Basic Math Examples

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

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

Step 1

Convert

5 \frac{1}{3}

$5 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

5 + \frac{1}{3} - 3 \frac{2}{3}

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

Step 1.2

Add

5

$5$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

5

$5$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

3

$3$ .

\frac{15 + 1}{3} - 3 \frac{2}{3}

$\frac{15 + 1}{3} - 3 \frac{2}{3}$

Step 1.2.4.2

Add

15

$15$ and

1

$1$ .

\frac{16}{3} - 3 \frac{2}{3}

$\frac{16}{3} - 3 \frac{2}{3}$

\frac{16}{3} - 3 \frac{2}{3}

$\frac{16}{3} - 3 \frac{2}{3}$

\frac{16}{3} - 3 \frac{2}{3}

$\frac{16}{3} - 3 \frac{2}{3}$

\frac{16}{3} - 3 \frac{2}{3}

$\frac{16}{3} - 3 \frac{2}{3}$

Step 2

Convert

3 \frac{2}{3}

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

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Step 2.1

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

\frac{16}{3} - (3 + \frac{2}{3})

$\frac{16}{3} - (3 + \frac{2}{3})$

Step 2.2

Add

3

$3$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 2.2.1

To write

3

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{16}{3} - (3 \cdot \frac{3}{3} + \frac{2}{3})

$\frac{16}{3} - (3 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{16}{3} - (\frac{3 \cdot 3}{3} + \frac{2}{3})

$\frac{16}{3} - (\frac{3 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{16}{3} - \frac{3 \cdot 3 + 2}{3}

$\frac{16}{3} - \frac{3 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

3

$3$ .

\frac{16}{3} - \frac{9 + 2}{3}

$\frac{16}{3} - \frac{9 + 2}{3}$

Step 2.2.4.2

Add

9

$9$ and

2

$2$ .

\frac{16}{3} - \frac{11}{3}

$\frac{16}{3} - \frac{11}{3}$

\frac{16}{3} - \frac{11}{3}

$\frac{16}{3} - \frac{11}{3}$

\frac{16}{3} - \frac{11}{3}

$\frac{16}{3} - \frac{11}{3}$

\frac{16}{3} - \frac{11}{3}

$\frac{16}{3} - \frac{11}{3}$

Step 3

Combine the numerators over the common denominator.

\frac{16 - 11}{3}

$\frac{16 - 11}{3}$

Step 4

Subtract

11

$11$ from

16

$16$ .

\frac{5}{3}

$\frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{5}{3}

$\frac{5}{3}$

Decimal Form:

1. ¯ 6

$1.\overline{6}$

Mixed Number Form:

1 \frac{2}{3}

$1 \frac{2}{3}$