Pre-Algebra Examples

$\frac{1}{4} \cdot (3 m - 4) - \frac{1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1

Simplify $\frac{1}{4} \cdot (3 m - 4) - \frac{1}{5}$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$\frac{1}{4} (3 m) + \frac{1}{4} \cdot - 4 - \frac{1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.1.2

Multiply $\frac{1}{4} (3 m)$ .

Tap for more steps...

Step 1.1.2.1

Combine $3$ and $\frac{1}{4}$ .

$\frac{3}{4} m + \frac{1}{4} \cdot - 4 - \frac{1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.1.2.2

Combine $\frac{3}{4}$ and $m$ .

$\frac{3 m}{4} + \frac{1}{4} \cdot - 4 - \frac{1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.1.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.1.3.1

Factor $4$ out of $- 4$ .

$\frac{3 m}{4} + \frac{1}{4} \cdot (4 (- 1)) - \frac{1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.1.3.2

Cancel the common factor.

$\frac{3 m}{4} + \frac{1}{4} \cdot (4 \cdot - 1) - \frac{1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.1.3.3

Rewrite the expression.

$\frac{3 m}{4} - 1 - \frac{1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 m}{4} - 1 \cdot \frac{5}{5} - \frac{1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.3

Combine $- 1$ and $\frac{5}{5}$ .

$\frac{3 m}{4} + \frac{- 1 \cdot 5}{5} - \frac{1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 m}{4} + \frac{- 1 \cdot 5 - 1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $- 1$ by $5$ .

$\frac{3 m}{4} + \frac{- 5 - 1}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.5.2

Subtract $1$ from $- 5$ .

$\frac{3 m}{4} + \frac{- 6}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 1.6

Move the negative in front of the fraction.

$\frac{3 m}{4} - \frac{6}{5} = \frac{1}{4} m + \frac{3}{10}$

Step 2

Combine $\frac{1}{4}$ and $m$ .

$\frac{3 m}{4} - \frac{6}{5} = \frac{m}{4} + \frac{3}{10}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{m}{4}$ from both sides of the equation.

$\frac{3 m}{4} - \frac{6}{5} - \frac{m}{4} = \frac{3}{10}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 m - m}{4} + \frac{- 6}{5} = \frac{3}{10}$

Step 3.3

Subtract $m$ from $3 m$ .

$\frac{2 m}{4} + \frac{- 6}{5} = \frac{3}{10}$

Step 3.4

Simplify each term.

Tap for more steps...

Step 3.4.1

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 3.4.1.1

Factor $2$ out of $2 m$ .

$\frac{2 (m)}{4} + \frac{- 6}{5} = \frac{3}{10}$

Step 3.4.1.2

Cancel the common factors.

Tap for more steps...

Step 3.4.1.2.1

Factor $2$ out of $4$ .

$\frac{2 m}{2 \cdot 2} + \frac{- 6}{5} = \frac{3}{10}$

Step 3.4.1.2.2

Cancel the common factor.

$\frac{2 m}{2 \cdot 2} + \frac{- 6}{5} = \frac{3}{10}$

Step 3.4.1.2.3

Rewrite the expression.

$\frac{m}{2} + \frac{- 6}{5} = \frac{3}{10}$

Step 3.4.2

Move the negative in front of the fraction.

$\frac{m}{2} - \frac{6}{5} = \frac{3}{10}$

Step 4

Move all terms not containing $m$ to the right side of the equation.

Tap for more steps...

Step 4.1

Add $\frac{6}{5}$ to both sides of the equation.

$\frac{m}{2} = \frac{3}{10} + \frac{6}{5}$

Step 4.2

To write $\frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{m}{2} = \frac{3}{10} + \frac{6}{5} \cdot \frac{2}{2}$

Step 4.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.3.1

Multiply $\frac{6}{5}$ by $\frac{2}{2}$ .

$\frac{m}{2} = \frac{3}{10} + \frac{6 \cdot 2}{5 \cdot 2}$

Step 4.3.2

Multiply $5$ by $2$ .

$\frac{m}{2} = \frac{3}{10} + \frac{6 \cdot 2}{10}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{m}{2} = \frac{3 + 6 \cdot 2}{10}$

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply $6$ by $2$ .

$\frac{m}{2} = \frac{3 + 12}{10}$

Step 4.5.2

Add $3$ and $12$ .

$\frac{m}{2} = \frac{15}{10}$

Step 4.6

Cancel the common factor of $15$ and $10$ .

Tap for more steps...

Step 4.6.1

Factor $5$ out of $15$ .

$\frac{m}{2} = \frac{5 (3)}{10}$

Step 4.6.2

Cancel the common factors.

Tap for more steps...

Step 4.6.2.1

Factor $5$ out of $10$ .

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

Step 4.6.2.2

Cancel the common factor.

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

Step 4.6.2.3

Rewrite the expression.

$\frac{m}{2} = \frac{3}{2}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$m = 3$