{5}{6}$

Step 1.2.2

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

$(\frac{2 \cdot 2}{2} + \frac{1}{2}) \div \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} \div \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $2$ .

$\frac{4 + 1}{2} \div \frac{5}{6}$

Step 1.2.4.2

Add $4$ and $1$ .

$\frac{5}{2} \div \frac{5}{6}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2} \cdot \frac{6}{5}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{6}{5}$

Step 3.2

Rewrite the expression.

$\frac{1}{2} \cdot 6$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $6$ .

$\frac{1}{2} \cdot (2 (3))$

Step 4.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 3)$

Step 4.3

Rewrite the expression.

$3$