Basic Math Examples

$\frac{9}{3} \cdot 2 - 3 (4 - 1) + 5 \cdot 2 \frac{1}{2}$

Step 1

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

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Step 1.1

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

$\frac{9}{3} \cdot 2 - 3 (4 - 1) + 5 \cdot (2 + \frac{1}{2})$

Step 1.2

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

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Step 1.2.1

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

$\frac{9}{3} \cdot 2 - 3 (4 - 1) + 5 \cdot (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 1.2.2

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

$\frac{9}{3} \cdot 2 - 3 (4 - 1) + 5 \cdot (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{9}{3} \cdot 2 - 3 (4 - 1) + 5 \cdot \frac{2 \cdot 2 + 1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $2$ .

$\frac{9}{3} \cdot 2 - 3 (4 - 1) + 5 \cdot \frac{4 + 1}{2}$

Step 1.2.4.2

Add $4$ and $1$ .

$\frac{9}{3} \cdot 2 - 3 (4 - 1) + 5 \cdot \frac{5}{2}$

Step 2

Simplify each term.

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Step 2.1

Divide $9$ by $3$ .

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

Step 2.2

Multiply $3$ by $2$ .

$6 - 3 (4 - 1) + 5 \cdot \frac{5}{2}$

Step 2.3

Subtract $1$ from $4$ .

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

Step 2.4

Multiply $- 3$ by $3$ .

$6 - 9 + 5 \cdot \frac{5}{2}$

Step 2.5

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

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Step 2.5.1

Combine $5$ and $\frac{5}{2}$ .

$6 - 9 + \frac{5 \cdot 5}{2}$

Step 2.5.2

Multiply $5$ by $5$ .

$6 - 9 + \frac{25}{2}$

Step 3

Find the common denominator.

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Step 3.1

Write $6$ as a fraction with denominator $1$ .

$\frac{6}{1} - 9 + \frac{25}{2}$

Step 3.2

Multiply $\frac{6}{1}$ by $\frac{2}{2}$ .

$\frac{6}{1} \cdot \frac{2}{2} - 9 + \frac{25}{2}$

Step 3.3

Multiply $\frac{6}{1}$ by $\frac{2}{2}$ .

$\frac{6 \cdot 2}{2} - 9 + \frac{25}{2}$

Step 3.4

Write $- 9$ as a fraction with denominator $1$ .

$\frac{6 \cdot 2}{2} + \frac{- 9}{1} + \frac{25}{2}$

Step 3.5

Multiply $\frac{- 9}{1}$ by $\frac{2}{2}$ .

$\frac{6 \cdot 2}{2} + \frac{- 9}{1} \cdot \frac{2}{2} + \frac{25}{2}$

Step 3.6

Multiply $\frac{- 9}{1}$ by $\frac{2}{2}$ .

$\frac{6 \cdot 2}{2} + \frac{- 9 \cdot 2}{2} + \frac{25}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 \cdot 2 - 9 \cdot 2 + 25}{2}$

Step 5

Simplify each term.

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Step 5.1

Multiply $6$ by $2$ .

$\frac{12 - 9 \cdot 2 + 25}{2}$

Step 5.2

Multiply $- 9$ by $2$ .

$\frac{12 - 18 + 25}{2}$

Step 6

Simplify by adding and subtracting.

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Step 6.1

Subtract $18$ from $12$ .

$\frac{- 6 + 25}{2}$

Step 6.2

Add $- 6$ and $25$ .

$\frac{19}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{2}$

Decimal Form:

$9.5$

Mixed Number Form:

$9 \frac{1}{2}$