Algebra Examples

$\frac{m}{3} - \frac{2 m}{5} = \frac{1}{5}$

Step 1

Simplify $\frac{m}{3} - \frac{2 m}{5}$ .

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Step 1.1

To write $\frac{m}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{m}{3} \cdot \frac{5}{5} - \frac{2 m}{5} = \frac{1}{5}$

Step 1.2

To write $- \frac{2 m}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{m}{3} \cdot \frac{5}{5} - \frac{2 m}{5} \cdot \frac{3}{3} = \frac{1}{5}$

Step 1.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{m}{3}$ by $\frac{5}{5}$ .

$\frac{m \cdot 5}{3 \cdot 5} - \frac{2 m}{5} \cdot \frac{3}{3} = \frac{1}{5}$

Step 1.3.2

Multiply $3$ by $5$ .

$\frac{m \cdot 5}{15} - \frac{2 m}{5} \cdot \frac{3}{3} = \frac{1}{5}$

Step 1.3.3

Multiply $\frac{2 m}{5}$ by $\frac{3}{3}$ .

$\frac{m \cdot 5}{15} - \frac{2 m \cdot 3}{5 \cdot 3} = \frac{1}{5}$

Step 1.3.4

Multiply $5$ by $3$ .

$\frac{m \cdot 5}{15} - \frac{2 m \cdot 3}{15} = \frac{1}{5}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{m \cdot 5 - 2 m \cdot 3}{15} = \frac{1}{5}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $m$ out of $m \cdot 5 - 2 m \cdot 3$ .

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Step 1.5.1.1

Factor $m$ out of $m \cdot 5$ .

$\frac{m (5) - 2 m \cdot 3}{15} = \frac{1}{5}$

Step 1.5.1.2

Factor $m$ out of $- 2 m \cdot 3$ .

$\frac{m (5) + m (- 2 \cdot 3)}{15} = \frac{1}{5}$

Step 1.5.1.3

Factor $m$ out of $m (5) + m (- 2 \cdot 3)$ .

$\frac{m (5 - 2 \cdot 3)}{15} = \frac{1}{5}$

Step 1.5.2

Multiply $- 2$ by $3$ .

$\frac{m (5 - 6)}{15} = \frac{1}{5}$

Step 1.5.3

Subtract $6$ from $5$ .

$\frac{m \cdot - 1}{15} = \frac{1}{5}$

Step 1.6

Simplify the expression.

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Step 1.6.1

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

$\frac{- 1 \cdot m}{15} = \frac{1}{5}$

Step 1.6.2

Move the negative in front of the fraction.

$- \frac{m}{15} = \frac{1}{5}$

Step 2

Multiply both sides of the equation by $- 15$ .

$- 15 (- \frac{m}{15}) = - 15 (\frac{1}{5})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 15 (- \frac{m}{15})$ .

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Step 3.1.1.1

Cancel the common factor of $15$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{m}{15}$ into the numerator.

$- 15 \frac{- m}{15} = - 15 (\frac{1}{5})$

Step 3.1.1.1.2

Factor $15$ out of $- 15$ .

$15 (- 1) \frac{- m}{15} = - 15 (\frac{1}{5})$

Step 3.1.1.1.3

Cancel the common factor.

$15 \cdot - 1 \frac{- m}{15} = - 15 (\frac{1}{5})$

Step 3.1.1.1.4

Rewrite the expression.

$- - m = - 15 (\frac{1}{5})$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 m = - 15 (\frac{1}{5})$

Step 3.1.1.2.2

Multiply $m$ by $1$ .

$m = - 15 (\frac{1}{5})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Factor $5$ out of $- 15$ .

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

Step 3.2.1.2

Cancel the common factor.

$m = 5 \cdot - 3 \frac{1}{5}$

Step 3.2.1.3

Rewrite the expression.

$m = - 3$