Basic Math Examples

$\frac{1}{2} \cdot (y - 2) + 2 = \frac{3}{8} \cdot (3 y - 4)$

Step 1

Simplify $\frac{1}{2} \cdot (y - 2) + 2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{2} y + \frac{1}{2} \cdot - 2 + 2 = \frac{3}{8} \cdot (3 y - 4)$

Step 1.1.2

Combine $\frac{1}{2}$ and $y$ .

$\frac{y}{2} + \frac{1}{2} \cdot - 2 + 2 = \frac{3}{8} \cdot (3 y - 4)$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Factor $2$ out of $- 2$ .

$\frac{y}{2} + \frac{1}{2} \cdot (2 (- 1)) + 2 = \frac{3}{8} \cdot (3 y - 4)$

Step 1.1.3.2

Cancel the common factor.

$\frac{y}{2} + \frac{1}{2} \cdot (2 \cdot - 1) + 2 = \frac{3}{8} \cdot (3 y - 4)$

Step 1.1.3.3

Rewrite the expression.

$\frac{y}{2} - 1 + 2 = \frac{3}{8} \cdot (3 y - 4)$

Step 1.2

Add $- 1$ and $2$ .

$\frac{y}{2} + 1 = \frac{3}{8} \cdot (3 y - 4)$

Step 2

Simplify $\frac{3}{8} \cdot (3 y - 4)$ .

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Step 2.1

Apply the distributive property.

$\frac{y}{2} + 1 = \frac{3}{8} (3 y) + \frac{3}{8} \cdot - 4$

Step 2.2

Multiply $\frac{3}{8} (3 y)$ .

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Step 2.2.1

Combine $3$ and $\frac{3}{8}$ .

$\frac{y}{2} + 1 = \frac{3 \cdot 3}{8} y + \frac{3}{8} \cdot - 4$

Step 2.2.2

Multiply $3$ by $3$ .

$\frac{y}{2} + 1 = \frac{9}{8} y + \frac{3}{8} \cdot - 4$

Step 2.2.3

Combine $\frac{9}{8}$ and $y$ .

$\frac{y}{2} + 1 = \frac{9 y}{8} + \frac{3}{8} \cdot - 4$

Step 2.3

Cancel the common factor of $4$ .

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Step 2.3.1

Factor $4$ out of $8$ .

$\frac{y}{2} + 1 = \frac{9 y}{8} + \frac{3}{4 (2)} \cdot - 4$

Step 2.3.2

Factor $4$ out of $- 4$ .

$\frac{y}{2} + 1 = \frac{9 y}{8} + \frac{3}{4 \cdot 2} \cdot (4 \cdot - 1)$

Step 2.3.3

Cancel the common factor.

$\frac{y}{2} + 1 = \frac{9 y}{8} + \frac{3}{4 \cdot 2} \cdot (4 \cdot - 1)$

Step 2.3.4

Rewrite the expression.

$\frac{y}{2} + 1 = \frac{9 y}{8} + \frac{3}{2} \cdot - 1$

Step 2.4

Combine $\frac{3}{2}$ and $- 1$ .

$\frac{y}{2} + 1 = \frac{9 y}{8} + \frac{3 \cdot - 1}{2}$

Step 2.5

Simplify the expression.

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Step 2.5.1

Multiply $3$ by $- 1$ .

$\frac{y}{2} + 1 = \frac{9 y}{8} + \frac{- 3}{2}$

Step 2.5.2

Move the negative in front of the fraction.

$\frac{y}{2} + 1 = \frac{9 y}{8} - \frac{3}{2}$

Step 3

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

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Step 3.1

Subtract $\frac{9 y}{8}$ from both sides of the equation.

$\frac{y}{2} + 1 - \frac{9 y}{8} = - \frac{3}{2}$

Step 3.2

To write $\frac{y}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{y}{2} \cdot \frac{4}{4} - \frac{9 y}{8} + 1 = - \frac{3}{2}$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{y}{2}$ by $\frac{4}{4}$ .

$\frac{y \cdot 4}{2 \cdot 4} - \frac{9 y}{8} + 1 = - \frac{3}{2}$

Step 3.3.2

Multiply $2$ by $4$ .

