Basic Math Examples

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

Step 1

Simplify $\frac{3 y}{4} + \frac{y - 2}{3}$ .

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Step 1.1

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

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

Step 1.2

To write $\frac{y - 2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $4$ by $3$ .

$\frac{3 y \cdot 3}{12} + \frac{y - 2}{3} \cdot \frac{4}{4} = \frac{2 y + 1}{2} - 1$

Step 1.3.3

Multiply $\frac{y - 2}{3}$ by $\frac{4}{4}$ .

$\frac{3 y \cdot 3}{12} + \frac{(y - 2) \cdot 4}{3 \cdot 4} = \frac{2 y + 1}{2} - 1$

Step 1.3.4

Multiply $3$ by $4$ .

$\frac{3 y \cdot 3}{12} + \frac{(y - 2) \cdot 4}{12} = \frac{2 y + 1}{2} - 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 y \cdot 3 + (y - 2) \cdot 4}{12} = \frac{2 y + 1}{2} - 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $3$ by $3$ .

$\frac{9 y + (y - 2) \cdot 4}{12} = \frac{2 y + 1}{2} - 1$

Step 1.5.2

Apply the distributive property.

$\frac{9 y + y \cdot 4 - 2 \cdot 4}{12} = \frac{2 y + 1}{2} - 1$

Step 1.5.3

Move $4$ to the left of $y$ .

$\frac{9 y + 4 \cdot y - 2 \cdot 4}{12} = \frac{2 y + 1}{2} - 1$

Step 1.5.4

Multiply $- 2$ by $4$ .

$\frac{9 y + 4 \cdot y - 8}{12} = \frac{2 y + 1}{2} - 1$

Step 1.5.5

Add $9 y$ and $4 y$ .

$\frac{13 y - 8}{12} = \frac{2 y + 1}{2} - 1$

Step 2

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

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Step 2.1

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

$\frac{13 y - 8}{12} = \frac{2 y + 1}{2} - 1 \cdot \frac{2}{2}$

Step 2.2

Simplify terms.

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Step 2.2.1

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

$\frac{13 y - 8}{12} = \frac{2 y + 1}{2} + \frac{- 1 \cdot 2}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{13 y - 8}{12} = \frac{2 y + 1 - 1 \cdot 2}{2}$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Multiply $- 1$ by $2$ .

$\frac{13 y - 8}{12} = \frac{2 y + 1 - 2}{2}$

Step 2.3.2

Subtract $2$ from $1$ .

$\frac{13 y - 8}{12} = \frac{2 y - 1}{2}$

Step 3

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

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Step 3.1

Subtract $\frac{2 y - 1}{2}$ from both sides of the equation.

$\frac{13 y - 8}{12} - \frac{2 y - 1}{2} = 0$

Step 3.2

To write $- \frac{2 y - 1}{2}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{13 y - 8}{12} - \frac{2 y - 1}{2} \cdot \frac{6}{6} = 0$

Step 3.3

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

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Step 3.3.1

Multiply $\frac{2 y - 1}{2}$ by $\frac{6}{6}$ .

$\frac{13 y - 8}{12} - \frac{(2 y - 1) \cdot 6}{2 \cdot 6} = 0$

Step 3.3.2

Multiply $2$ by $6$ .

$\frac{13 y - 8}{12} - \frac{(2 y - 1) \cdot 6}{12} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{13 y - 8 - (2 y - 1) \cdot 6}{12} = 0$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Apply the distributive property.

$\frac{13 y - 8 + (- (2 y) - - 1) \cdot 6}{12} = 0$

Step 3.5.2

Multiply $2$ by $- 1$ .

$\frac{13 y - 8 + (- 2 y - - 1) \cdot 6}{12} = 0$

Step 3.5.3

Multiply $- 1$ by $- 1$ .

$\frac{13 y - 8 + (- 2 y + 1) \cdot 6}{12} = 0$

Step 3.5.4

Apply the distributive property.

$\frac{13 y - 8 - 2 y \cdot 6 + 1 \cdot 6}{12} = 0$

Step 3.5.5

Multiply $6$ by $- 2$ .

$\frac{13 y - 8 - 12 y + 1 \cdot 6}{12} = 0$

Step 3.5.6

Multiply $6$ by $1$ .

$\frac{13 y - 8 - 12 y + 6}{12} = 0$

Step 3.5.7

Subtract $12 y$ from $13 y$ .

$\frac{y - 8 + 6}{12} = 0$

Step 3.5.8

Add $- 8$ and $6$ .

$\frac{y - 2}{12} = 0$

Step 4

Set the numerator equal to zero.

$y - 2 = 0$

Step 5

Add $2$ to both sides of the equation.

$y = 2$