Basic Math Examples

$\frac{13}{8} \div \frac{1}{4} - \frac{2}{11} \cdot \frac{10}{5}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{13}{8} \cdot 4 - \frac{2}{11} \cdot \frac{10}{5}$

Step 1.2

Cancel the common factor of $4$ .

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Step 1.2.1

Factor $4$ out of $8$ .

$\frac{13}{4 (2)} \cdot 4 - \frac{2}{11} \cdot \frac{10}{5}$

Step 1.2.2

Cancel the common factor.

$\frac{13}{4 \cdot 2} \cdot 4 - \frac{2}{11} \cdot \frac{10}{5}$

Step 1.2.3

Rewrite the expression.

$\frac{13}{2} - \frac{2}{11} \cdot \frac{10}{5}$

Step 1.3

Divide $10$ by $5$ .

$\frac{13}{2} - \frac{2}{11} \cdot 2$

Step 1.4

Multiply $- \frac{2}{11} \cdot 2$ .

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Step 1.4.1

Multiply $2$ by $- 1$ .

$\frac{13}{2} - 2 (\frac{2}{11})$

Step 1.4.2

Combine $- 2$ and $\frac{2}{11}$ .

$\frac{13}{2} + \frac{- 2 \cdot 2}{11}$

Step 1.4.3

Multiply $- 2$ by $2$ .

$\frac{13}{2} + \frac{- 4}{11}$

Step 1.5

Move the negative in front of the fraction.

$\frac{13}{2} - \frac{4}{11}$

Step 2

To write $\frac{13}{2}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{13}{2} \cdot \frac{11}{11} - \frac{4}{11}$

Step 3

To write $- \frac{4}{11}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13}{2} \cdot \frac{11}{11} - \frac{4}{11} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $22$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{13}{2}$ by $\frac{11}{11}$ .

$\frac{13 \cdot 11}{2 \cdot 11} - \frac{4}{11} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $11$ .

$\frac{13 \cdot 11}{22} - \frac{4}{11} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{4}{11}$ by $\frac{2}{2}$ .

$\frac{13 \cdot 11}{22} - \frac{4 \cdot 2}{11 \cdot 2}$

Step 4.4

Multiply $11$ by $2$ .

$\frac{13 \cdot 11}{22} - \frac{4 \cdot 2}{22}$

Step 5

Combine the numerators over the common denominator.

$\frac{13 \cdot 11 - 4 \cdot 2}{22}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $13$ by $11$ .

$\frac{143 - 4 \cdot 2}{22}$

Step 6.2

Multiply $- 4$ by $2$ .

$\frac{143 - 8}{22}$

Step 6.3

Subtract $8$ from $143$ .

$\frac{135}{22}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{135}{22}$

Decimal Form:

$6.1\overline{36}$

Mixed Number Form:

$6 \frac{3}{22}$