Basic Math Examples

$\frac{5}{6} y - \frac{7}{12} = \frac{3}{4} y - \frac{13}{6}$

Step 1

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

$\frac{5 y}{6} - \frac{7}{12} = \frac{3}{4} y - \frac{13}{6}$

Step 2

Combine $\frac{3}{4}$ and $y$ .

$\frac{5 y}{6} - \frac{7}{12} = \frac{3 y}{4} - \frac{13}{6}$

Step 3

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

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Step 3.1

Subtract $\frac{3 y}{4}$ from both sides of the equation.

$\frac{5 y}{6} - \frac{7}{12} - \frac{3 y}{4} = - \frac{13}{6}$

Step 3.2

To write $\frac{5 y}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 y}{6} \cdot \frac{2}{2} - \frac{3 y}{4} - \frac{7}{12} = - \frac{13}{6}$

Step 3.3

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

$\frac{5 y}{6} \cdot \frac{2}{2} - \frac{3 y}{4} \cdot \frac{3}{3} - \frac{7}{12} = - \frac{13}{6}$

Step 3.4

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

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Step 3.4.1

Multiply $\frac{5 y}{6}$ by $\frac{2}{2}$ .

$\frac{5 y \cdot 2}{6 \cdot 2} - \frac{3 y}{4} \cdot \frac{3}{3} - \frac{7}{12} = - \frac{13}{6}$

Step 3.4.2

Multiply $6$ by $2$ .

$\frac{5 y \cdot 2}{12} - \frac{3 y}{4} \cdot \frac{3}{3} - \frac{7}{12} = - \frac{13}{6}$

Step 3.4.3

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

$\frac{5 y \cdot 2}{12} - \frac{3 y \cdot 3}{4 \cdot 3} - \frac{7}{12} = - \frac{13}{6}$

Step 3.4.4

Multiply $4$ by $3$ .

$\frac{5 y \cdot 2}{12} - \frac{3 y \cdot 3}{12} - \frac{7}{12} = - \frac{13}{6}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{5 y \cdot 2 - 3 y \cdot 3}{12} - \frac{7}{12} = - \frac{13}{6}$

Step 3.6

Combine the numerators over the common denominator.

$\frac{5 y \cdot 2 - 3 y \cdot 3 - 7}{12} = - \frac{13}{6}$

Step 3.7

Simplify each term.

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Step 3.7.1

Multiply $2$ by $5$ .

$\frac{10 y - 3 y \cdot 3 - 7}{12} = - \frac{13}{6}$

Step 3.7.2

Multiply $3$ by $- 3$ .

$\frac{10 y - 9 y - 7}{12} = - \frac{13}{6}$

Step 3.8

Subtract $9 y$ from $10 y$ .

$\frac{y - 7}{12} = - \frac{13}{6}$

Step 4

Multiply both sides of the equation by $12$ .

$12 \frac{y - 7}{12} = 12 (- \frac{13}{6})$

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

Cancel the common factor of $12$ .

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Step 5.1.1.1

Cancel the common factor.

$12 \frac{y - 7}{12} = 12 (- \frac{13}{6})$

Step 5.1.1.2

Rewrite the expression.

$y - 7 = 12 (- \frac{13}{6})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $12 (- \frac{13}{6})$ .

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Step 5.2.1.1

Cancel the common factor of $6$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{13}{6}$ into the numerator.

$y - 7 = 12 (\frac{- 13}{6})$

Step 5.2.1.1.2

Factor $6$ out of $12$ .

$y - 7 = 6 (2) \frac{- 13}{6}$

Step 5.2.1.1.3

Cancel the common factor.

$y - 7 = 6 \cdot 2 \frac{- 13}{6}$

Step 5.2.1.1.4

Rewrite the expression.

$y - 7 = 2 \cdot - 13$

Step 5.2.1.2

Multiply $2$ by $- 13$ .

$y - 7 = - 26$

Step 6

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

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Step 6.1

Add $7$ to both sides of the equation.

$y = - 26 + 7$

Step 6.2

Add $- 26$ and $7$ .

$y = - 19$