Basic Math Examples

$(\frac{2}{3} y + 0.25 y) = y + 2$

Step 1

Simplify $\frac{2}{3} y + 0.25 y$ .

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Step 1.1

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

$\frac{2 y}{3} + 0.25 y = y + 2$

Step 1.2

To write $0.25 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 y}{3} + 0.25 y \cdot \frac{3}{3} = y + 2$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $0.25 y$ and $\frac{3}{3}$ .

$\frac{2 y}{3} + \frac{0.25 y \cdot 3}{3} = y + 2$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{2 y + 0.25 y \cdot 3}{3} = y + 2$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $0.25 y$ out of $2 y + 0.25 y \cdot 3$ .

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Step 1.4.1.1

Move $y$ .

$\frac{2 y + 0.25 \cdot 3 y}{3} = y + 2$

Step 1.4.1.2

Factor $0.25 y$ out of $2 y$ .

$\frac{0.25 y (8) + 0.25 \cdot 3 y}{3} = y + 2$

Step 1.4.1.3

Factor $0.25 y$ out of $0.25 \cdot 3 y$ .

$\frac{0.25 y (8) + 0.25 y (3)}{3} = y + 2$

Step 1.4.1.4

Factor $0.25 y$ out of $0.25 y (8) + 0.25 y (3)$ .

$\frac{0.25 y (8 + 3)}{3} = y + 2$

Step 1.4.2

Multiply $8 + 3$ by $0.25$ .

$\frac{2.75 y}{3} = y + 2$

Step 1.5

Simplify with factoring out.

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Step 1.5.1

Factor $2.75$ out of $2.75 y$ .

$\frac{2.75 (y)}{3} = y + 2$

Step 1.5.2

Factor $3$ out of $3$ .

$\frac{2.75 (y)}{3 (1)} = y + 2$

Step 1.6

Separate fractions.

$\frac{2.75}{3} \cdot \frac{y}{1} = y + 2$

Step 1.7

Divide $2.75$ by $3$ .

$0.91\overline{6} \frac{y}{1} = y + 2$

Step 1.8

Divide $y$ by $1$ .

$0.91\overline{6} y = y + 2$

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.

$0.91\overline{6} y - y = 2$

Step 2.2

Subtract $y$ from $0.91\overline{6} y$ .

$- 0.08\overline{3} y = 2$

Step 3

Divide each term in $- 0.08\overline{3} y = 2$ by $- 0.08\overline{3}$ and simplify.

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Step 3.1

Divide each term in $- 0.08\overline{3} y = 2$ by $- 0.08\overline{3}$ .

$\frac{- 0.08\overline{3} y}{- 0.08\overline{3}} = \frac{2}{- 0.08\overline{3}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 0.08\overline{3}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 0.08\overline{3} y}{- 0.08\overline{3}} = \frac{2}{- 0.08\overline{3}}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{- 0.08\overline{3}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $2$ by $- 0.08\overline{3}$ .

$y = - 24$