Pre-Algebra Examples

$\frac{5 m}{8} - \frac{6}{8} + \frac{3 m}{8} = \frac{2}{8}$

Step 1

Simplify $\frac{5 m}{8} - \frac{6}{8} + \frac{3 m}{8}$ .

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Step 1.1

Combine the numerators over the common denominator.

$\frac{5 m - 6 + 3 m}{8} = \frac{2}{8}$

Step 1.2

Add $5 m$ and $3 m$ .

$\frac{8 m - 6}{8} = \frac{2}{8}$

Step 1.3

Cancel the common factor of $8 m - 6$ and $8$ .

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Step 1.3.1

Factor $2$ out of $8 m$ .

$\frac{2 (4 m) - 6}{8} = \frac{2}{8}$

Step 1.3.2

Factor $2$ out of $- 6$ .

$\frac{2 (4 m) + 2 (- 3)}{8} = \frac{2}{8}$

Step 1.3.3

Factor $2$ out of $2 (4 m) + 2 (- 3)$ .

$\frac{2 (4 m - 3)}{8} = \frac{2}{8}$

Step 1.3.4

Cancel the common factors.

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Step 1.3.4.1

Factor $2$ out of $8$ .

$\frac{2 (4 m - 3)}{2 (4)} = \frac{2}{8}$

Step 1.3.4.2

Cancel the common factor.

$\frac{2 (4 m - 3)}{2 \cdot 4} = \frac{2}{8}$

Step 1.3.4.3

Rewrite the expression.

$\frac{4 m - 3}{4} = \frac{2}{8}$

Step 2

Cancel the common factor of $2$ and $8$ .

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Step 2.1

Factor $2$ out of $2$ .

$\frac{4 m - 3}{4} = \frac{2 (1)}{8}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $8$ .

$\frac{4 m - 3}{4} = \frac{2 \cdot 1}{2 \cdot 4}$

Step 2.2.2

Cancel the common factor.

$\frac{4 m - 3}{4} = \frac{2 \cdot 1}{2 \cdot 4}$

Step 2.2.3

Rewrite the expression.

$\frac{4 m - 3}{4} = \frac{1}{4}$

Step 3

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

$4 m - 3 = 1$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$4 m = 1 + 3$

Step 4.2

Add $1$ and $3$ .

$4 m = 4$

Step 5

Divide each term in $4 m = 4$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 m = 4$ by $4$ .

$\frac{4 m}{4} = \frac{4}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 m}{4} = \frac{4}{4}$

Step 5.2.1.2

Divide $m$ by $1$ .

$m = \frac{4}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $4$ by $4$ .

$m = 1$