Basic Math Examples

7 \frac{9}{12} + 2 \frac{11}{12}

$7 \frac{9}{12} + 2 \frac{11}{12}$

Step 1

Convert

7 \frac{9}{12}

$7 \frac{9}{12}$ to an improper fraction.

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Step 1.1

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

7 + \frac{9}{12} + 2 \frac{11}{12}

$7 + \frac{9}{12} + 2 \frac{11}{12}$

Step 1.2

Add

7

$7$ and

\frac{9}{12}

$\frac{9}{12}$ .

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Step 1.2.1

To write

7

$7$ as a fraction with a common denominator, multiply by

\frac{12}{12}

$\frac{12}{12}$ .

7 \cdot \frac{12}{12} + \frac{9}{12} + 2 \frac{11}{12}

$7 \cdot \frac{12}{12} + \frac{9}{12} + 2 \frac{11}{12}$

Step 1.2.2

Combine

7

$7$ and

\frac{12}{12}

$\frac{12}{12}$ .

\frac{7 \cdot 12}{12} + \frac{9}{12} + 2 \frac{11}{12}

$\frac{7 \cdot 12}{12} + \frac{9}{12} + 2 \frac{11}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{7 \cdot 12 + 9}{12} + 2 \frac{11}{12}

$\frac{7 \cdot 12 + 9}{12} + 2 \frac{11}{12}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

7

$7$ by

12

$12$ .

\frac{84 + 9}{12} + 2 \frac{11}{12}

$\frac{84 + 9}{12} + 2 \frac{11}{12}$

Step 1.2.4.2

Add

84

$84$ and

9

$9$ .

\frac{93}{12} + 2 \frac{11}{12}

$\frac{93}{12} + 2 \frac{11}{12}$

\frac{93}{12} + 2 \frac{11}{12}

$\frac{93}{12} + 2 \frac{11}{12}$

\frac{93}{12} + 2 \frac{11}{12}

$\frac{93}{12} + 2 \frac{11}{12}$

\frac{93}{12} + 2 \frac{11}{12}

$\frac{93}{12} + 2 \frac{11}{12}$

Step 2

Convert

2 \frac{11}{12}

$2 \frac{11}{12}$ to an improper fraction.

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Step 2.1

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

\frac{93}{12} + 2 + \frac{11}{12}

$\frac{93}{12} + 2 + \frac{11}{12}$

Step 2.2

Add

2

$2$ and

\frac{11}{12}

$\frac{11}{12}$ .

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Step 2.2.1

To write

2

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

\frac{12}{12}

$\frac{12}{12}$ .

\frac{93}{12} + 2 \cdot \frac{12}{12} + \frac{11}{12}

$\frac{93}{12} + 2 \cdot \frac{12}{12} + \frac{11}{12}$

Step 2.2.2

Combine

2

$2$ and

\frac{12}{12}

$\frac{12}{12}$ .

\frac{93}{12} + \frac{2 \cdot 12}{12} + \frac{11}{12}

$\frac{93}{12} + \frac{2 \cdot 12}{12} + \frac{11}{12}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{93}{12} + \frac{2 \cdot 12 + 11}{12}

$\frac{93}{12} + \frac{2 \cdot 12 + 11}{12}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

12

$12$ .

\frac{93}{12} + \frac{24 + 11}{12}

$\frac{93}{12} + \frac{24 + 11}{12}$

Step 2.2.4.2

Add

24

$24$ and

11

$11$ .

\frac{93}{12} + \frac{35}{12}

$\frac{93}{12} + \frac{35}{12}$

\frac{93}{12} + \frac{35}{12}

$\frac{93}{12} + \frac{35}{12}$

\frac{93}{12} + \frac{35}{12}

$\frac{93}{12} + \frac{35}{12}$

\frac{93}{12} + \frac{35}{12}

$\frac{93}{12} + \frac{35}{12}$

Step 3

Combine the numerators over the common denominator.

\frac{93 + 35}{12}

$\frac{93 + 35}{12}$

Step 4

Add

93

$93$ and

35

$35$ .

\frac{128}{12}

$\frac{128}{12}$

Step 5

Cancel the common factor of

128

$128$ and

12

$12$ .

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Step 5.1

Factor

4

$4$ out of

128

$128$ .

$\frac{4 (32)}{12}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

$4$ out of

$12$ .

$\frac{4 \cdot 32}{4 \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{4 \cdot 32}{4 \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{32}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{32}{3}$

Decimal Form:

$10.\overline{6}$

Mixed Number Form:

$10 \frac{2}{3}$