Pre-Algebra Examples

$13 \frac{3}{10} - 2 \frac{1}{5}$

Step 1

Convert $13 \frac{3}{10}$ to an improper fraction.

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Step 1.1

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

$13 + \frac{3}{10} - 2 \frac{1}{5}$

Step 1.2

Add $13$ and $\frac{3}{10}$ .

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Step 1.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$13 \cdot \frac{10}{10} + \frac{3}{10} - 2 \frac{1}{5}$

Step 1.2.2

Combine $13$ and $\frac{10}{10}$ .

$\frac{13 \cdot 10}{10} + \frac{3}{10} - 2 \frac{1}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{13 \cdot 10 + 3}{10} - 2 \frac{1}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $13$ by $10$ .

$\frac{130 + 3}{10} - 2 \frac{1}{5}$

Step 1.2.4.2

Add $130$ and $3$ .

$\frac{133}{10} - 2 \frac{1}{5}$

Step 2

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

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Step 2.1

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

$\frac{133}{10} - (2 + \frac{1}{5})$

Step 2.2

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

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Step 2.2.1

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

$\frac{133}{10} - (2 \cdot \frac{5}{5} + \frac{1}{5})$

Step 2.2.2

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

$\frac{133}{10} - (\frac{2 \cdot 5}{5} + \frac{1}{5})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{133}{10} - \frac{2 \cdot 5 + 1}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $5$ .

$\frac{133}{10} - \frac{10 + 1}{5}$

Step 2.2.4.2

Add $10$ and $1$ .

$\frac{133}{10} - \frac{11}{5}$

Step 3

To write $- \frac{11}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{133}{10} - \frac{11}{5} \cdot \frac{2}{2}$

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 $\frac{11}{5}$ by $\frac{2}{2}$ .

$\frac{133}{10} - \frac{11 \cdot 2}{5 \cdot 2}$

Step 4.2

Multiply $5$ by $2$ .

$\frac{133}{10} - \frac{11 \cdot 2}{10}$

Step 5

Combine the numerators over the common denominator.

$\frac{133 - 11 \cdot 2}{10}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 11$ by $2$ .

$\frac{133 - 22}{10}$

Step 6.2

Subtract $22$ from $133$ .

$\frac{111}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{111}{10}$

Decimal Form:

$11.1$

Mixed Number Form:

$11 \frac{1}{10}$