Basic Math Examples

$6 \frac{3}{4} \div 5 \frac{1}{2}$

Step 1

Convert $6 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$(6 + \frac{3}{4}) \div 5 \frac{1}{2}$

Step 1.2

Add $6$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(6 \cdot \frac{4}{4} + \frac{3}{4}) \div 5 \frac{1}{2}$

Step 1.2.2

Combine $6$ and $\frac{4}{4}$ .

$(\frac{6 \cdot 4}{4} + \frac{3}{4}) \div 5 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 4 + 3}{4} \div 5 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $4$ .

$\frac{24 + 3}{4} \div 5 \frac{1}{2}$

Step 1.2.4.2

Add $24$ and $3$ .

$\frac{27}{4} \div 5 \frac{1}{2}$

Step 2

Convert $5 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{27}{4} \div (5 + \frac{1}{2})$

Step 2.2

Add $5$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{27}{4} \div (5 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine $5$ and $\frac{2}{2}$ .

$\frac{27}{4} \div (\frac{5 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{27}{4} \div \frac{5 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $2$ .

$\frac{27}{4} \div \frac{10 + 1}{2}$

Step 2.2.4.2

Add $10$ and $1$ .

$\frac{27}{4} \div \frac{11}{2}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{27}{4} \cdot \frac{2}{11}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $4$ .

$\frac{27}{2 (2)} \cdot \frac{2}{11}$

Step 4.2

Cancel the common factor.

$\frac{27}{2 \cdot 2} \cdot \frac{2}{11}$

Step 4.3

Rewrite the expression.

$\frac{27}{2} \cdot \frac{1}{11}$

Step 5

Multiply $\frac{27}{2}$ by $\frac{1}{11}$ .

$\frac{27}{2 \cdot 11}$

Step 6

Multiply $2$ by $11$ .

$\frac{27}{22}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{22}$

Decimal Form:

$1.2\overline{27}$

Mixed Number Form:

$1 \frac{5}{22}$