Basic Math Examples

\frac{11}{12} - \frac{5}{6} - \frac{2}{3}

$\frac{11}{12} - \frac{5}{6} - \frac{2}{3}$

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{5}{6}

$\frac{5}{6}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{11}{12} - (\frac{5}{6} \cdot \frac{2}{2}) - \frac{2}{3}

$\frac{11}{12} - (\frac{5}{6} \cdot \frac{2}{2}) - \frac{2}{3}$

Step 1.2

Multiply

\frac{5}{6}

$\frac{5}{6}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{11}{12} - \frac{5 \cdot 2}{6 \cdot 2} - \frac{2}{3}

$\frac{11}{12} - \frac{5 \cdot 2}{6 \cdot 2} - \frac{2}{3}$

Step 1.3

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{11}{12} - \frac{5 \cdot 2}{6 \cdot 2} - (\frac{2}{3} \cdot \frac{4}{4})

$\frac{11}{12} - \frac{5 \cdot 2}{6 \cdot 2} - (\frac{2}{3} \cdot \frac{4}{4})$

Step 1.4

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{11}{12} - \frac{5 \cdot 2}{6 \cdot 2} - \frac{2 \cdot 4}{3 \cdot 4}

$\frac{11}{12} - \frac{5 \cdot 2}{6 \cdot 2} - \frac{2 \cdot 4}{3 \cdot 4}$

Step 1.5

Reorder the factors of

6 \cdot 2

$6 \cdot 2$ .

\frac{11}{12} - \frac{5 \cdot 2}{2 \cdot 6} - \frac{2 \cdot 4}{3 \cdot 4}

$\frac{11}{12} - \frac{5 \cdot 2}{2 \cdot 6} - \frac{2 \cdot 4}{3 \cdot 4}$

Step 1.6

Multiply

2

$2$ by

6

$6$ .

\frac{11}{12} - \frac{5 \cdot 2}{12} - \frac{2 \cdot 4}{3 \cdot 4}

$\frac{11}{12} - \frac{5 \cdot 2}{12} - \frac{2 \cdot 4}{3 \cdot 4}$

Step 1.7

Multiply

3

$3$ by

4

$4$ .

\frac{11}{12} - \frac{5 \cdot 2}{12} - \frac{2 \cdot 4}{12}

$\frac{11}{12} - \frac{5 \cdot 2}{12} - \frac{2 \cdot 4}{12}$

\frac{11}{12} - \frac{5 \cdot 2}{12} - \frac{2 \cdot 4}{12}

$\frac{11}{12} - \frac{5 \cdot 2}{12} - \frac{2 \cdot 4}{12}$

Step 2

Combine the numerators over the common denominator.

\frac{11 - 5 \cdot 2 - 2 \cdot 4}{12}

$\frac{11 - 5 \cdot 2 - 2 \cdot 4}{12}$

Step 3

Simplify each term.

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Step 3.1

Multiply

- 5

$- 5$ by

2

$2$ .

\frac{11 - 10 - 2 \cdot 4}{12}

$\frac{11 - 10 - 2 \cdot 4}{12}$

Step 3.2

Multiply

- 2

$- 2$ by

4

$4$ .

\frac{11 - 10 - 8}{12}

$\frac{11 - 10 - 8}{12}$

\frac{11 - 10 - 8}{12}

$\frac{11 - 10 - 8}{12}$

Step 4

Simplify the expression.

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Step 4.1

Subtract

10

$10$ from

11

$11$ .

\frac{1 - 8}{12}

$\frac{1 - 8}{12}$

Step 4.2

Subtract

8

$8$ from

1

$1$ .

\frac{- 7}{12}

$\frac{- 7}{12}$

Step 4.3

Move the negative in front of the fraction.

- \frac{7}{12}

$- \frac{7}{12}$

- \frac{7}{12}

$- \frac{7}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

- \frac{7}{12}

$- \frac{7}{12}$

Decimal Form:

- 0.58 ¯ 3

$- 0.58\overline{3}$