Basic Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

To write $m$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Subtract $m$ from $m \cdot 4$ .

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Step 2.5.1

Reorder $m$ and $4$ .

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

Step 2.5.2

Subtract $m$ from $4 \cdot m$ .

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

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

Step 3

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

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Step 3.1

Subtract $\frac{2}{3}$ from both sides of the equation.

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

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $3$ .

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

Step 3.5.2

Subtract $2$ from $- 3$ .

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

Step 3.6

Move the negative in front of the fraction.

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

Step 4

Multiply both sides of the equation by $\frac{4}{3}$ .

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

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{4}{3} \cdot \frac{3 m}{4}$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Cancel the common factor.

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

Step 5.1.1.1.2

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $3 m$ .

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

$m = \frac{4}{3} (- \frac{5}{3})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{4}{3} (- \frac{5}{3})$ .

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Step 5.2.1.1

Multiply $\frac{4}{3}$ by $\frac{5}{3}$ .

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

Step 5.2.1.2

Multiply $4$ by $5$ .

$m = - \frac{20}{3 \cdot 3}$

Step 5.2.1.3

Multiply $3$ by $3$ .

$m = - \frac{20}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{20}{9}$

Decimal Form:

$m = - 2.\overline{2}$

Mixed Number Form:

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