Basic Math Examples

$(- 2 \frac{2}{15}) (- 5 \frac{3}{20}) \div 2 \frac{9}{10}$

Step 1

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

Tap for more steps...

Step 1.1

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

$- (2 + \frac{2}{15}) (- 5 \frac{3}{20}) \div 2 \frac{9}{10}$

Step 1.2

Add $2$ and $\frac{2}{15}$ .

Tap for more steps...

Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$- (2 \cdot \frac{15}{15} + \frac{2}{15}) (- 5 \frac{3}{20}) \div 2 \frac{9}{10}$

Step 1.2.2

Combine $2$ and $\frac{15}{15}$ .

$- (\frac{2 \cdot 15}{15} + \frac{2}{15}) (- 5 \frac{3}{20}) \div 2 \frac{9}{10}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 15 + 2}{15} (- 5 \frac{3}{20}) \div 2 \frac{9}{10}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $2$ by $15$ .

$- \frac{30 + 2}{15} (- 5 \frac{3}{20}) \div 2 \frac{9}{10}$

Step 1.2.4.2

Add $30$ and $2$ .

$- \frac{32}{15} (- 5 \frac{3}{20}) \div 2 \frac{9}{10}$

Step 2

Convert $5 \frac{3}{20}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$- \frac{32}{15} (- (5 + \frac{3}{20})) \div 2 \frac{9}{10}$

Step 2.2

Add $5$ and $\frac{3}{20}$ .

Tap for more steps...

Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$- \frac{32}{15} (- (5 \cdot \frac{20}{20} + \frac{3}{20})) \div 2 \frac{9}{10}$

Step 2.2.2

Combine $5$ and $\frac{20}{20}$ .

$- \frac{32}{15} (- (\frac{5 \cdot 20}{20} + \frac{3}{20})) \div 2 \frac{9}{10}$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{32}{15} (- \frac{5 \cdot 20 + 3}{20}) \div 2 \frac{9}{10}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $5$ by $20$ .

$- \frac{32}{15} (- \frac{100 + 3}{20}) \div 2 \frac{9}{10}$

Step 2.2.4.2

Add $100$ and $3$ .

$- \frac{32}{15} (- \frac{103}{20}) \div 2 \frac{9}{10}$

Step 3

Convert $2 \frac{9}{10}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

$- \frac{32}{15} (- \frac{103}{20}) \div (2 + \frac{9}{10})$

Step 3.2

Add $2$ and $\frac{9}{10}$ .

Tap for more steps...

Step 3.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- \frac{32}{15} (- \frac{103}{20}) \div (2 \cdot \frac{10}{10} + \frac{9}{10})$

Step 3.2.2

Combine $2$ and $\frac{10}{10}$ .

$- \frac{32}{15} (- \frac{103}{20}) \div (\frac{2 \cdot 10}{10} + \frac{9}{10})$

Step 3.2.3

Combine the numerators over the common denominator.

$- \frac{32}{15} (- \frac{103}{20}) \div \frac{2 \cdot 10 + 9}{10}$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply $2$ by $10$ .

$- \frac{32}{15} (- \frac{103}{20}) \div \frac{20 + 9}{10}$

Step 3.2.4.2

Add $20$ and $9$ .

$- \frac{32}{15} (- \frac{103}{20}) \div \frac{29}{10}$

Step 4

To divide by a fraction, multiply by its reciprocal.

$- \frac{32}{15} (- \frac{103}{20}) \frac{10}{29}$

Step 5

Cancel the common factor of $4$ .

Tap for more steps...

Step 5.1

Move the leading negative in $- \frac{32}{15}$ into the numerator.

$\frac{- 32}{15} (- \frac{103}{20}) \frac{10}{29}$

Step 5.2

Move the leading negative in $- \frac{103}{20}$ into the numerator.

$\frac{- 32}{15} \cdot \frac{- 103}{20} \frac{10}{29}$

Step 5.3

Factor $4$ out of $- 32$ .

$\frac{4 (- 8)}{15} \cdot \frac{- 103}{20} \frac{10}{29}$

Step 5.4

Factor $4$ out of $20$ .

$\frac{4 \cdot - 8}{15} \cdot \frac{- 103}{4 \cdot 5} \frac{10}{29}$

Step 5.5

Cancel the common factor.

$\frac{4 \cdot - 8}{15} \cdot \frac{- 103}{4 \cdot 5} \frac{10}{29}$

Step 5.6

Rewrite the expression.

$\frac{- 8}{15} \cdot \frac{- 103}{5} \frac{10}{29}$

Step 6

Multiply $\frac{- 8}{15}$ by $\frac{- 103}{5}$ .

$\frac{- 8 \cdot - 103}{15 \cdot 5} \cdot \frac{10}{29}$

Step 7

Multiply.

Tap for more steps...

Step 7.1

Multiply $- 8$ by $- 103$ .

$\frac{824}{15 \cdot 5} \cdot \frac{10}{29}$

Step 7.2

Multiply $15$ by $5$ .

$\frac{824}{75} \cdot \frac{10}{29}$

Step 8

Cancel the common factor of $5$ .

Tap for more steps...

Step 8.1

Factor $5$ out of $75$ .

$\frac{824}{5 (15)} \cdot \frac{10}{29}$

Step 8.2

Factor $5$ out of $10$ .

$\frac{824}{5 \cdot 15} \cdot \frac{5 \cdot 2}{29}$

Step 8.3

Cancel the common factor.

$\frac{824}{5 \cdot 15} \cdot \frac{5 \cdot 2}{29}$

Step 8.4

Rewrite the expression.

$\frac{824}{15} \cdot \frac{2}{29}$

Step 9

Multiply $\frac{824}{15}$ by $\frac{2}{29}$ .

$\frac{824 \cdot 2}{15 \cdot 29}$

Step 10

Multiply.

Tap for more steps...

Step 10.1

Multiply $824$ by $2$ .

$\frac{1648}{15 \cdot 29}$

Step 10.2

Multiply $15$ by $29$ .

$\frac{1648}{435}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{1648}{435}$

Decimal Form:

$3.78850574 \dots$

Mixed Number Form:

$3 \frac{343}{435}$