Pre-Algebra Examples

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

Step 1

Convert $2 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $2$ and $\frac{3}{5}$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

$\frac{10 + 3}{5} \div 1 \frac{1}{5}$

Step 1.2.4.2

Add $10$ and $3$ .

$\frac{13}{5} \div 1 \frac{1}{5}$

Step 2

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

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Step 2.1

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

$\frac{13}{5} \div (1 + \frac{1}{5})$

Step 2.2

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

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{13}{5} \div (\frac{5}{5} + \frac{1}{5})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{13}{5} \div \frac{5 + 1}{5}$

Step 2.2.3

Add $5$ and $1$ .

$\frac{13}{5} \div \frac{6}{5}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{13}{5} \cdot \frac{5}{6}$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Cancel the common factor.

$\frac{13}{5} \cdot \frac{5}{6}$

Step 4.2

Rewrite the expression.

$13 (\frac{1}{6})$

Step 5

Combine $13$ and $\frac{1}{6}$ .

$\frac{13}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{6}$

Decimal Form:

$2.1\overline{6}$

Mixed Number Form:

$2 \frac{1}{6}$