Basic Math Examples

$\frac{w}{5} + \frac{3}{10} = \frac{w}{2}$

Step 1

Multiply both sides by $2$ .

$(\frac{w}{5} + \frac{3}{10}) \cdot 2 = \frac{w}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{w}{5} + \frac{3}{10}) \cdot 2$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$\frac{w}{5} \cdot 2 + \frac{3}{10} \cdot 2 = \frac{w}{2} \cdot 2$

Step 2.1.1.1.2

Combine $\frac{w}{5}$ and $2$ .

$\frac{w \cdot 2}{5} + \frac{3}{10} \cdot 2 = \frac{w}{2} \cdot 2$

Step 2.1.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.1.3.1

Factor $2$ out of $10$ .

$\frac{w \cdot 2}{5} + \frac{3}{2 (5)} \cdot 2 = \frac{w}{2} \cdot 2$

Step 2.1.1.1.3.2

Cancel the common factor.

$\frac{w \cdot 2}{5} + \frac{3}{2 \cdot 5} \cdot 2 = \frac{w}{2} \cdot 2$

Step 2.1.1.1.3.3

Rewrite the expression.

$\frac{w \cdot 2}{5} + \frac{3}{5} = \frac{w}{2} \cdot 2$

Step 2.1.1.2

Move $2$ to the left of $w$ .

$\frac{2 w}{5} + \frac{3}{5} = \frac{w}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 w}{5} + \frac{3}{5} = \frac{w}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$\frac{2 w}{5} + \frac{3}{5} = w$

Step 3

Solve for $w$ .

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Step 3.1

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

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Step 3.1.1

Subtract $w$ from both sides of the equation.

$\frac{2 w}{5} + \frac{3}{5} - w = 0$

Step 3.1.2

To write $- w$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 w}{5} - w \cdot \frac{5}{5} + \frac{3}{5} = 0$

Step 3.1.3

Combine $- w$ and $\frac{5}{5}$ .

$\frac{2 w}{5} + \frac{- w \cdot 5}{5} + \frac{3}{5} = 0$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{2 w - w \cdot 5}{5} + \frac{3}{5} = 0$

Step 3.1.5

Combine the numerators over the common denominator.

$\frac{2 w - w \cdot 5 + 3}{5} = 0$

Step 3.1.6

Multiply $5$ by $- 1$ .

$\frac{2 w - 5 w + 3}{5} = 0$

Step 3.1.7

Subtract $5 w$ from $2 w$ .

$\frac{- 3 w + 3}{5} = 0$

Step 3.1.8

Factor $3$ out of $- 3 w + 3$ .

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Step 3.1.8.1

Factor $3$ out of $- 3 w$ .

$\frac{3 (- w) + 3}{5} = 0$

Step 3.1.8.2

Factor $3$ out of $3$ .

$\frac{3 (- w) + 3 (1)}{5} = 0$

Step 3.1.8.3

Factor $3$ out of $3 (- w) + 3 (1)$ .

$\frac{3 (- w + 1)}{5} = 0$

Step 3.1.9

Factor $- 1$ out of $- w$ .

$\frac{3 (- (w) + 1)}{5} = 0$

Step 3.1.10

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{3 (- (w) - 1 (- 1))}{5} = 0$

Step 3.1.11

Factor $- 1$ out of $- (w) - 1 (- 1)$ .

$\frac{3 (- (w - 1))}{5} = 0$

Step 3.1.12

Rewrite $- (w - 1)$ as $- 1 (w - 1)$ .

$\frac{3 (- 1 (w - 1))}{5} = 0$

Step 3.1.13

Move the negative in front of the fraction.

$- \frac{3 (w - 1)}{5} = 0$

Step 3.2

Set the numerator equal to zero.

$3 (w - 1) = 0$

Step 3.3

Solve the equation for $w$ .

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Step 3.3.1

Divide each term in $3 (w - 1) = 0$ by $3$ and simplify.

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Step 3.3.1.1

Divide each term in $3 (w - 1) = 0$ by $3$ .

$\frac{3 (w - 1)}{3} = \frac{0}{3}$

Step 3.3.1.2

Simplify the left side.

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Step 3.3.1.2.1

Cancel the common factor of $3$ .

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Step 3.3.1.2.1.1

Cancel the common factor.

$\frac{3 (w - 1)}{3} = \frac{0}{3}$

Step 3.3.1.2.1.2

Divide $w - 1$ by $1$ .

$w - 1 = \frac{0}{3}$

Step 3.3.1.3

Simplify the right side.

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Step 3.3.1.3.1

Divide $0$ by $3$ .

$w - 1 = 0$

Step 3.3.2

Add $1$ to both sides of the equation.

$w = 1$