Basic Math Examples

$- (\frac{5}{2} - \frac{3}{2}) + \frac{7}{3} - \frac{5}{2} \cdot (\frac{3}{2} - 2)$

Step 1

Simplify each term.

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Step 1.1

Combine the numerators over the common denominator.

$- \frac{5 - 3}{2} + \frac{7}{3} - \frac{5}{2} \cdot (\frac{3}{2} - 2)$

Step 1.2

Subtract $3$ from $5$ .

$- \frac{2}{2} + \frac{7}{3} - \frac{5}{2} \cdot (\frac{3}{2} - 2)$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Cancel the common factor.

$- \frac{2}{2} + \frac{7}{3} - \frac{5}{2} \cdot (\frac{3}{2} - 2)$

Step 1.3.2

Rewrite the expression.

$- 1 \cdot 1 + \frac{7}{3} - \frac{5}{2} \cdot (\frac{3}{2} - 2)$

Step 1.4

Multiply $- 1$ by $1$ .

$- 1 + \frac{7}{3} - \frac{5}{2} \cdot (\frac{3}{2} - 2)$

Step 1.5

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

$- 1 + \frac{7}{3} - \frac{5}{2} \cdot (\frac{3}{2} - 2 \cdot \frac{2}{2})$

Step 1.6

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

$- 1 + \frac{7}{3} - \frac{5}{2} \cdot (\frac{3}{2} + \frac{- 2 \cdot 2}{2})$

Step 1.7

Combine the numerators over the common denominator.

$- 1 + \frac{7}{3} - \frac{5}{2} \cdot \frac{3 - 2 \cdot 2}{2}$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Multiply $- 2$ by $2$ .

$- 1 + \frac{7}{3} - \frac{5}{2} \cdot \frac{3 - 4}{2}$

Step 1.8.2

Subtract $4$ from $3$ .

$- 1 + \frac{7}{3} - \frac{5}{2} \cdot \frac{- 1}{2}$

Step 1.9

Move the negative in front of the fraction.

$- 1 + \frac{7}{3} - \frac{5}{2} \cdot (- \frac{1}{2})$

Step 1.10

Multiply $- \frac{5}{2} (- \frac{1}{2})$ .

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Step 1.10.1

Multiply $- 1$ by $- 1$ .

$- 1 + \frac{7}{3} + 1 (\frac{5}{2}) \frac{1}{2}$

Step 1.10.2

Multiply $\frac{5}{2}$ by $1$ .

$- 1 + \frac{7}{3} + \frac{5}{2} \cdot \frac{1}{2}$

Step 1.10.3

Multiply $\frac{5}{2}$ by $\frac{1}{2}$ .

$- 1 + \frac{7}{3} + \frac{5}{2 \cdot 2}$

Step 1.10.4

Multiply $2$ by $2$ .

$- 1 + \frac{7}{3} + \frac{5}{4}$

Step 2

Find the common denominator.

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Step 2.1

Write $- 1$ as a fraction with denominator $1$ .

$\frac{- 1}{1} + \frac{7}{3} + \frac{5}{4}$

Step 2.2

Multiply $\frac{- 1}{1}$ by $\frac{12}{12}$ .

$\frac{- 1}{1} \cdot \frac{12}{12} + \frac{7}{3} + \frac{5}{4}$

Step 2.3

Multiply $\frac{- 1}{1}$ by $\frac{12}{12}$ .

$\frac{- 1 \cdot 12}{12} + \frac{7}{3} + \frac{5}{4}$

Step 2.4

Multiply $\frac{7}{3}$ by $\frac{4}{4}$ .

$\frac{- 1 \cdot 12}{12} + \frac{7}{3} \cdot \frac{4}{4} + \frac{5}{4}$

Step 2.5

Multiply $\frac{7}{3}$ by $\frac{4}{4}$ .

$\frac{- 1 \cdot 12}{12} + \frac{7 \cdot 4}{3 \cdot 4} + \frac{5}{4}$

Step 2.6

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$\frac{- 1 \cdot 12}{12} + \frac{7 \cdot 4}{3 \cdot 4} + \frac{5}{4} \cdot \frac{3}{3}$

Step 2.7

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$\frac{- 1 \cdot 12}{12} + \frac{7 \cdot 4}{3 \cdot 4} + \frac{5 \cdot 3}{4 \cdot 3}$

Step 2.8

Multiply $3$ by $4$ .

$\frac{- 1 \cdot 12}{12} + \frac{7 \cdot 4}{12} + \frac{5 \cdot 3}{4 \cdot 3}$

Step 2.9

Reorder the factors of $4 \cdot 3$ .

$\frac{- 1 \cdot 12}{12} + \frac{7 \cdot 4}{12} + \frac{5 \cdot 3}{3 \cdot 4}$

Step 2.10

Multiply $3$ by $4$ .

$\frac{- 1 \cdot 12}{12} + \frac{7 \cdot 4}{12} + \frac{5 \cdot 3}{12}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 1 \cdot 12 + 7 \cdot 4 + 5 \cdot 3}{12}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 1$ by $12$ .

$\frac{- 12 + 7 \cdot 4 + 5 \cdot 3}{12}$

Step 4.2

Multiply $7$ by $4$ .

$\frac{- 12 + 28 + 5 \cdot 3}{12}$

Step 4.3

Multiply $5$ by $3$ .

$\frac{- 12 + 28 + 15}{12}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $- 12$ and $28$ .

$\frac{16 + 15}{12}$

Step 5.2

Add $16$ and $15$ .

$\frac{31}{12}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{31}{12}$

Decimal Form:

$2.58\overline{3}$

Mixed Number Form:

$2 \frac{7}{12}$