Basic Math Examples

$\frac{a}{6} - \frac{2}{3} = \frac{5 a}{18}$

Step 1

Multiply both sides by $18$ .

$(\frac{a}{6} - \frac{2}{3}) \cdot 18 = \frac{5 a}{18} \cdot 18$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{a}{6} - \frac{2}{3}) \cdot 18$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$\frac{a}{6} \cdot 18 - \frac{2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Step 2.1.1.1.2

Cancel the common factor of $6$ .

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Step 2.1.1.1.2.1

Factor $6$ out of $18$ .

$\frac{a}{6} \cdot (6 (3)) - \frac{2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Step 2.1.1.1.2.2

Cancel the common factor.

$\frac{a}{6} \cdot (6 \cdot 3) - \frac{2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Step 2.1.1.1.2.3

Rewrite the expression.

$a \cdot 3 - \frac{2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Step 2.1.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.1.3.1

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

$a \cdot 3 + \frac{- 2}{3} \cdot 18 = \frac{5 a}{18} \cdot 18$

Step 2.1.1.1.3.2

Factor $3$ out of $18$ .

$a \cdot 3 + \frac{- 2}{3} \cdot (3 (6)) = \frac{5 a}{18} \cdot 18$

Step 2.1.1.1.3.3

Cancel the common factor.

$a \cdot 3 + \frac{- 2}{3} \cdot (3 \cdot 6) = \frac{5 a}{18} \cdot 18$

Step 2.1.1.1.3.4

Rewrite the expression.

$a \cdot 3 - 2 \cdot 6 = \frac{5 a}{18} \cdot 18$

Step 2.1.1.1.4

Multiply $- 2$ by $6$ .

$a \cdot 3 - 12 = \frac{5 a}{18} \cdot 18$

Step 2.1.1.2

Move $3$ to the left of $a$ .

$3 a - 12 = \frac{5 a}{18} \cdot 18$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $18$ .

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Step 2.2.1.1

Cancel the common factor.

$3 a - 12 = \frac{5 a}{18} \cdot 18$

Step 2.2.1.2

Rewrite the expression.

$3 a - 12 = 5 a$

Step 3

Solve for $a$ .

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Step 3.1

Move all terms containing $a$ to the left side of the equation.

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Step 3.1.1

Subtract $5 a$ from both sides of the equation.

$3 a - 12 - 5 a = 0$

Step 3.1.2

Subtract $5 a$ from $3 a$ .

$- 2 a - 12 = 0$

Step 3.2

Add $12$ to both sides of the equation.

$- 2 a = 12$

Step 3.3

Divide each term in $- 2 a = 12$ by $- 2$ and simplify.

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Step 3.3.1

Divide each term in $- 2 a = 12$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{12}{- 2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{12}{- 2}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{12}{- 2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $12$ by $- 2$ .

$a = - 6$