Algebra Examples

$(\frac{- 3}{5} \div \frac{4}{10}) (\frac{- 1}{2} + \frac{1}{3})$

Step 1

Move the negative in front of the fraction.

$- \frac{3}{5} \div \frac{4}{10} (\frac{- 1}{2} + \frac{1}{3})$

Step 2

Cancel the common factor of $4$ and $10$ .

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Step 2.1

Factor $2$ out of $4$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $10$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

To divide by a fraction, multiply by its reciprocal.

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

Step 4

Cancel the common factor of $5$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Combine $- 3$ and $\frac{1}{2}$ .

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

Step 6

Move the negative in front of fractions.

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Step 6.1

Move the negative in front of the fraction.

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

Step 6.2

Move the negative in front of the fraction.

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

Step 7

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 8

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 9

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 9.2

Multiply $2$ by $3$ .

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

Step 9.3

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

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

Step 9.4

Multiply $3$ by $2$ .

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

Step 10

Simplify the expression.

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Step 10.1

Combine the numerators over the common denominator.

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

Step 10.2

Add $- 3$ and $2$ .

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

Step 11

Cancel the common factor of $3$ .

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Step 11.1

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

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

Step 11.2

Factor $3$ out of $- 3$ .

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

Step 11.3

Factor $3$ out of $6$ .

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

Step 11.4

Cancel the common factor.

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

Step 11.5

Rewrite the expression.

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

Step 12

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

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

Step 13

Multiply.

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Step 13.1

Multiply $- 1$ by $- 1$ .

$\frac{1}{2 \cdot 2}$

Step 13.2

Multiply $2$ by $2$ .

$\frac{1}{4}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$