Basic Math Examples

$- 2 \frac{2}{3} - \frac{3}{4}$

Step 1

Convert

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

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Step 1.1

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

$- (2 + \frac{2}{3}) - \frac{3}{4}$

Step 1.2

Add

$2$ and

$\frac{2}{3}$ .

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Step 1.2.1

To write

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

$\frac{3}{3}$ .

$- (2 \cdot \frac{3}{3} + \frac{2}{3}) - \frac{3}{4}$

Step 1.2.2

Combine

$2$ and

$\frac{3}{3}$ .

$- (\frac{2 \cdot 3}{3} + \frac{2}{3}) - \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 3 + 2}{3} - \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$3$ .

$- \frac{6 + 2}{3} - \frac{3}{4}$

Step 1.2.4.2

Add

$6$ and

$2$ .

$- \frac{8}{3} - \frac{3}{4}$

Step 2

To write

$- \frac{8}{3}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$- \frac{8}{3} \cdot \frac{4}{4} - \frac{3}{4}$

Step 3

To write

$- \frac{3}{4}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$- \frac{8}{3} \cdot \frac{4}{4} - \frac{3}{4} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of

$12$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{8}{3}$ by

$\frac{4}{4}$ .

$- \frac{8 \cdot 4}{3 \cdot 4} - \frac{3}{4} \cdot \frac{3}{3}$

Step 4.2

Multiply

$3$ by

$4$ .

$- \frac{8 \cdot 4}{12} - \frac{3}{4} \cdot \frac{3}{3}$

Step 4.3

Multiply

$\frac{3}{4}$ by

$\frac{3}{3}$ .

$- \frac{8 \cdot 4}{12} - \frac{3 \cdot 3}{4 \cdot 3}$

Step 4.4

Multiply

$4$ by

$3$ .

$- \frac{8 \cdot 4}{12} - \frac{3 \cdot 3}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 8 \cdot 4 - 3 \cdot 3}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$- 8$ by

$4$ .

$\frac{- 32 - 3 \cdot 3}{12}$

Step 6.2

Multiply

$- 3$ by

$3$ .

$\frac{- 32 - 9}{12}$

Step 6.3

Subtract

$9$ from

$- 32$ .

$\frac{- 41}{12}$

Step 7

Move the negative in front of the fraction.

$- \frac{41}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{41}{12}$

Decimal Form:

$- 3.41\overline{6}$

Mixed Number Form:

$- 3 \frac{5}{12}$