Pre-Algebra Examples

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

Step 1

Rewrite the equation as $\frac{4 m - 2}{6} = \frac{3}{4}$ .

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

Step 2

Cancel the common factor of $4 m - 2$ and $6$ .

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Step 2.1

Factor $2$ out of $4 m$ .

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

Step 2.2

Factor $2$ out of $- 2$ .

$\frac{2 (2 m) + 2 (- 1)}{6} = \frac{3}{4}$

Step 2.3

Factor $2$ out of $2 (2 m) + 2 (- 1)$ .

$\frac{2 (2 m - 1)}{6} = \frac{3}{4}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $6$ .

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

Step 2.4.2

Cancel the common factor.

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

Step 2.4.3

Rewrite the expression.

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

Step 3

Multiply both sides by $3$ .

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

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{3}{4} \cdot 3$ .

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Step 4.2.1.1

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

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

Step 4.2.1.2

Multiply $3$ by $3$ .

$2 m - 1 = \frac{9}{4}$

Step 5

Solve for $m$ .

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Step 5.1

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

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Step 5.1.1

Add $1$ to both sides of the equation.

$2 m = \frac{9}{4} + 1$

Step 5.1.2

Write $1$ as a fraction with a common denominator.

$2 m = \frac{9}{4} + \frac{4}{4}$

Step 5.1.3

Combine the numerators over the common denominator.

$2 m = \frac{9 + 4}{4}$

Step 5.1.4

Add $9$ and $4$ .

$2 m = \frac{13}{4}$

Step 5.2

Divide each term in $2 m = \frac{13}{4}$ by $2$ and simplify.

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Step 5.2.1

Divide each term in $2 m = \frac{13}{4}$ by $2$ .

$\frac{2 m}{2} = \frac{\frac{13}{4}}{2}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $2$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{2 m}{2} = \frac{\frac{13}{4}}{2}$

Step 5.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{\frac{13}{4}}{2}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$m = \frac{13}{4} \cdot \frac{1}{2}$

Step 5.2.3.2

Multiply $\frac{13}{4} \cdot \frac{1}{2}$ .

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Step 5.2.3.2.1

Multiply $\frac{13}{4}$ by $\frac{1}{2}$ .

$m = \frac{13}{4 \cdot 2}$

Step 5.2.3.2.2

Multiply $4$ by $2$ .

$m = \frac{13}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \frac{13}{8}$

Decimal Form:

$m = 1.625$

Mixed Number Form:

$m = 1 \frac{5}{8}$