Basic Math Examples

$129 \frac{1}{2} \div 9 \frac{1}{4} = c$

Step 1

Simplify the left side.

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Step 1.1

Simplify $129 \frac{1}{2} \div 9 \frac{1}{4}$ .

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Step 1.1.1

Convert $129 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

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

$(129 + \frac{1}{2}) \div 9 \frac{1}{4} = c$

Step 1.1.1.2

Add $129$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

To write $129$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(129 \cdot \frac{2}{2} + \frac{1}{2}) \div 9 \frac{1}{4} = c$

Step 1.1.1.2.2

Combine $129$ and $\frac{2}{2}$ .

$(\frac{129 \cdot 2}{2} + \frac{1}{2}) \div 9 \frac{1}{4} = c$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{129 \cdot 2 + 1}{2} \div 9 \frac{1}{4} = c$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $129$ by $2$ .

$\frac{258 + 1}{2} \div 9 \frac{1}{4} = c$

Step 1.1.1.2.4.2

Add $258$ and $1$ .

$\frac{259}{2} \div 9 \frac{1}{4} = c$

Step 1.1.2

Convert $9 \frac{1}{4}$ to an improper fraction.

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Step 1.1.2.1

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

$\frac{259}{2} \div (9 + \frac{1}{4}) = c$

Step 1.1.2.2

Add $9$ and $\frac{1}{4}$ .

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Step 1.1.2.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{259}{2} \div (9 \cdot \frac{4}{4} + \frac{1}{4}) = c$

Step 1.1.2.2.2

Combine $9$ and $\frac{4}{4}$ .

$\frac{259}{2} \div (\frac{9 \cdot 4}{4} + \frac{1}{4}) = c$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{259}{2} \div \frac{9 \cdot 4 + 1}{4} = c$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $9$ by $4$ .

$\frac{259}{2} \div \frac{36 + 1}{4} = c$

Step 1.1.2.2.4.2

Add $36$ and $1$ .

$\frac{259}{2} \div \frac{37}{4} = c$

Step 1.1.3

To divide by a fraction, multiply by its reciprocal.

$\frac{259}{2} \cdot \frac{4}{37} = c$

Step 1.1.4

Cancel the common factor of $37$ .

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Step 1.1.4.1

Factor $37$ out of $259$ .

$\frac{37 (7)}{2} \cdot \frac{4}{37} = c$

Step 1.1.4.2

Cancel the common factor.

$\frac{37 \cdot 7}{2} \cdot \frac{4}{37} = c$

Step 1.1.4.3

Rewrite the expression.

$\frac{7}{2} \cdot 4 = c$

Step 1.1.5

Cancel the common factor of $2$ .

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Step 1.1.5.1

Factor $2$ out of $4$ .

$\frac{7}{2} \cdot (2 (2)) = c$

Step 1.1.5.2

Cancel the common factor.

$\frac{7}{2} \cdot (2 \cdot 2) = c$

Step 1.1.5.3

Rewrite the expression.

$7 \cdot 2 = c$

Step 1.1.6

Multiply $7$ by $2$ .

$14 = c$

Step 2

Rewrite the equation as $c = 14$ .

$c = 14$