Algebra Examples

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

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 $- \frac{3}{5}$ into the numerator.

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

Step 1.1.2

Factor $3$ out of $- 3$ .

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

Step 1.1.3

Cancel the common factor.

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

Step 1.1.4

Rewrite the expression.

$- \frac{5}{6} + \frac{- 1}{5}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{5}{6} - \frac{1}{5}$

Step 2

To write $- \frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{5}{6} \cdot \frac{5}{5} - \frac{1}{5}$

Step 3

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{5}{6} \cdot \frac{5}{5} - \frac{1}{5} \cdot \frac{6}{6}$

Step 4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{6}$ by $\frac{5}{5}$ .

$- \frac{5 \cdot 5}{6 \cdot 5} - \frac{1}{5} \cdot \frac{6}{6}$

Step 4.2

Multiply $6$ by $5$ .

$- \frac{5 \cdot 5}{30} - \frac{1}{5} \cdot \frac{6}{6}$

Step 4.3

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$- \frac{5 \cdot 5}{30} - \frac{6}{5 \cdot 6}$

Step 4.4

Multiply $5$ by $6$ .

$- \frac{5 \cdot 5}{30} - \frac{6}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 5 - 6}{30}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 5$ by $5$ .

$\frac{- 25 - 6}{30}$

Step 6.2

Subtract $6$ from $- 25$ .

$\frac{- 31}{30}$

Step 7

Move the negative in front of the fraction.

$- \frac{31}{30}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{31}{30}$

Decimal Form:

$- 1.0\overline{3}$

Mixed Number Form:

$- 1 \frac{1}{30}$