Basic Math Examples

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

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

Step 1

Convert

3 \frac{1}{3}

$3 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

3

$3$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

3

$3$ .

\frac{9 + 1}{3} \div 2 \frac{3}{5}

$\frac{9 + 1}{3} \div 2 \frac{3}{5}$

Step 1.2.4.2

Add

9

$9$ and

1

$1$ .

\frac{10}{3} \div 2 \frac{3}{5}

$\frac{10}{3} \div 2 \frac{3}{5}$

\frac{10}{3} \div 2 \frac{3}{5}

$\frac{10}{3} \div 2 \frac{3}{5}$

\frac{10}{3} \div 2 \frac{3}{5}

$\frac{10}{3} \div 2 \frac{3}{5}$

\frac{10}{3} \div 2 \frac{3}{5}

$\frac{10}{3} \div 2 \frac{3}{5}$

Step 2

Convert

2 \frac{3}{5}

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

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Step 2.1

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

\frac{10}{3} \div (2 + \frac{3}{5})

$\frac{10}{3} \div (2 + \frac{3}{5})$

Step 2.2

Add

2

$2$ and

\frac{3}{5}

$\frac{3}{5}$ .

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Step 2.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{10}{3} \div (2 \cdot \frac{5}{5} + \frac{3}{5})

$\frac{10}{3} \div (2 \cdot \frac{5}{5} + \frac{3}{5})$

Step 2.2.2

Combine

2

$2$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{10}{3} \div (\frac{2 \cdot 5}{5} + \frac{3}{5})

$\frac{10}{3} \div (\frac{2 \cdot 5}{5} + \frac{3}{5})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{10}{3} \div \frac{2 \cdot 5 + 3}{5}

$\frac{10}{3} \div \frac{2 \cdot 5 + 3}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

5

$5$ .

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

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

Step 2.2.4.2

Add

10

$10$ and

3

$3$ .

\frac{10}{3} \div \frac{13}{5}

$\frac{10}{3} \div \frac{13}{5}$

\frac{10}{3} \div \frac{13}{5}

$\frac{10}{3} \div \frac{13}{5}$

\frac{10}{3} \div \frac{13}{5}

$\frac{10}{3} \div \frac{13}{5}$

\frac{10}{3} \div \frac{13}{5}

$\frac{10}{3} \div \frac{13}{5}$

Step 3

To divide by a fraction, multiply by its reciprocal.

\frac{10}{3} \cdot \frac{5}{13}

$\frac{10}{3} \cdot \frac{5}{13}$

Step 4

Multiply

\frac{10}{3} \cdot \frac{5}{13}

$\frac{10}{3} \cdot \frac{5}{13}$ .

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Step 4.1

Multiply

\frac{10}{3}

$\frac{10}{3}$ by

\frac{5}{13}

$\frac{5}{13}$ .

\frac{10 \cdot 5}{3 \cdot 13}

$\frac{10 \cdot 5}{3 \cdot 13}$

Step 4.2

Multiply

10

$10$ by

5

$5$ .

\frac{50}{3 \cdot 13}

$\frac{50}{3 \cdot 13}$

Step 4.3

Multiply

3

$3$ by

13

$13$ .

\frac{50}{39}

$\frac{50}{39}$

\frac{50}{39}

$\frac{50}{39}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{50}{39}

$\frac{50}{39}$

Decimal Form:

1. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 282051

$1.\overline{282051}$

Mixed Number Form:

1 \frac{11}{39}

$1 \frac{11}{39}$