Basic Math Examples

\frac{m}{15 - 5} = \frac{m}{15 + 5} + 0.5

$\frac{m}{15 - 5} = \frac{m}{15 + 5} + 0.5$

Step 1

Multiply both sides by

15 - 5

$15 - 5$ .

\frac{m}{15 - 5} (15 - 5) = (\frac{m}{15 + 5} + 0.5) (15 - 5)

$\frac{m}{15 - 5} (15 - 5) = (\frac{m}{15 + 5} + 0.5) (15 - 5)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of

15 - 5

$15 - 5$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{m}{15 - 5} (15 - 5) = (\frac{m}{15 + 5} + 0.5) (15 - 5)$

Step 2.1.1.2

Rewrite the expression.

$m = (\frac{m}{15 + 5} + 0.5) (15 - 5)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify

$(\frac{m}{15 + 5} + 0.5) (15 - 5)$ .

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Step 2.2.1.1

Simplify by adding and subtracting.

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Step 2.2.1.1.1

Add

$15$ and

$5$ .

$m = (\frac{m}{20} + 0.5) (15 - 5)$

Step 2.2.1.1.2

Subtract

$5$ from

$15$ .

$m = (\frac{m}{20} + 0.5) \cdot 10$

Step 2.2.1.2

Apply the distributive property.

$m = \frac{m}{20} \cdot 10 + 0.5 \cdot 10$

Step 2.2.1.3

Cancel the common factor of

$10$ .

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Step 2.2.1.3.1

Factor

$10$ out of

$20$ .

$m = \frac{m}{10 (2)} \cdot 10 + 0.5 \cdot 10$

Step 2.2.1.3.2

Cancel the common factor.

$m = \frac{m}{10 \cdot 2} \cdot 10 + 0.5 \cdot 10$

Step 2.2.1.3.3

Rewrite the expression.

$m = \frac{m}{2} + 0.5 \cdot 10$

Step 2.2.1.4

Multiply

$0.5$ by

$10$ .

$m = \frac{m}{2} + 5$

Step 3

Solve for

$m$ .

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Step 3.1

Move all terms containing

$m$ to the left side of the equation.

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Step 3.1.1

Subtract

$\frac{m}{2}$ from both sides of the equation.

$m - \frac{m}{2} = 5$

Step 3.1.2

To write

$m$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$m \cdot \frac{2}{2} - \frac{m}{2} = 5$

Step 3.1.3

Combine

$m$ and

$\frac{2}{2}$ .

$\frac{m \cdot 2}{2} - \frac{m}{2} = 5$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{m \cdot 2 - m}{2} = 5$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Move

$2$ to the left of

$m$ .

$\frac{2 \cdot m - m}{2} = 5$

Step 3.1.5.2

Subtract

$m$ from

$2 m$ .

$\frac{m}{2} = 5$

Step 3.2

Multiply both sides of the equation by

$2$ .

$2 \frac{m}{2} = 2 \cdot 5$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Cancel the common factor of

$2$ .

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Step 3.3.1.1.1

Cancel the common factor.

$2 \frac{m}{2} = 2 \cdot 5$

Step 3.3.1.1.2

Rewrite the expression.

$m = 2 \cdot 5$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply

$2$ by

$5$ .

$m = 10$