Basic Math Examples

$\frac{1}{3} - 5 y + \frac{5}{6} = \frac{2}{3} - 2 y$

Step 1

Simplify $\frac{1}{3} - 5 y + \frac{5}{6}$ .

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Step 1.1

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 5 y + \frac{1}{3} \cdot \frac{2}{2} + \frac{5}{6} = \frac{2}{3} - 2 y$

Step 1.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$- 5 y + \frac{2}{3 \cdot 2} + \frac{5}{6} = \frac{2}{3} - 2 y$

Step 1.2.2

Multiply $3$ by $2$ .

$- 5 y + \frac{2}{6} + \frac{5}{6} = \frac{2}{3} - 2 y$

Step 1.3

Combine the numerators over the common denominator.

$- 5 y + \frac{2 + 5}{6} = \frac{2}{3} - 2 y$

Step 1.4

Add $2$ and $5$ .

$- 5 y + \frac{7}{6} = \frac{2}{3} - 2 y$

Step 2

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

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Step 2.1

Add $2 y$ to both sides of the equation.

$- 5 y + \frac{7}{6} + 2 y = \frac{2}{3}$

Step 2.2

Add $- 5 y$ and $2 y$ .

$- 3 y + \frac{7}{6} = \frac{2}{3}$

Step 3

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

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Step 3.1

Subtract $\frac{7}{6}$ from both sides of the equation.

$- 3 y = \frac{2}{3} - \frac{7}{6}$

Step 3.2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 3 y = \frac{2}{3} \cdot \frac{2}{2} - \frac{7}{6}$

Step 3.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$- 3 y = \frac{2 \cdot 2}{3 \cdot 2} - \frac{7}{6}$

Step 3.3.2

Multiply $3$ by $2$ .

$- 3 y = \frac{2 \cdot 2}{6} - \frac{7}{6}$

Step 3.4

Combine the numerators over the common denominator.

$- 3 y = \frac{2 \cdot 2 - 7}{6}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $2$ .

$- 3 y = \frac{4 - 7}{6}$

Step 3.5.2

Subtract $7$ from $4$ .

$- 3 y = \frac{- 3}{6}$

Step 3.6

Cancel the common factor of $- 3$ and $6$ .

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Step 3.6.1

Factor $3$ out of $- 3$ .

$- 3 y = \frac{3 (- 1)}{6}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $3$ out of $6$ .

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

Step 3.6.2.2

Cancel the common factor.

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

Step 3.6.2.3

Rewrite the expression.

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

Step 3.7

Move the negative in front of the fraction.

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

Step 4

Divide each term in $- 3 y = - \frac{1}{2}$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 y = - \frac{1}{2}$ by $- 3$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $y$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 4.3.2

Move the negative in front of the fraction.

$y = - \frac{1}{2} (- \frac{1}{3})$

Step 4.3.3

Multiply $- \frac{1}{2} (- \frac{1}{3})$ .

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Step 4.3.3.1

Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{1}{2}) \frac{1}{3}$

Step 4.3.3.2

Multiply $\frac{1}{2}$ by $1$ .

$y = \frac{1}{2} \cdot \frac{1}{3}$

Step 4.3.3.3

Multiply $\frac{1}{2}$ by $\frac{1}{3}$ .

$y = \frac{1}{2 \cdot 3}$

Step 4.3.3.4

Multiply $2$ by $3$ .

$y = \frac{1}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{1}{6}$

Decimal Form:

$y = 0.1\overline{6}$