Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

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

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

Step 1.1.2

Cancel the common factor.

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

Step 1.1.3

Rewrite the expression.

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

Step 1.2

Combine $- 2$ and $\frac{1}{5}$ .

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

Step 1.3

Move the negative in front of the fraction.

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

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

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

Step 1.4.2

Factor $3$ out of $- 3$ .

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

Step 1.4.3

Factor $3$ out of $6$ .

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

Step 1.4.4

Cancel the common factor.

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

Step 1.4.5

Rewrite the expression.

$- \frac{2}{5} + \frac{5}{2} + \frac{- 1}{5} \cdot \frac{1}{2}$

Step 1.5

Multiply $\frac{- 1}{5}$ by $\frac{1}{2}$ .

$- \frac{2}{5} + \frac{5}{2} + \frac{- 1}{5 \cdot 2}$

Step 1.6

Multiply $5$ by $2$ .

$- \frac{2}{5} + \frac{5}{2} + \frac{- 1}{10}$

Step 1.7

Move the negative in front of the fraction.

$- \frac{2}{5} + \frac{5}{2} - \frac{1}{10}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{2}{5}$ by $\frac{2}{2}$ .

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

Step 2.2

Multiply $\frac{2}{5}$ by $\frac{2}{2}$ .

$- \frac{2 \cdot 2}{5 \cdot 2} + \frac{5}{2} - \frac{1}{10}$

Step 2.3

Multiply $\frac{5}{2}$ by $\frac{5}{5}$ .

$- \frac{2 \cdot 2}{5 \cdot 2} + \frac{5}{2} \cdot \frac{5}{5} - \frac{1}{10}$

Step 2.4

Multiply $\frac{5}{2}$ by $\frac{5}{5}$ .

$- \frac{2 \cdot 2}{5 \cdot 2} + \frac{5 \cdot 5}{2 \cdot 5} - \frac{1}{10}$

Step 2.5

Reorder the factors of $5 \cdot 2$ .

$- \frac{2 \cdot 2}{2 \cdot 5} + \frac{5 \cdot 5}{2 \cdot 5} - \frac{1}{10}$

Step 2.6

Multiply $2$ by $5$ .

$- \frac{2 \cdot 2}{10} + \frac{5 \cdot 5}{2 \cdot 5} - \frac{1}{10}$

Step 2.7

Multiply $2$ by $5$ .

$- \frac{2 \cdot 2}{10} + \frac{5 \cdot 5}{10} - \frac{1}{10}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 2 + 5 \cdot 5 - 1}{10}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 2$ by $2$ .

$\frac{- 4 + 5 \cdot 5 - 1}{10}$

Step 4.2

Multiply $5$ by $5$ .

$\frac{- 4 + 25 - 1}{10}$

Step 5

Simplify the expression.

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Step 5.1

Add $- 4$ and $25$ .

$\frac{21 - 1}{10}$

Step 5.2

Subtract $1$ from $21$ .

$\frac{20}{10}$

Step 5.3

Divide $20$ by $10$ .

$2$