Basic Math Examples

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

Step 1

Convert

$3 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{5}{6} - (- \frac{2}{3})$

Step 1.2

Add

$3$ and

$\frac{5}{6}$ .

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Step 1.2.1

To write

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

$\frac{6}{6}$ .

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

Step 1.2.2

Combine

$3$ and

$\frac{6}{6}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$3$ by

$6$ .

$\frac{18 + 5}{6} - (- \frac{2}{3})$

Step 1.2.4.2

Add

$18$ and

$5$ .

$\frac{23}{6} - (- \frac{2}{3})$

Step 2

Multiply

$- (- \frac{2}{3})$ .

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Step 2.1

Multiply

$- 1$ by

$- 1$ .

$\frac{23}{6} + 1 (\frac{2}{3})$

Step 2.2

Multiply

$\frac{2}{3}$ by

$1$ .

$\frac{23}{6} + \frac{2}{3}$

Step 3

To write

$\frac{2}{3}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{23}{6} + \frac{2}{3} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of

$6$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{2}{3}$ by

$\frac{2}{2}$ .

$\frac{23}{6} + \frac{2 \cdot 2}{3 \cdot 2}$

Step 4.2

Multiply

$3$ by

$2$ .

$\frac{23}{6} + \frac{2 \cdot 2}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{23 + 2 \cdot 2}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$2$ by

$2$ .

$\frac{23 + 4}{6}$

Step 6.2

Add

$23$ and

$4$ .

$\frac{27}{6}$

Step 7

Cancel the common factor of

$27$ and

$6$ .

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Step 7.1

Factor

$3$ out of

$27$ .

$\frac{3 (9)}{6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor

$3$ out of

$6$ .

$\frac{3 \cdot 9}{3 \cdot 2}$

Step 7.2.2

Cancel the common factor.

$\frac{3 \cdot 9}{3 \cdot 2}$

Step 7.2.3

Rewrite the expression.

$\frac{9}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{2}$

Decimal Form:

$4.5$

Mixed Number Form:

$4 \frac{1}{2}$