Basic Math Examples

$(- 3 \frac{1}{2}) - 2 \frac{2}{3}$

Step 1

Convert $3 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$- (3 + \frac{1}{2}) - 2 \frac{2}{3}$

Step 1.2

Add $3$ and $\frac{1}{2}$ .

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Step 1.2.1

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

$- (3 \cdot \frac{2}{2} + \frac{1}{2}) - 2 \frac{2}{3}$

Step 1.2.2

Combine $3$ and $\frac{2}{2}$ .

$- (\frac{3 \cdot 2}{2} + \frac{1}{2}) - 2 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{3 \cdot 2 + 1}{2} - 2 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $2$ .

$- \frac{6 + 1}{2} - 2 \frac{2}{3}$

Step 1.2.4.2

Add $6$ and $1$ .

$- \frac{7}{2} - 2 \frac{2}{3}$

Step 2

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

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Step 2.1

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

$- \frac{7}{2} - (2 + \frac{2}{3})$

Step 2.2

Add $2$ and $\frac{2}{3}$ .

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Step 2.2.1

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

$- \frac{7}{2} - (2 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine $2$ and $\frac{3}{3}$ .

$- \frac{7}{2} - (\frac{2 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{7}{2} - \frac{2 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $3$ .

$- \frac{7}{2} - \frac{6 + 2}{3}$

Step 2.2.4.2

Add $6$ and $2$ .

$- \frac{7}{2} - \frac{8}{3}$

Step 3

To write $- \frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7}{2} \cdot \frac{3}{3} - \frac{8}{3}$

Step 4

To write $- \frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{7}{2} \cdot \frac{3}{3} - \frac{8}{3} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{7}{2}$ by $\frac{3}{3}$ .

$- \frac{7 \cdot 3}{2 \cdot 3} - \frac{8}{3} \cdot \frac{2}{2}$

Step 5.2

Multiply $2$ by $3$ .

$- \frac{7 \cdot 3}{6} - \frac{8}{3} \cdot \frac{2}{2}$

Step 5.3

Multiply $\frac{8}{3}$ by $\frac{2}{2}$ .

$- \frac{7 \cdot 3}{6} - \frac{8 \cdot 2}{3 \cdot 2}$

Step 5.4

Multiply $3$ by $2$ .

$- \frac{7 \cdot 3}{6} - \frac{8 \cdot 2}{6}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 7 \cdot 3 - 8 \cdot 2}{6}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 7$ by $3$ .

$\frac{- 21 - 8 \cdot 2}{6}$

Step 7.2

Multiply $- 8$ by $2$ .

$\frac{- 21 - 16}{6}$

Step 7.3

Subtract $16$ from $- 21$ .

$\frac{- 37}{6}$

Step 8

Move the negative in front of the fraction.

$- \frac{37}{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{37}{6}$

Decimal Form:

$- 6.1\overline{6}$

Mixed Number Form:

$- 6 \frac{1}{6}$