Basic Math Examples

$- 500 \cdot 0.5 + \frac{4}{5} \cdot (y (1)) - \frac{3}{5} \cdot (y (2)) = 0$

Step 1

Simplify $- 500 \cdot 0.5 + \frac{4}{5} y \cdot 1 - \frac{3}{5} y \cdot 2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply $- 500$ by $0.5$ .

$- 250 + \frac{4}{5} y \cdot 1 - \frac{3}{5} y \cdot 2 = 0$

Step 1.1.2

Combine $\frac{4}{5}$ and $y$ .

$- 250 + \frac{4 y}{5} \cdot 1 - \frac{3}{5} y \cdot 2 = 0$

Step 1.1.3

Multiply $\frac{4 y}{5}$ by $1$ .

$- 250 + \frac{4 y}{5} - \frac{3}{5} y \cdot 2 = 0$

Step 1.1.4

Combine $y$ and $\frac{3}{5}$ .

$- 250 + \frac{4 y}{5} - \frac{y \cdot 3}{5} \cdot 2 = 0$

Step 1.1.5

Move $3$ to the left of $y$ .

$- 250 + \frac{4 y}{5} - \frac{3 \cdot y}{5} \cdot 2 = 0$

Step 1.1.6

Multiply $- \frac{3 y}{5} \cdot 2$ .

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Step 1.1.6.1

Multiply $2$ by $- 1$ .

$- 250 + \frac{4 y}{5} - 2 \frac{3 y}{5} = 0$

Step 1.1.6.2

Combine $- 2$ and $\frac{3 y}{5}$ .

$- 250 + \frac{4 y}{5} + \frac{- 2 (3 y)}{5} = 0$

Step 1.1.6.3

Multiply $3$ by $- 2$ .

$- 250 + \frac{4 y}{5} + \frac{- 6 y}{5} = 0$

Step 1.1.7

Move the negative in front of the fraction.

$- 250 + \frac{4 y}{5} - \frac{6 y}{5} = 0$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$- 250 + \frac{4 y - 6 y}{5} = 0$

Step 1.2.2

Subtract $6 y$ from $4 y$ .

$- 250 + \frac{- 2 y}{5} = 0$

Step 1.2.3

Move the negative in front of the fraction.

$- 250 - \frac{2 y}{5} = 0$

Step 2

Add $250$ to both sides of the equation.

$- \frac{2 y}{5} = 250$

Step 3

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} (- \frac{2 y}{5}) = - \frac{5}{2} \cdot 250$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{5}{2} (- \frac{2 y}{5})$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} (- \frac{2 y}{5}) = - \frac{5}{2} \cdot 250$

Step 4.1.1.1.2

Move the leading negative in $- \frac{2 y}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 y}{5} = - \frac{5}{2} \cdot 250$

Step 4.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 y}{5} = - \frac{5}{2} \cdot 250$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 y}{5} = - \frac{5}{2} \cdot 250$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 y) = - \frac{5}{2} \cdot 250$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

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

$\frac{- 1}{2} (2 (- y)) = - \frac{5}{2} \cdot 250$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- y)) = - \frac{5}{2} \cdot 250$

Step 4.1.1.2.3

Rewrite the expression.

$- - y = - \frac{5}{2} \cdot 250$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{5}{2} \cdot 250$

Step 4.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{5}{2} \cdot 250$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{5}{2} \cdot 250$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$y = \frac{- 5}{2} \cdot 250$

Step 4.2.1.1.2

Factor $2$ out of $250$ .

$y = \frac{- 5}{2} \cdot (2 (125))$

Step 4.2.1.1.3

Cancel the common factor.

$y = \frac{- 5}{2} \cdot (2 \cdot 125)$

Step 4.2.1.1.4

Rewrite the expression.

$y = - 5 \cdot 125$

Step 4.2.1.2

Multiply $- 5$ by $125$ .

$y = - 625$