Basic Math Examples

$- \frac{2}{3} \cdot (- \frac{2}{5} + \frac{7}{1}) \div \frac{1}{3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$- \frac{2}{3} \cdot (- \frac{2}{5} + \frac{7}{1}) \cdot 3$

Step 2

Divide $7$ by $1$ .

$- \frac{2}{3} \cdot (- \frac{2}{5} + 7) \cdot 3$

Step 3

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{2}{3} \cdot (- \frac{2}{5} + 7 \cdot \frac{5}{5}) \cdot 3$

Step 4

Combine $7$ and $\frac{5}{5}$ .

$- \frac{2}{3} \cdot (- \frac{2}{5} + \frac{7 \cdot 5}{5}) \cdot 3$

Step 5

Combine the numerators over the common denominator.

$- \frac{2}{3} \cdot \frac{- 2 + 7 \cdot 5}{5} \cdot 3$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $7$ by $5$ .

$- \frac{2}{3} \cdot \frac{- 2 + 35}{5} \cdot 3$

Step 6.2

Add $- 2$ and $35$ .

$- \frac{2}{3} \cdot \frac{33}{5} \cdot 3$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{33}{5} \cdot 3$

Step 7.2

Factor $3$ out of $33$ .

$\frac{- 2}{3} \cdot \frac{3 (11)}{5} \cdot 3$

Step 7.3

Cancel the common factor.

$\frac{- 2}{3} \cdot \frac{3 \cdot 11}{5} \cdot 3$

Step 7.4

Rewrite the expression.

$- 2 \cdot \frac{11}{5} \cdot 3$

Step 8

Combine $- 2$ and $\frac{11}{5}$ .

$\frac{- 2 \cdot 11}{5} \cdot 3$

Step 9

Simplify the expression.

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Step 9.1

Multiply $- 2$ by $11$ .

$\frac{- 22}{5} \cdot 3$

Step 9.2

Move the negative in front of the fraction.

$- \frac{22}{5} \cdot 3$

Step 10

Multiply $- \frac{22}{5} \cdot 3$ .

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Step 10.1

Multiply $3$ by $- 1$ .

$- 3 (\frac{22}{5})$

Step 10.2

Combine $- 3$ and $\frac{22}{5}$ .

$\frac{- 3 \cdot 22}{5}$

Step 10.3

Multiply $- 3$ by $22$ .

$\frac{- 66}{5}$

Step 11

Move the negative in front of the fraction.

$- \frac{66}{5}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{66}{5}$

Decimal Form:

$- 13.2$

Mixed Number Form:

$- 13 \frac{1}{5}$