Basic Math Examples

2 \frac{1}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$2 \frac{1}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

Step 1

Convert

2 \frac{1}{5}

$2 \frac{1}{5}$ 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{1}{5}) \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$(2 + \frac{1}{5}) \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

Step 1.2

Add

2

$2$ and

\frac{1}{5}

$\frac{1}{5}$ .

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Step 1.2.1

To write

2

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

\frac{5}{5}

$\frac{5}{5}$ .

(2 \cdot \frac{5}{5} + \frac{1}{5}) \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$(2 \cdot \frac{5}{5} + \frac{1}{5}) \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

Step 1.2.2

Combine

2

$2$ and

\frac{5}{5}

$\frac{5}{5}$ .

(\frac{2 \cdot 5}{5} + \frac{1}{5}) \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$(\frac{2 \cdot 5}{5} + \frac{1}{5}) \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 5 + 1}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$\frac{2 \cdot 5 + 1}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

5

$5$ .

\frac{10 + 1}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$\frac{10 + 1}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

Step 1.2.4.2

Add

10

$10$ and

1

$1$ .

\frac{11}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

\frac{11}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

\frac{11}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

\frac{11}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- 2 \frac{2}{15}) \div 3 \frac{1}{10}$

Step 2

Convert

2 \frac{2}{15}

$2 \frac{2}{15}$ to an improper fraction.

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Step 2.1

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

\frac{11}{5} \cdot (- (2 + \frac{2}{15})) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- (2 + \frac{2}{15})) \div 3 \frac{1}{10}$

Step 2.2

Add

2

$2$ and

\frac{2}{15}

$\frac{2}{15}$ .

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Step 2.2.1

To write

2

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

\frac{15}{15}

$\frac{15}{15}$ .

\frac{11}{5} \cdot (- (2 \cdot \frac{15}{15} + \frac{2}{15})) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- (2 \cdot \frac{15}{15} + \frac{2}{15})) \div 3 \frac{1}{10}$

Step 2.2.2

Combine

2

$2$ and

\frac{15}{15}

$\frac{15}{15}$ .

\frac{11}{5} \cdot (- (\frac{2 \cdot 15}{15} + \frac{2}{15})) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- (\frac{2 \cdot 15}{15} + \frac{2}{15})) \div 3 \frac{1}{10}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{11}{5} \cdot (- \frac{2 \cdot 15 + 2}{15}) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- \frac{2 \cdot 15 + 2}{15}) \div 3 \frac{1}{10}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

15

$15$ .

\frac{11}{5} \cdot (- \frac{30 + 2}{15}) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- \frac{30 + 2}{15}) \div 3 \frac{1}{10}$

Step 2.2.4.2

Add

30

$30$ and

2

$2$ .

\frac{11}{5} \cdot (- \frac{32}{15}) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- \frac{32}{15}) \div 3 \frac{1}{10}$

\frac{11}{5} \cdot (- \frac{32}{15}) \div 3 \frac{1}{10}

$\frac{11}{5} \cdot (- \frac{32}{15}) \div 3 \frac{1}{10}$

Step 3

Convert

$3 \frac{1}{10}$ to an improper fraction.

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Step 3.1

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

$\frac{11}{5} \cdot (- \frac{32}{15}) \div (3 + \frac{1}{10})$

Step 3.2

Add

$3$ and

$\frac{1}{10}$ .

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Step 3.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{10}{10}$ .

$\frac{11}{5} \cdot (- \frac{32}{15}) \div (3 \cdot \frac{10}{10} + \frac{1}{10})$

Step 3.2.2

Combine

$3$ and

$\frac{10}{10}$ .

$\frac{11}{5} \cdot (- \frac{32}{15}) \div (\frac{3 \cdot 10}{10} + \frac{1}{10})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{11}{5} \cdot (- \frac{32}{15}) \div \frac{3 \cdot 10 + 1}{10}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

$3$ by

$10$ .

$\frac{11}{5} \cdot (- \frac{32}{15}) \div \frac{30 + 1}{10}$

Step 3.2.4.2

Add

$30$ and

$1$ .

$\frac{11}{5} \cdot (- \frac{32}{15}) \div \frac{31}{10}$

Step 4

To divide by a fraction, multiply by its reciprocal.

$\frac{11}{5} \cdot (- \frac{32}{15}) \frac{10}{31}$

Step 5

Multiply

$\frac{11}{5} (- \frac{32}{15})$ .

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Step 5.1

Multiply

$\frac{11}{5}$ by

$\frac{32}{15}$ .

$- \frac{11 \cdot 32}{5 \cdot 15} \cdot \frac{10}{31}$

Step 5.2

Multiply

$11$ by

$32$ .

$- \frac{352}{5 \cdot 15} \cdot \frac{10}{31}$

Step 5.3

Multiply

$5$ by

$15$ .

$- \frac{352}{75} \cdot \frac{10}{31}$

Step 6

Cancel the common factor of

$5$ .

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Step 6.1

Move the leading negative in

$- \frac{352}{75}$ into the numerator.

$\frac{- 352}{75} \cdot \frac{10}{31}$

Step 6.2

Factor

$5$ out of

$75$ .

$\frac{- 352}{5 (15)} \cdot \frac{10}{31}$

Step 6.3

Factor

$5$ out of

$10$ .

$\frac{- 352}{5 \cdot 15} \cdot \frac{5 \cdot 2}{31}$

Step 6.4

Cancel the common factor.

$\frac{- 352}{5 \cdot 15} \cdot \frac{5 \cdot 2}{31}$

Step 6.5

Rewrite the expression.

$\frac{- 352}{15} \cdot \frac{2}{31}$

Step 7

Multiply

$\frac{- 352}{15}$ by

$\frac{2}{31}$ .

$\frac{- 352 \cdot 2}{15 \cdot 31}$

Step 8

Simplify the expression.

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Step 8.1

Multiply

$- 352$ by

$2$ .

$\frac{- 704}{15 \cdot 31}$

Step 8.2

Multiply

$15$ by

$31$ .

$\frac{- 704}{465}$

Step 8.3

Move the negative in front of the fraction.

$- \frac{704}{465}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{704}{465}$

Decimal Form:

$- 1.51397849 \dots$

Mixed Number Form:

$- 1 \frac{239}{465}$