Pre-Algebra Examples

$333 \frac{1}{4} \div 15 \frac{1}{2}$

Step 1

Convert $333 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

$(333 + \frac{1}{4}) \div 15 \frac{1}{2}$

Step 1.2

Add $333$ and $\frac{1}{4}$ .

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Step 1.2.1

To write $333$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(333 \cdot \frac{4}{4} + \frac{1}{4}) \div 15 \frac{1}{2}$

Step 1.2.2

Combine $333$ and $\frac{4}{4}$ .

$(\frac{333 \cdot 4}{4} + \frac{1}{4}) \div 15 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{333 \cdot 4 + 1}{4} \div 15 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $333$ by $4$ .

$\frac{1332 + 1}{4} \div 15 \frac{1}{2}$

Step 1.2.4.2

Add $1332$ and $1$ .

$\frac{1333}{4} \div 15 \frac{1}{2}$

Step 2

Convert $15 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{1333}{4} \div (15 + \frac{1}{2})$

Step 2.2

Add $15$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $15$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1333}{4} \div (15 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine $15$ and $\frac{2}{2}$ .

$\frac{1333}{4} \div (\frac{15 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{1333}{4} \div \frac{15 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $15$ by $2$ .

$\frac{1333}{4} \div \frac{30 + 1}{2}$

Step 2.2.4.2

Add $30$ and $1$ .

$\frac{1333}{4} \div \frac{31}{2}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{1333}{4} \cdot \frac{2}{31}$

Step 4

Cancel the common factor of $31$ .

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Step 4.1

Factor $31$ out of $1333$ .

$\frac{31 (43)}{4} \cdot \frac{2}{31}$

Step 4.2

Cancel the common factor.

$\frac{31 \cdot 43}{4} \cdot \frac{2}{31}$

Step 4.3

Rewrite the expression.

$\frac{43}{4} \cdot 2$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $4$ .

$\frac{43}{2 (2)} \cdot 2$

Step 5.2

Cancel the common factor.

$\frac{43}{2 \cdot 2} \cdot 2$

Step 5.3

Rewrite the expression.

$\frac{43}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{43}{2}$

Decimal Form:

$21.5$

Mixed Number Form:

$21 \frac{1}{2}$