Pre-Algebra Examples

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

Step 1

Simplify the left side.

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Step 1.1

Simplify $2 \frac{1}{2} \cdot m - 2 \frac{1}{3}$ .

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Step 1.1.1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.1.1.2

Add $2$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

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

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

Step 1.1.1.2.2

Combine $2$ and $\frac{2}{2}$ .

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

Step 1.1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $2$ .

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

Step 1.1.1.2.4.2

Add $4$ and $1$ .

$\frac{5}{2} \cdot m - 2 \frac{1}{3} = - \frac{1}{4}$

Step 1.1.2

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 1.1.2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{5}{2} \cdot m - (2 + \frac{1}{3}) = - \frac{1}{4}$

Step 1.1.2.2

Add $2$ and $\frac{1}{3}$ .

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Step 1.1.2.2.1

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

$\frac{5}{2} \cdot m - (2 \cdot \frac{3}{3} + \frac{1}{3}) = - \frac{1}{4}$

Step 1.1.2.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{5}{2} \cdot m - (\frac{2 \cdot 3}{3} + \frac{1}{3}) = - \frac{1}{4}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{5}{2} \cdot m - \frac{2 \cdot 3 + 1}{3} = - \frac{1}{4}$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $2$ by $3$ .

$\frac{5}{2} \cdot m - \frac{6 + 1}{3} = - \frac{1}{4}$

Step 1.1.2.2.4.2

Add $6$ and $1$ .

$\frac{5}{2} \cdot m - \frac{7}{3} = - \frac{1}{4}$

Step 1.1.3

Combine $\frac{5}{2}$ and $m$ .

$\frac{5 m}{2} - \frac{7}{3} = - \frac{1}{4}$

Step 2

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

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Step 2.1

Add $\frac{7}{3}$ to both sides of the equation.

$\frac{5 m}{2} = - \frac{1}{4} + \frac{7}{3}$

Step 2.2

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 m}{2} = - \frac{1}{4} \cdot \frac{3}{3} + \frac{7}{3}$

Step 2.3

To write $\frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 m}{2} = - \frac{1}{4} \cdot \frac{3}{3} + \frac{7}{3} \cdot \frac{4}{4}$

Step 2.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{5 m}{2} = - \frac{3}{4 \cdot 3} + \frac{7}{3} \cdot \frac{4}{4}$

Step 2.4.2

Multiply $4$ by $3$ .

$\frac{5 m}{2} = - \frac{3}{12} + \frac{7}{3} \cdot \frac{4}{4}$

Step 2.4.3

Multiply $\frac{7}{3}$ by $\frac{4}{4}$ .

$\frac{5 m}{2} = - \frac{3}{12} + \frac{7 \cdot 4}{3 \cdot 4}$

Step 2.4.4

Multiply $3$ by $4$ .

$\frac{5 m}{2} = - \frac{3}{12} + \frac{7 \cdot 4}{12}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{5 m}{2} = \frac{- 3 + 7 \cdot 4}{12}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $7$ by $4$ .

$\frac{5 m}{2} = \frac{- 3 + 28}{12}$

Step 2.6.2

Add $- 3$ and $28$ .

$\frac{5 m}{2} = \frac{25}{12}$

Step 3

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 m}{2} = \frac{2}{5} \cdot \frac{25}{12}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{2}{5} \cdot \frac{5 m}{2}$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 m}{2} = \frac{2}{5} \cdot \frac{25}{12}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 m) = \frac{2}{5} \cdot \frac{25}{12}$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 m$ .

$\frac{1}{5} (5 (m)) = \frac{2}{5} \cdot \frac{25}{12}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 m) = \frac{2}{5} \cdot \frac{25}{12}$

Step 4.1.1.2.3

Rewrite the expression.

$m = \frac{2}{5} \cdot \frac{25}{12}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{5} \cdot \frac{25}{12}$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $12$ .

$m = \frac{2}{5} \cdot \frac{25}{2 (6)}$

Step 4.2.1.1.2

Cancel the common factor.

$m = \frac{2}{5} \cdot \frac{25}{2 \cdot 6}$

Step 4.2.1.1.3

Rewrite the expression.

$m = \frac{1}{5} \cdot \frac{25}{6}$

Step 4.2.1.2

Cancel the common factor of $5$ .

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Step 4.2.1.2.1

Factor $5$ out of $25$ .

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

Step 4.2.1.2.2

Cancel the common factor.

$m = \frac{1}{5} \cdot \frac{5 \cdot 5}{6}$

Step 4.2.1.2.3

Rewrite the expression.

$m = \frac{5}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = \frac{5}{6}$

Decimal Form:

$m = 0.8\overline{3}$