Pre-Algebra Examples

$(\frac{1}{2} + \frac{2}{5}) \div \frac{5}{11}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(\frac{1}{2} + \frac{2}{5}) \frac{11}{5}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{1}{2} \cdot \frac{5}{5} + \frac{2}{5}) \frac{11}{5}$

Step 3

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

$(\frac{1}{2} \cdot \frac{5}{5} + \frac{2}{5} \cdot \frac{2}{2}) \frac{11}{5}$

Step 4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$(\frac{5}{2 \cdot 5} + \frac{2}{5} \cdot \frac{2}{2}) \frac{11}{5}$

Step 4.2

Multiply $2$ by $5$ .

$(\frac{5}{10} + \frac{2}{5} \cdot \frac{2}{2}) \frac{11}{5}$

Step 4.3

Multiply $\frac{2}{5}$ by $\frac{2}{2}$ .

$(\frac{5}{10} + \frac{2 \cdot 2}{5 \cdot 2}) \frac{11}{5}$

Step 4.4

Multiply $5$ by $2$ .

$(\frac{5}{10} + \frac{2 \cdot 2}{10}) \frac{11}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 + 2 \cdot 2}{10} \cdot \frac{11}{5}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $2$ .

$\frac{5 + 4}{10} \cdot \frac{11}{5}$

Step 6.2

Add $5$ and $4$ .

$\frac{9}{10} \cdot \frac{11}{5}$

Step 7

Multiply $\frac{9}{10} \cdot \frac{11}{5}$ .

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Step 7.1

Multiply $\frac{9}{10}$ by $\frac{11}{5}$ .

$\frac{9 \cdot 11}{10 \cdot 5}$

Step 7.2

Multiply $9$ by $11$ .

$\frac{99}{10 \cdot 5}$

Step 7.3

Multiply $10$ by $5$ .

$\frac{99}{50}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{99}{50}$

Decimal Form:

$1.98$

Mixed Number Form:

$1 \frac{49}{50}$