Basic Math Examples

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

Step 1

Simplify $\frac{1}{3} y - \frac{1}{4} \cdot (y - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{3}$ and $y$ .

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Combine $y$ and $\frac{1}{4}$ .

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

Step 1.1.4

Multiply $- \frac{1}{4} \cdot - 1$ .

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Step 1.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 1.1.4.2

Multiply $\frac{1}{4}$ by $1$ .

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

Step 1.2

To write $\frac{y}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 1.3

To write $- \frac{y}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{y}{3}$ by $\frac{4}{4}$ .

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

Step 1.4.2

Multiply $3$ by $4$ .

$\frac{y \cdot 4}{12} - \frac{y}{4} \cdot \frac{3}{3} + \frac{1}{4} = 3 y$

Step 1.4.3

Multiply $\frac{y}{4}$ by $\frac{3}{3}$ .

$\frac{y \cdot 4}{12} - \frac{y \cdot 3}{4 \cdot 3} + \frac{1}{4} = 3 y$

Step 1.4.4

Multiply $4$ by $3$ .

$\frac{y \cdot 4}{12} - \frac{y \cdot 3}{12} + \frac{1}{4} = 3 y$

Step 1.5

Combine the numerators over the common denominator.

$\frac{y \cdot 4 - y \cdot 3}{12} + \frac{1}{4} = 3 y$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $y$ out of $y \cdot 4 - y \cdot 3$ .

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Step 1.6.1.1.1

Factor $y$ out of $y \cdot 4$ .

$\frac{y (4) - y \cdot 3}{12} + \frac{1}{4} = 3 y$

Step 1.6.1.1.2

Factor $y$ out of $- y \cdot 3$ .

$\frac{y (4) + y (- 1 \cdot 3)}{12} + \frac{1}{4} = 3 y$

Step 1.6.1.1.3

Factor $y$ out of $y (4) + y (- 1 \cdot 3)$ .

$\frac{y (4 - 1 \cdot 3)}{12} + \frac{1}{4} = 3 y$

Step 1.6.1.2

Multiply $- 1$ by $3$ .

$\frac{y (4 - 3)}{12} + \frac{1}{4} = 3 y$

Step 1.6.1.3

Subtract $3$ from $4$ .

$\frac{y \cdot 1}{12} + \frac{1}{4} = 3 y$

Step 1.6.2

Multiply $y$ by $1$ .

$\frac{y}{12} + \frac{1}{4} = 3 y$

Step 2

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

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Step 2.1

Subtract $3 y$ from both sides of the equation.

$\frac{y}{12} + \frac{1}{4} - 3 y = 0$

Step 2.2

To write $- 3 y$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{y}{12} - 3 y \cdot \frac{12}{12} + \frac{1}{4} = 0$

Step 2.3

Combine $- 3 y$ and $\frac{12}{12}$ .

$\frac{y}{12} + \frac{- 3 y \cdot 12}{12} + \frac{1}{4} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{y - 3 y \cdot 12}{12} + \frac{1}{4} = 0$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $y$ out of $y - 3 y \cdot 12$ .

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Step 2.5.1.1.1

Raise $y$ to the power of $1$ .

$\frac{y^{1} - 3 y \cdot 12}{12} + \frac{1}{4} = 0$

Step 2.5.1.1.2

Factor $y$ out of $y^{1}$ .

$\frac{y \cdot 1 - 3 y \cdot 12}{12} + \frac{1}{4} = 0$

Step 2.5.1.1.3

Factor $y$ out of $- 3 y \cdot 12$ .

$\frac{y \cdot 1 + y (- 3 \cdot 12)}{12} + \frac{1}{4} = 0$

Step 2.5.1.1.4

Factor $y$ out of $y \cdot 1 + y (- 3 \cdot 12)$ .

$\frac{y (1 - 3 \cdot 12)}{12} + \frac{1}{4} = 0$

Step 2.5.1.2

Multiply $- 3$ by $12$ .

$\frac{y (1 - 36)}{12} + \frac{1}{4} = 0$

Step 2.5.1.3

Subtract $36$ from $1$ .

$\frac{y \cdot - 35}{12} + \frac{1}{4} = 0$

Step 2.5.2

Move $- 35$ to the left of $y$ .

$\frac{- 35 \cdot y}{12} + \frac{1}{4} = 0$

Step 2.5.3

Move the negative in front of the fraction.

$- \frac{35 y}{12} + \frac{1}{4} = 0$

Step 3

Subtract $\frac{1}{4}$ from both sides of the equation.

$- \frac{35 y}{12} = - \frac{1}{4}$

Step 4

Multiply both sides of the equation by $- \frac{12}{35}$ .

$- \frac{12}{35} (- \frac{35 y}{12}) = - \frac{12}{35} (- \frac{1}{4})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{12}{35} (- \frac{35 y}{12})$ .

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Step 5.1.1.1

Cancel the common factor of $12$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{12}{35}$ into the numerator.

$\frac{- 12}{35} (- \frac{35 y}{12}) = - \frac{12}{35} (- \frac{1}{4})$

Step 5.1.1.1.2

Move the leading negative in $- \frac{35 y}{12}$ into the numerator.

$\frac{- 12}{35} \cdot \frac{- 35 y}{12} = - \frac{12}{35} (- \frac{1}{4})$

Step 5.1.1.1.3

Factor $12$ out of $- 12$ .

$\frac{12 (- 1)}{35} \cdot \frac{- 35 y}{12} = - \frac{12}{35} (- \frac{1}{4})$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{12 \cdot - 1}{35} \cdot \frac{- 35 y}{12} = - \frac{12}{35} (- \frac{1}{4})$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{35} (- 35 y) = - \frac{12}{35} (- \frac{1}{4})$

Step 5.1.1.2

Cancel the common factor of $35$ .

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Step 5.1.1.2.1

Factor $35$ out of $- 35 y$ .

$\frac{- 1}{35} (35 (- y)) = - \frac{12}{35} (- \frac{1}{4})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{35} (35 (- y)) = - \frac{12}{35} (- \frac{1}{4})$

Step 5.1.1.2.3

Rewrite the expression.

$- - y = - \frac{12}{35} (- \frac{1}{4})$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{12}{35} (- \frac{1}{4})$

Step 5.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{12}{35} (- \frac{1}{4})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{12}{35} (- \frac{1}{4})$ .

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Step 5.2.1.1

Cancel the common factor of $4$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{12}{35}$ into the numerator.

$y = \frac{- 12}{35} (- \frac{1}{4})$

Step 5.2.1.1.2

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$y = \frac{- 12}{35} \cdot \frac{- 1}{4}$

Step 5.2.1.1.3

Factor $4$ out of $- 12$ .

$y = \frac{4 (- 3)}{35} \cdot \frac{- 1}{4}$

Step 5.2.1.1.4

Cancel the common factor.

$y = \frac{4 \cdot - 3}{35} \cdot \frac{- 1}{4}$

Step 5.2.1.1.5

Rewrite the expression.

$y = \frac{- 3}{35} \cdot - 1$

Step 5.2.1.2

Combine $\frac{- 3}{35}$ and $- 1$ .

$y = \frac{- 3 \cdot - 1}{35}$

Step 5.2.1.3

Multiply $- 3$ by $- 1$ .

$y = \frac{3}{35}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{35}$

Decimal Form:

$y = 0.0\overline{857142}$