Basic Math Examples

$\frac{2}{3} \cdot (39 - y) = 56$

Step 1

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

$\frac{3}{2} (\frac{2}{3} \cdot (39 - y)) = \frac{3}{2} \cdot 56$

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 $\frac{3}{2} (\frac{2}{3} \cdot (39 - y))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} \cdot 39 + \frac{2}{3} (- y)) = \frac{3}{2} \cdot 56$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $39$ .

$\frac{3}{2} (\frac{2}{3} \cdot (3 (13)) + \frac{2}{3} (- y)) = \frac{3}{2} \cdot 56$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{3}{2} (\frac{2}{3} \cdot (3 \cdot 13) + \frac{2}{3} (- y)) = \frac{3}{2} \cdot 56$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{3}{2} (2 \cdot 13 + \frac{2}{3} (- y)) = \frac{3}{2} \cdot 56$

Step 2.1.1.3

Multiply $2$ by $13$ .

$\frac{3}{2} (26 + \frac{2}{3} (- y)) = \frac{3}{2} \cdot 56$

Step 2.1.1.4

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

$\frac{3}{2} (26 - \frac{2 y}{3}) = \frac{3}{2} \cdot 56$

Step 2.1.1.5

Apply the distributive property.

$\frac{3}{2} \cdot 26 + \frac{3}{2} (- \frac{2 y}{3}) = \frac{3}{2} \cdot 56$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Factor $2$ out of $26$ .

$\frac{3}{2} \cdot (2 (13)) + \frac{3}{2} (- \frac{2 y}{3}) = \frac{3}{2} \cdot 56$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{3}{2} \cdot (2 \cdot 13) + \frac{3}{2} (- \frac{2 y}{3}) = \frac{3}{2} \cdot 56$

Step 2.1.1.6.3

Rewrite the expression.

$3 \cdot 13 + \frac{3}{2} (- \frac{2 y}{3}) = \frac{3}{2} \cdot 56$

Step 2.1.1.7

Multiply $3$ by $13$ .

$39 + \frac{3}{2} (- \frac{2 y}{3}) = \frac{3}{2} \cdot 56$

Step 2.1.1.8

Cancel the common factor of $3$ .

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Step 2.1.1.8.1

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

$39 + \frac{3}{2} \cdot \frac{- 2 y}{3} = \frac{3}{2} \cdot 56$

Step 2.1.1.8.2

Cancel the common factor.

$39 + \frac{3}{2} \cdot \frac{- 2 y}{3} = \frac{3}{2} \cdot 56$

Step 2.1.1.8.3

Rewrite the expression.

$39 + \frac{1}{2} (- 2 y) = \frac{3}{2} \cdot 56$

Step 2.1.1.9

Cancel the common factor of $2$ .

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Step 2.1.1.9.1

Factor $2$ out of $- 2 y$ .

$39 + \frac{1}{2} (2 (- y)) = \frac{3}{2} \cdot 56$

Step 2.1.1.9.2

Cancel the common factor.

$39 + \frac{1}{2} (2 (- y)) = \frac{3}{2} \cdot 56$

Step 2.1.1.9.3

Rewrite the expression.

$39 - y = \frac{3}{2} \cdot 56$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} \cdot 56$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $56$ .

$39 - y = \frac{3}{2} \cdot (2 (28))$

Step 2.2.1.1.2

Cancel the common factor.

$39 - y = \frac{3}{2} \cdot (2 \cdot 28)$

Step 2.2.1.1.3

Rewrite the expression.

$39 - y = 3 \cdot 28$

Step 2.2.1.2

Multiply $3$ by $28$ .

$39 - y = 84$

Step 3

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

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Step 3.1

Subtract $39$ from both sides of the equation.

$- y = 84 - 39$

Step 3.2

Subtract $39$ from $84$ .

$- y = 45$

Step 4

Divide each term in $- y = 45$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- y = 45$ by $- 1$ .

$\frac{- y}{- 1} = \frac{45}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{45}{- 1}$

Step 4.2.2

Divide $y$ by $1$ .

$y = \frac{45}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $45$ by $- 1$ .

$y = - 45$