Basic Math Examples

$\frac{50}{52} + \frac{y}{2} + 5111 = y + 50$

Step 1

Simplify $\frac{50}{52} + \frac{y}{2} + 5111$ .

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Step 1.1

Cancel the common factor of $50$ and $52$ .

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Step 1.1.1

Factor $2$ out of $50$ .

$\frac{2 (25)}{52} + \frac{y}{2} + 5111 = y + 50$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $52$ .

$\frac{2 \cdot 25}{2 \cdot 26} + \frac{y}{2} + 5111 = y + 50$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 \cdot 25}{2 \cdot 26} + \frac{y}{2} + 5111 = y + 50$

Step 1.1.2.3

Rewrite the expression.

$\frac{25}{26} + \frac{y}{2} + 5111 = y + 50$

Step 1.2

To write $5111$ as a fraction with a common denominator, multiply by $\frac{26}{26}$ .

$\frac{y}{2} + \frac{25}{26} + 5111 \cdot \frac{26}{26} = y + 50$

Step 1.3

Combine $5111$ and $\frac{26}{26}$ .

$\frac{y}{2} + \frac{25}{26} + \frac{5111 \cdot 26}{26} = y + 50$

Step 1.4

Combine the numerators over the common denominator.

$\frac{y}{2} + \frac{25 + 5111 \cdot 26}{26} = y + 50$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $5111$ by $26$ .

$\frac{y}{2} + \frac{25 + 132886}{26} = y + 50$

Step 1.5.2

Add $25$ and $132886$ .

$\frac{y}{2} + \frac{132911}{26} = y + 50$

Step 2

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

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Step 2.1

Subtract $y$ from both sides of the equation.

$\frac{y}{2} + \frac{132911}{26} - y = 50$

Step 2.2

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

$\frac{y}{2} - y \cdot \frac{2}{2} + \frac{132911}{26} = 50$

Step 2.3

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

$\frac{y}{2} + \frac{- y \cdot 2}{2} + \frac{132911}{26} = 50$

Step 2.4

Combine the numerators over the common denominator.

$\frac{y - y \cdot 2}{2} + \frac{132911}{26} = 50$

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 $y - y \cdot 2$ .

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Step 2.5.1.1.1

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

$\frac{y^{1} - y \cdot 2}{2} + \frac{132911}{26} = 50$

Step 2.5.1.1.2

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

$\frac{y \cdot 1 - y \cdot 2}{2} + \frac{132911}{26} = 50$

Step 2.5.1.1.3

Factor $y$ out of $- y \cdot 2$ .

$\frac{y \cdot 1 + y (- 1 \cdot 2)}{2} + \frac{132911}{26} = 50$

Step 2.5.1.1.4

Factor $y$ out of $y \cdot 1 + y (- 1 \cdot 2)$ .

$\frac{y (1 - 1 \cdot 2)}{2} + \frac{132911}{26} = 50$

Step 2.5.1.2

Multiply $- 1$ by $2$ .

$\frac{y (1 - 2)}{2} + \frac{132911}{26} = 50$

Step 2.5.1.3

Subtract $2$ from $1$ .

$\frac{y \cdot - 1}{2} + \frac{132911}{26} = 50$

Step 2.5.2

Move $- 1$ to the left of $y$ .

$\frac{- 1 \cdot y}{2} + \frac{132911}{26} = 50$

Step 2.5.3

Move the negative in front of the fraction.

$- \frac{y}{2} + \frac{132911}{26} = 50$

Step 3

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

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Step 3.1

Subtract $\frac{132911}{26}$ from both sides of the equation.

$- \frac{y}{2} = 50 - \frac{132911}{26}$

Step 3.2

To write $50$ as a fraction with a common denominator, multiply by $\frac{26}{26}$ .

$- \frac{y}{2} = 50 \cdot \frac{26}{26} - \frac{132911}{26}$

Step 3.3

Combine $50$ and $\frac{26}{26}$ .

$- \frac{y}{2} = \frac{50 \cdot 26}{26} - \frac{132911}{26}$

Step 3.4

Combine the numerators over the common denominator.

$- \frac{y}{2} = \frac{50 \cdot 26 - 132911}{26}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $50$ by $26$ .

$- \frac{y}{2} = \frac{1300 - 132911}{26}$

Step 3.5.2

Subtract $132911$ from $1300$ .

$- \frac{y}{2} = \frac{- 131611}{26}$

Step 3.6

Move the negative in front of the fraction.

$- \frac{y}{2} = - \frac{131611}{26}$

Step 4

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{y}{2}) = - 2 (- \frac{131611}{26})$

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 $- 2 (- \frac{y}{2})$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

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

$- 2 \frac{- y}{2} = - 2 (- \frac{131611}{26})$

Step 5.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- y}{2} = - 2 (- \frac{131611}{26})$

Step 5.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- y}{2} = - 2 (- \frac{131611}{26})$

Step 5.1.1.1.4

Rewrite the expression.

$- - y = - 2 (- \frac{131611}{26})$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 2 (- \frac{131611}{26})$

Step 5.1.1.2.2

Multiply $y$ by $1$ .

$y = - 2 (- \frac{131611}{26})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- 2 (- \frac{131611}{26})$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{131611}{26}$ into the numerator.

$y = - 2 (\frac{- 131611}{26})$

Step 5.2.1.1.2

Factor $2$ out of $- 2$ .

$y = 2 (- 1) \frac{- 131611}{26}$

Step 5.2.1.1.3

Factor $2$ out of $26$ .

$y = 2 \cdot - 1 \frac{- 131611}{2 \cdot 13}$

Step 5.2.1.1.4

Cancel the common factor.

$y = 2 \cdot - 1 \frac{- 131611}{2 \cdot 13}$

Step 5.2.1.1.5

Rewrite the expression.

$y = - \frac{- 131611}{13}$

Step 5.2.1.2

Move the negative in front of the fraction.

$y = - - \frac{131611}{13}$

Step 5.2.1.3

Multiply $- - \frac{131611}{13}$ .

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Step 5.2.1.3.1

Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{131611}{13})$

Step 5.2.1.3.2

Multiply $\frac{131611}{13}$ by $1$ .

$y = \frac{131611}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{131611}{13}$

Decimal Form:

$y = 10123.92307692 \dots$

Mixed Number Form:

$y = 10123 \frac{12}{13}$