Basic Math Examples

$\frac{10 a c}{11} = - 3$

Step 1

Multiply both sides of the equation by $\frac{11}{10}$ .

$\frac{11}{10} \cdot \frac{10 a c}{11} = \frac{11}{10} \cdot - 3$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{11}{10} \cdot \frac{10 a c}{11}$ .

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Step 2.1.1.1

Cancel the common factor of $11$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{11}{10} \cdot \frac{10 a c}{11} = \frac{11}{10} \cdot - 3$

Step 2.1.1.1.2

Rewrite the expression.

$\frac{1}{10} (10 a c) = \frac{11}{10} \cdot - 3$

Step 2.1.1.2

Cancel the common factor of $10$ .

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Step 2.1.1.2.1

Factor $10$ out of $10 a c$ .

$\frac{1}{10} (10 (a c)) = \frac{11}{10} \cdot - 3$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{1}{10} (10 (a c)) = \frac{11}{10} \cdot - 3$

Step 2.1.1.2.3

Rewrite the expression.

$a c = \frac{11}{10} \cdot - 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{11}{10} \cdot - 3$ .

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Step 2.2.1.1

Multiply $\frac{11}{10} \cdot - 3$ .

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Step 2.2.1.1.1

Combine $\frac{11}{10}$ and $- 3$ .

$a c = \frac{11 \cdot - 3}{10}$

Step 2.2.1.1.2

Multiply $11$ by $- 3$ .

$a c = \frac{- 33}{10}$

Step 2.2.1.2

Move the negative in front of the fraction.

$a c = - \frac{33}{10}$

Step 3

Divide each term in $a c = - \frac{33}{10}$ by $c$ and simplify.

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Step 3.1

Divide each term in $a c = - \frac{33}{10}$ by $c$ .

$\frac{a c}{c} = \frac{- \frac{33}{10}}{c}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $c$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{a c}{c} = \frac{- \frac{33}{10}}{c}$

Step 3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- \frac{33}{10}}{c}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$a = - \frac{33}{10} \cdot \frac{1}{c}$

Step 3.3.2

Multiply $\frac{1}{c}$ by $\frac{33}{10}$ .

$a = - \frac{33}{c \cdot 10}$

Step 3.3.3

Move $10$ to the left of $c$ .

$a = - \frac{33}{10 c}$