Basic Math Examples

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

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

Step 1

Convert

2 \frac{1}{2}

$2 \frac{1}{2}$ 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})

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

Step 1.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

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

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

2

$2$ .

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

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

Step 1.2.4.2

Add

4

$4$ and

1

$1$ .

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

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

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

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

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

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

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

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

Step 2

Simplify each term.

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Step 2.1

Divide

9

$9$ by

3

$3$ .

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

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

Step 2.2

Multiply

3

$3$ by

2

$2$ .

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

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

Step 2.3

Subtract

1

$1$ from

4

$4$ .

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

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

Step 2.4

Multiply

- 3

$- 3$ by

3

$3$ .

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

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

Step 2.5

Multiply

5 (\frac{5}{2})

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

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Step 2.5.1

Combine

5

$5$ and

\frac{5}{2}

$\frac{5}{2}$ .

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

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

Step 2.5.2

Multiply

5

$5$ by

5

$5$ .

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

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

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

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

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

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

Step 3

Find the common denominator.

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Step 3.1

Write

6

$6$ as a fraction with denominator

1

$1$ .

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

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

Step 3.2

Multiply

\frac{6}{1}

$\frac{6}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 3.3

Multiply

\frac{6}{1}

$\frac{6}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 3.4

Write

- 9

$- 9$ as a fraction with denominator

1

$1$ .

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

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

Step 3.5

Multiply

\frac{- 9}{1}

$\frac{- 9}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 3.6

Multiply

\frac{- 9}{1}

$\frac{- 9}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

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

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

Step 5

Simplify each term.

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Step 5.1

Multiply

6

$6$ by

2

$2$ .

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

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

Step 5.2

Multiply

- 9

$- 9$ by

2

$2$ .

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

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

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

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

Step 6

Simplify by adding and subtracting.

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Step 6.1

Subtract

18

$18$ from

12

$12$ .

\frac{- 6 + 25}{2}

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

Step 6.2

Add

- 6

$- 6$ and

25

$25$ .

\frac{19}{2}

$\frac{19}{2}$

\frac{19}{2}

$\frac{19}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{19}{2}

$\frac{19}{2}$

Decimal Form:

9.5

$9.5$

Mixed Number Form:

9 \frac{1}{2}

$9 \frac{1}{2}$