$\frac{y \cdot 4}{8} - \frac{9 y}{8} + 1 = - \frac{3}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{y \cdot 4 - 9 y}{8} + 1 = - \frac{3}{2}$

Step 3.5

Subtract $9 y$ from $y \cdot 4$ .

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Step 3.5.1

Reorder $y$ and $4$ .

$\frac{4 \cdot y - 9 y}{8} + 1 = - \frac{3}{2}$

Step 3.5.2

Subtract $9 y$ from $4 \cdot y$ .

$\frac{- 5 \cdot y}{8} + 1 = - \frac{3}{2}$

Step 3.6

Move the negative in front of the fraction.

$- \frac{5 y}{8} + 1 = - \frac{3}{2}$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$- \frac{5 y}{8} = - \frac{3}{2} - 1$

Step 4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5 y}{8} = - \frac{3}{2} - 1 \cdot \frac{2}{2}$

Step 4.3

Combine $- 1$ and $\frac{2}{2}$ .

$- \frac{5 y}{8} = - \frac{3}{2} + \frac{- 1 \cdot 2}{2}$

Step 4.4

Combine the numerators over the common denominator.

$- \frac{5 y}{8} = \frac{- 3 - 1 \cdot 2}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 1$ by $2$ .

$- \frac{5 y}{8} = \frac{- 3 - 2}{2}$

Step 4.5.2

Subtract $2$ from $- 3$ .

$- \frac{5 y}{8} = \frac{- 5}{2}$

Step 4.6

Move the negative in front of the fraction.

$- \frac{5 y}{8} = - \frac{5}{2}$

Step 5

Multiply both sides of the equation by $- \frac{8}{5}$ .

$- \frac{8}{5} (- \frac{5 y}{8}) = - \frac{8}{5} (- \frac{5}{2})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- \frac{8}{5} (- \frac{5 y}{8})$ .

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Step 6.1.1.1

Cancel the common factor of $8$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$\frac{- 8}{5} (- \frac{5 y}{8}) = - \frac{8}{5} (- \frac{5}{2})$

Step 6.1.1.1.2

Move the leading negative in $- \frac{5 y}{8}$ into the numerator.

$\frac{- 8}{5} \cdot \frac{- 5 y}{8} = - \frac{8}{5} (- \frac{5}{2})$

Step 6.1.1.1.3

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{5} \cdot \frac{- 5 y}{8} = - \frac{8}{5} (- \frac{5}{2})$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{8 \cdot - 1}{5} \cdot \frac{- 5 y}{8} = - \frac{8}{5} (- \frac{5}{2})$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 y) = - \frac{8}{5} (- \frac{5}{2})$

Step 6.1.1.2

Cancel the common factor of $5$ .

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Step 6.1.1.2.1

Factor $5$ out of $- 5 y$ .

$\frac{- 1}{5} (5 (- y)) = - \frac{8}{5} (- \frac{5}{2})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- y)) = - \frac{8}{5} (- \frac{5}{2})$

Step 6.1.1.2.3

Rewrite the expression.

$- - y = - \frac{8}{5} (- \frac{5}{2})$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{8}{5} (- \frac{5}{2})$

Step 6.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{8}{5} (- \frac{5}{2})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{8}{5} (- \frac{5}{2})$ .

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$y = \frac{- 8}{5} (- \frac{5}{2})$

Step 6.2.1.1.2

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$y = \frac{- 8}{5} \cdot \frac{- 5}{2}$

Step 6.2.1.1.3

Factor $2$ out of $- 8$ .

$y = \frac{2 (- 4)}{5} \cdot \frac{- 5}{2}$

Step 6.2.1.1.4

Cancel the common factor.

$y = \frac{2 \cdot - 4}{5} \cdot \frac{- 5}{2}$

Step 6.2.1.1.5

Rewrite the expression.

$y = \frac{- 4}{5} \cdot - 5$

Step 6.2.1.2

Cancel the common factor of $5$ .

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Step 6.2.1.2.1

Factor $5$ out of $- 5$ .

$y = \frac{- 4}{5} \cdot (5 (- 1))$

Step 6.2.1.2.2

Cancel the common factor.

$y = \frac{- 4}{5} \cdot (5 \cdot - 1)$

Step 6.2.1.2.3

Rewrite the expression.

$y = - 4 \cdot - 1$

Step 6.2.1.3

Multiply $- 4$ by $- 1$ .

$y = 4$