Basic Math Examples

$- \frac{5}{3} r - 2 r = - \frac{11}{9}$

Step 1

Simplify $- \frac{5}{3} r - 2 r$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $r$ and $\frac{5}{3}$ .

$- \frac{r \cdot 5}{3} - 2 r = - \frac{11}{9}$

Step 1.1.2

Move $5$ to the left of $r$ .

$- \frac{5 r}{3} - 2 r = - \frac{11}{9}$

Step 1.2

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

$- \frac{5 r}{3} - 2 r \cdot \frac{3}{3} = - \frac{11}{9}$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$- \frac{5 r}{3} + \frac{- 2 r \cdot 3}{3} = - \frac{11}{9}$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{- 5 r - 2 r \cdot 3}{3} = - \frac{11}{9}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $r$ out of $- 5 r - 2 r \cdot 3$ .

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Step 1.4.1.1

Factor $r$ out of $- 5 r$ .

$\frac{r \cdot - 5 - 2 r \cdot 3}{3} = - \frac{11}{9}$

Step 1.4.1.2

Factor $r$ out of $- 2 r \cdot 3$ .

$\frac{r \cdot - 5 + r (- 2 \cdot 3)}{3} = - \frac{11}{9}$

Step 1.4.1.3

Factor $r$ out of $r \cdot - 5 + r (- 2 \cdot 3)$ .

$\frac{r (- 5 - 2 \cdot 3)}{3} = - \frac{11}{9}$

Step 1.4.2

Multiply $- 2$ by $3$ .

$\frac{r (- 5 - 6)}{3} = - \frac{11}{9}$

Step 1.4.3

Subtract $6$ from $- 5$ .

$\frac{r \cdot - 11}{3} = - \frac{11}{9}$

Step 1.5

Simplify the expression.

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Step 1.5.1

Move $- 11$ to the left of $r$ .

$\frac{- 11 \cdot r}{3} = - \frac{11}{9}$

Step 1.5.2

Move the negative in front of the fraction.

$- \frac{11 r}{3} = - \frac{11}{9}$

Step 2

Multiply both sides of the equation by $- \frac{3}{11}$ .

$- \frac{3}{11} (- \frac{11 r}{3}) = - \frac{3}{11} (- \frac{11}{9})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- \frac{3}{11} (- \frac{11 r}{3})$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{3}{11}$ into the numerator.

$\frac{- 3}{11} (- \frac{11 r}{3}) = - \frac{3}{11} (- \frac{11}{9})$

Step 3.1.1.1.2

Move the leading negative in $- \frac{11 r}{3}$ into the numerator.

$\frac{- 3}{11} \cdot \frac{- 11 r}{3} = - \frac{3}{11} (- \frac{11}{9})$

Step 3.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{11} \cdot \frac{- 11 r}{3} = - \frac{3}{11} (- \frac{11}{9})$

Step 3.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{11} \cdot \frac{- 11 r}{3} = - \frac{3}{11} (- \frac{11}{9})$

Step 3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{11} (- 11 r) = - \frac{3}{11} (- \frac{11}{9})$

Step 3.1.1.2

Cancel the common factor of $11$ .

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Step 3.1.1.2.1

Factor $11$ out of $- 11 r$ .

$\frac{- 1}{11} (11 (- r)) = - \frac{3}{11} (- \frac{11}{9})$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{11} (11 (- r)) = - \frac{3}{11} (- \frac{11}{9})$

Step 3.1.1.2.3

Rewrite the expression.

$- - r = - \frac{3}{11} (- \frac{11}{9})$

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 r = - \frac{3}{11} (- \frac{11}{9})$

Step 3.1.1.3.2

Multiply $r$ by $1$ .

$r = - \frac{3}{11} (- \frac{11}{9})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{3}{11} (- \frac{11}{9})$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{3}{11}$ into the numerator.

$r = \frac{- 3}{11} (- \frac{11}{9})$

Step 3.2.1.1.2

Move the leading negative in $- \frac{11}{9}$ into the numerator.

$r = \frac{- 3}{11} \cdot \frac{- 11}{9}$

Step 3.2.1.1.3

Factor $3$ out of $- 3$ .

$r = \frac{3 (- 1)}{11} \cdot \frac{- 11}{9}$

Step 3.2.1.1.4

Factor $3$ out of $9$ .

$r = \frac{3 \cdot - 1}{11} \cdot \frac{- 11}{3 \cdot 3}$

Step 3.2.1.1.5

Cancel the common factor.

$r = \frac{3 \cdot - 1}{11} \cdot \frac{- 11}{3 \cdot 3}$

Step 3.2.1.1.6

Rewrite the expression.

$r = \frac{- 1}{11} \cdot \frac{- 11}{3}$

Step 3.2.1.2

Cancel the common factor of $11$ .

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Step 3.2.1.2.1

Factor $11$ out of $- 11$ .

$r = \frac{- 1}{11} \cdot \frac{11 (- 1)}{3}$

Step 3.2.1.2.2

Cancel the common factor.

$r = \frac{- 1}{11} \cdot \frac{11 \cdot - 1}{3}$

Step 3.2.1.2.3

Rewrite the expression.

$r = - \frac{- 1}{3}$

Step 3.2.1.3

Move the negative in front of the fraction.

$r = - - \frac{1}{3}$

Step 3.2.1.4

Multiply $- - \frac{1}{3}$ .

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Step 3.2.1.4.1

Multiply $- 1$ by $- 1$ .

$r = 1 (\frac{1}{3})$

Step 3.2.1.4.2

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

$r = \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = \frac{1}{3}$

Decimal Form:

$r = 0.\overline{3}$