Basic Math Examples

21 + 8 \frac{2}{3}

$21 + 8 \frac{2}{3}$

Step 1

Convert

8 \frac{2}{3}

$8 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

21 + 8 + \frac{2}{3}

$21 + 8 + \frac{2}{3}$

Step 1.2

Add

8

$8$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

To write

8

$8$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

21 + 8 \cdot \frac{3}{3} + \frac{2}{3}

$21 + 8 \cdot \frac{3}{3} + \frac{2}{3}$

Step 1.2.2

Combine

8

$8$ and

\frac{3}{3}

$\frac{3}{3}$ .

21 + \frac{8 \cdot 3}{3} + \frac{2}{3}

$21 + \frac{8 \cdot 3}{3} + \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

21 + \frac{8 \cdot 3 + 2}{3}

$21 + \frac{8 \cdot 3 + 2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

8

$8$ by

3

$3$ .

21 + \frac{24 + 2}{3}

$21 + \frac{24 + 2}{3}$

Step 1.2.4.2

Add

24

$24$ and

2

$2$ .

21 + \frac{26}{3}

$21 + \frac{26}{3}$

21 + \frac{26}{3}

$21 + \frac{26}{3}$

21 + \frac{26}{3}

$21 + \frac{26}{3}$

21 + \frac{26}{3}

$21 + \frac{26}{3}$

Step 2

To write

21

$21$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

21 \cdot \frac{3}{3} + \frac{26}{3}

$21 \cdot \frac{3}{3} + \frac{26}{3}$

Step 3

Combine

21

$21$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{21 \cdot 3}{3} + \frac{26}{3}

$\frac{21 \cdot 3}{3} + \frac{26}{3}$

Step 4

Combine the numerators over the common denominator.

\frac{21 \cdot 3 + 26}{3}

$\frac{21 \cdot 3 + 26}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

21

$21$ by

3

$3$ .

\frac{63 + 26}{3}

$\frac{63 + 26}{3}$

Step 5.2

Add

63

$63$ and

26

$26$ .

\frac{89}{3}

$\frac{89}{3}$

\frac{89}{3}

$\frac{89}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{89}{3}

$\frac{89}{3}$

Decimal Form:

29.\overline{6}

$29.\overline{6}$

Mixed Number Form:

29 \frac{2}{3}

$29 \frac{2}{3}$