Algebra Examples

$- \frac{5}{3} (- \frac{2}{7} + \frac{4}{5})$

Step 1

To write $- \frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{5}{3} \cdot (- \frac{2}{7} \cdot \frac{5}{5} + \frac{4}{5})$

Step 2

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{5}{3} \cdot (- \frac{2}{7} \cdot \frac{5}{5} + \frac{4}{5} \cdot \frac{7}{7})$

Step 3

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2}{7}$ by $\frac{5}{5}$ .

$- \frac{5}{3} \cdot (- \frac{2 \cdot 5}{7 \cdot 5} + \frac{4}{5} \cdot \frac{7}{7})$

Step 3.2

Multiply $7$ by $5$ .

$- \frac{5}{3} \cdot (- \frac{2 \cdot 5}{35} + \frac{4}{5} \cdot \frac{7}{7})$

Step 3.3

Multiply $\frac{4}{5}$ by $\frac{7}{7}$ .

$- \frac{5}{3} \cdot (- \frac{2 \cdot 5}{35} + \frac{4 \cdot 7}{5 \cdot 7})$

Step 3.4

Multiply $5$ by $7$ .

$- \frac{5}{3} \cdot (- \frac{2 \cdot 5}{35} + \frac{4 \cdot 7}{35})$

Step 4

Combine the numerators over the common denominator.

$- \frac{5}{3} \cdot \frac{- 2 \cdot 5 + 4 \cdot 7}{35}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 2$ by $5$ .

$- \frac{5}{3} \cdot \frac{- 10 + 4 \cdot 7}{35}$

Step 5.2

Multiply $4$ by $7$ .

$- \frac{5}{3} \cdot \frac{- 10 + 28}{35}$

Step 5.3

Add $- 10$ and $28$ .

$- \frac{5}{3} \cdot \frac{18}{35}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

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

$\frac{- 5}{3} \cdot \frac{18}{35}$

Step 6.2

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{3} \cdot \frac{18}{35}$

Step 6.3

Factor $5$ out of $35$ .

$\frac{5 \cdot - 1}{3} \cdot \frac{18}{5 \cdot 7}$

Step 6.4

Cancel the common factor.

$\frac{5 \cdot - 1}{3} \cdot \frac{18}{5 \cdot 7}$

Step 6.5

Rewrite the expression.

$\frac{- 1}{3} \cdot \frac{18}{7}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Factor $3$ out of $18$ .

$\frac{- 1}{3} \cdot \frac{3 (6)}{7}$

Step 7.2

Cancel the common factor.

$\frac{- 1}{3} \cdot \frac{3 \cdot 6}{7}$

Step 7.3

Rewrite the expression.

$- 1 \cdot \frac{6}{7}$

Step 8

Rewrite $- 1 (\frac{6}{7})$ as $- (\frac{6}{7})$ .

$- \frac{6}{7}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{6}{7}$

Decimal Form:

$- 0.\overline{857142}$