Basic Math Examples

- 2 \frac{2}{3} \cdot 4 \frac{1}{10}

$- 2 \frac{2}{3} \cdot 4 \frac{1}{10}$

Step 1

Convert

2 \frac{2}{3}

$2 \frac{2}{3}$ 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}) \cdot 4 \frac{1}{10}

$- (2 + \frac{2}{3}) \cdot 4 \frac{1}{10}$

Step 1.2

Add

2

$2$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

To write

2

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

\frac{3}{3}

$\frac{3}{3}$ .

- (2 \cdot \frac{3}{3} + \frac{2}{3}) \cdot 4 \frac{1}{10}

$- (2 \cdot \frac{3}{3} + \frac{2}{3}) \cdot 4 \frac{1}{10}$

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

- (\frac{2 \cdot 3}{3} + \frac{2}{3}) \cdot 4 \frac{1}{10}

$- (\frac{2 \cdot 3}{3} + \frac{2}{3}) \cdot 4 \frac{1}{10}$

Step 1.2.3

Combine the numerators over the common denominator.

- \frac{2 \cdot 3 + 2}{3} \cdot 4 \frac{1}{10}

$- \frac{2 \cdot 3 + 2}{3} \cdot 4 \frac{1}{10}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

3

$3$ .

- \frac{6 + 2}{3} \cdot 4 \frac{1}{10}

$- \frac{6 + 2}{3} \cdot 4 \frac{1}{10}$

Step 1.2.4.2

Add

6

$6$ and

2

$2$ .

- \frac{8}{3} \cdot 4 \frac{1}{10}

$- \frac{8}{3} \cdot 4 \frac{1}{10}$

- \frac{8}{3} \cdot 4 \frac{1}{10}

$- \frac{8}{3} \cdot 4 \frac{1}{10}$

- \frac{8}{3} \cdot 4 \frac{1}{10}

$- \frac{8}{3} \cdot 4 \frac{1}{10}$

- \frac{8}{3} \cdot 4 \frac{1}{10}

$- \frac{8}{3} \cdot 4 \frac{1}{10}$

Step 2

Convert

4 \frac{1}{10}

$4 \frac{1}{10}$ to an improper fraction.

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Step 2.1

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

- \frac{8}{3} \cdot (4 + \frac{1}{10})

$- \frac{8}{3} \cdot (4 + \frac{1}{10})$

Step 2.2

Add

4

$4$ and

\frac{1}{10}

$\frac{1}{10}$ .

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Step 2.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{10}{10}

$\frac{10}{10}$ .

- \frac{8}{3} \cdot (4 \cdot \frac{10}{10} + \frac{1}{10})

$- \frac{8}{3} \cdot (4 \cdot \frac{10}{10} + \frac{1}{10})$

Step 2.2.2

Combine

4

$4$ and

\frac{10}{10}

$\frac{10}{10}$ .

- \frac{8}{3} \cdot (\frac{4 \cdot 10}{10} + \frac{1}{10})

$- \frac{8}{3} \cdot (\frac{4 \cdot 10}{10} + \frac{1}{10})$

Step 2.2.3

Combine the numerators over the common denominator.

- \frac{8}{3} \cdot \frac{4 \cdot 10 + 1}{10}

$- \frac{8}{3} \cdot \frac{4 \cdot 10 + 1}{10}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

4

$4$ by

10

$10$ .

- \frac{8}{3} \cdot \frac{40 + 1}{10}

$- \frac{8}{3} \cdot \frac{40 + 1}{10}$

Step 2.2.4.2

Add

40

$40$ and

1

$1$ .

- \frac{8}{3} \cdot \frac{41}{10}

$- \frac{8}{3} \cdot \frac{41}{10}$

- \frac{8}{3} \cdot \frac{41}{10}

$- \frac{8}{3} \cdot \frac{41}{10}$

- \frac{8}{3} \cdot \frac{41}{10}

$- \frac{8}{3} \cdot \frac{41}{10}$

- \frac{8}{3} \cdot \frac{41}{10}

$- \frac{8}{3} \cdot \frac{41}{10}$

Step 3

Cancel the common factor of

2

$2$ .

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Step 3.1

Move the leading negative in

- \frac{8}{3}

$- \frac{8}{3}$ into the numerator.

\frac{- 8}{3} \cdot \frac{41}{10}

$\frac{- 8}{3} \cdot \frac{41}{10}$

Step 3.2

Factor

$2$ out of

$- 8$ .

$\frac{2 (- 4)}{3} \cdot \frac{41}{10}$

Step 3.3

Factor

$2$ out of

$10$ .

$\frac{2 \cdot - 4}{3} \cdot \frac{41}{2 \cdot 5}$

Step 3.4

Cancel the common factor.

$\frac{2 \cdot - 4}{3} \cdot \frac{41}{2 \cdot 5}$

Step 3.5

Rewrite the expression.

$\frac{- 4}{3} \cdot \frac{41}{5}$

Step 4

Multiply

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

$\frac{41}{5}$ .

$\frac{- 4 \cdot 41}{3 \cdot 5}$

Step 5

Simplify the expression.

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Step 5.1

Multiply

$- 4$ by

$41$ .

$\frac{- 164}{3 \cdot 5}$

Step 5.2

Multiply

$3$ by

$5$ .

$\frac{- 164}{15}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{164}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{164}{15}$

Decimal Form:

$- 10.9\overline{3}$

Mixed Number Form:

$- 10 \frac{14}{15}$