Basic Math Examples

$(a \cdot \frac{2}{3}) + (b \cdot \frac{5}{6} - 30) + c = 180$

Step 1

Simplify each term.

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Step 1.1

Combine $a$ and $\frac{2}{3}$ .

$\frac{a \cdot 2}{3} + b \cdot \frac{5}{6} - 30 + c = 180$

Step 1.2

Move $2$ to the left of $a$ .

$\frac{2 \cdot a}{3} + b \cdot \frac{5}{6} - 30 + c = 180$

Step 1.3

Combine $b$ and $\frac{5}{6}$ .

$\frac{2 a}{3} + \frac{b \cdot 5}{6} - 30 + c = 180$

Step 1.4

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

$\frac{2 a}{3} + \frac{5 b}{6} - 30 + c = 180$

Step 2

Move all terms not containing $a$ to the right side of the equation.

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Step 2.1

Subtract $\frac{5 b}{6}$ from both sides of the equation.

$\frac{2 a}{3} - 30 + c = 180 - \frac{5 b}{6}$

Step 2.2

Add $30$ to both sides of the equation.

$\frac{2 a}{3} + c = 180 - \frac{5 b}{6} + 30$

Step 2.3

Subtract $c$ from both sides of the equation.

$\frac{2 a}{3} = 180 - \frac{5 b}{6} + 30 - c$

Step 2.4

Add $180$ and $30$ .

$\frac{2 a}{3} = - \frac{5 b}{6} + 210 - c$

Step 3

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 a}{3} = \frac{3}{2} (- \frac{5 b}{6} + 210 - c)$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{2} \cdot \frac{2 a}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 a}{3} = \frac{3}{2} (- \frac{5 b}{6} + 210 - c)$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 a) = \frac{3}{2} (- \frac{5 b}{6} + 210 - c)$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $2 a$ .

$\frac{1}{2} (2 (a)) = \frac{3}{2} (- \frac{5 b}{6} + 210 - c)$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 a) = \frac{3}{2} (- \frac{5 b}{6} + 210 - c)$

Step 4.1.1.2.3

Rewrite the expression.

$a = \frac{3}{2} (- \frac{5 b}{6} + 210 - c)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{2} (- \frac{5 b}{6} + 210 - c)$ .

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Step 4.2.1.1

Apply the distributive property.

$a = \frac{3}{2} (- \frac{5 b}{6}) + \frac{3}{2} \cdot 210 + \frac{3}{2} (- c)$

Step 4.2.1.2

Simplify.

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Step 4.2.1.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.2.1.1

Move the leading negative in $- \frac{5 b}{6}$ into the numerator.

$a = \frac{3}{2} \cdot \frac{- 5 b}{6} + \frac{3}{2} \cdot 210 + \frac{3}{2} (- c)$

Step 4.2.1.2.1.2

Factor $3$ out of $6$ .

$a = \frac{3}{2} \cdot \frac{- 5 b}{3 (2)} + \frac{3}{2} \cdot 210 + \frac{3}{2} (- c)$

Step 4.2.1.2.1.3

Cancel the common factor.

$a = \frac{3}{2} \cdot \frac{- 5 b}{3 \cdot 2} + \frac{3}{2} \cdot 210 + \frac{3}{2} (- c)$

Step 4.2.1.2.1.4

Rewrite the expression.

$a = \frac{1}{2} \cdot \frac{- 5 b}{2} + \frac{3}{2} \cdot 210 + \frac{3}{2} (- c)$

Step 4.2.1.2.2

Multiply $\frac{1}{2}$ by $\frac{- 5 b}{2}$ .

$a = \frac{- 5 b}{2 \cdot 2} + \frac{3}{2} \cdot 210 + \frac{3}{2} (- c)$

Step 4.2.1.2.3

Multiply $2$ by $2$ .

$a = \frac{- 5 b}{4} + \frac{3}{2} \cdot 210 + \frac{3}{2} (- c)$

Step 4.2.1.2.4

Cancel the common factor of $2$ .

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Step 4.2.1.2.4.1

Factor $2$ out of $210$ .

$a = \frac{- 5 b}{4} + \frac{3}{2} \cdot (2 (105)) + \frac{3}{2} (- c)$

Step 4.2.1.2.4.2

Cancel the common factor.

$a = \frac{- 5 b}{4} + \frac{3}{2} \cdot (2 \cdot 105) + \frac{3}{2} (- c)$

Step 4.2.1.2.4.3

Rewrite the expression.

$a = \frac{- 5 b}{4} + 3 \cdot 105 + \frac{3}{2} (- c)$

Step 4.2.1.2.5

Multiply $3$ by $105$ .

$a = \frac{- 5 b}{4} + 315 + \frac{3}{2} (- c)$

Step 4.2.1.2.6

Combine $\frac{3}{2}$ and $c$ .

$a = \frac{- 5 b}{4} + 315 - \frac{3 c}{2}$

Step 4.2.1.3

Move the negative in front of the fraction.

$a = - \frac{5 b}{4} + 315 - \frac{3 c}{2}$

Step 5

Move $315$ .

$a = - \frac{5 b}{4} - \frac{3 c}{2} + 315$