Basic Math Examples

$12 \frac{5}{6} - 9 \frac{8}{27}$

Step 1

Convert

$12 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$12 + \frac{5}{6} - 9 \frac{8}{27}$

Step 1.2

Add

$12$ and

$\frac{5}{6}$ .

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Step 1.2.1

To write

$12$ as a fraction with a common denominator, multiply by

$\frac{6}{6}$ .

$12 \cdot \frac{6}{6} + \frac{5}{6} - 9 \frac{8}{27}$

Step 1.2.2

Combine

$12$ and

$\frac{6}{6}$ .

$\frac{12 \cdot 6}{6} + \frac{5}{6} - 9 \frac{8}{27}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{12 \cdot 6 + 5}{6} - 9 \frac{8}{27}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$12$ by

$6$ .

$\frac{72 + 5}{6} - 9 \frac{8}{27}$

Step 1.2.4.2

Add

$72$ and

$5$ .

$\frac{77}{6} - 9 \frac{8}{27}$

Step 2

Convert

$9 \frac{8}{27}$ to an improper fraction.

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Step 2.1

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

$\frac{77}{6} - (9 + \frac{8}{27})$

Step 2.2

Add

$9$ and

$\frac{8}{27}$ .

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Step 2.2.1

To write

$9$ as a fraction with a common denominator, multiply by

$\frac{27}{27}$ .

$\frac{77}{6} - (9 \cdot \frac{27}{27} + \frac{8}{27})$

Step 2.2.2

Combine

$9$ and

$\frac{27}{27}$ .

$\frac{77}{6} - (\frac{9 \cdot 27}{27} + \frac{8}{27})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{77}{6} - \frac{9 \cdot 27 + 8}{27}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$9$ by

$27$ .

$\frac{77}{6} - \frac{243 + 8}{27}$

Step 2.2.4.2

Add

$243$ and

$8$ .

$\frac{77}{6} - \frac{251}{27}$

Step 3

To write

$\frac{77}{6}$ as a fraction with a common denominator, multiply by

$\frac{9}{9}$ .

$\frac{77}{6} \cdot \frac{9}{9} - \frac{251}{27}$

Step 4

To write

$- \frac{251}{27}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{77}{6} \cdot \frac{9}{9} - \frac{251}{27} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of

$54$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{77}{6}$ by

$\frac{9}{9}$ .

$\frac{77 \cdot 9}{6 \cdot 9} - \frac{251}{27} \cdot \frac{2}{2}$

Step 5.2

Multiply

$6$ by

$9$ .

$\frac{77 \cdot 9}{54} - \frac{251}{27} \cdot \frac{2}{2}$

Step 5.3

Multiply

$\frac{251}{27}$ by

$\frac{2}{2}$ .

$\frac{77 \cdot 9}{54} - \frac{251 \cdot 2}{27 \cdot 2}$

Step 5.4

Multiply

$27$ by

$2$ .

$\frac{77 \cdot 9}{54} - \frac{251 \cdot 2}{54}$

Step 6

Combine the numerators over the common denominator.

$\frac{77 \cdot 9 - 251 \cdot 2}{54}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$77$ by

$9$ .

$\frac{693 - 251 \cdot 2}{54}$

Step 7.2

Multiply

$- 251$ by

$2$ .

$\frac{693 - 502}{54}$

Step 7.3

Subtract

$502$ from

$693$ .

$\frac{191}{54}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{191}{54}$

Decimal Form:

$3.5\overline{370}$

Mixed Number Form:

$3 \frac{29}{54}$