Pre-Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

Multiply $\frac{2 - m}{6} \cdot \frac{1}{4}$ .

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Step 3.1

Multiply $\frac{2 - m}{6}$ by $\frac{1}{4}$ .

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

Step 3.2

Multiply $6$ by $4$ .

$(m - 2) \frac{2 - m}{24}$

Step 4

Apply the distributive property.

$m \frac{2 - m}{24} - 2 \frac{2 - m}{24}$

Step 5

Combine $m$ and $\frac{2 - m}{24}$ .

$\frac{m (2 - m)}{24} - 2 \frac{2 - m}{24}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $- 2$ .

$\frac{m (2 - m)}{24} + 2 (- 1) \frac{2 - m}{24}$

Step 6.2

Factor $2$ out of $24$ .

$\frac{m (2 - m)}{24} + 2 \cdot - 1 \frac{2 - m}{2 \cdot 12}$

Step 6.3

Cancel the common factor.

$\frac{m (2 - m)}{24} + 2 \cdot - 1 \frac{2 - m}{2 \cdot 12}$

Step 6.4

Rewrite the expression.

$\frac{m (2 - m)}{24} - 1 \frac{2 - m}{12}$

Step 7

Rewrite $- 1 \frac{2 - m}{12}$ as $- \frac{2 - m}{12}$ .

$\frac{m (2 - m)}{24} - \frac{2 - m}{12}$

Step 8

To write $- \frac{2 - m}{12}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{m (2 - m)}{24} - \frac{2 - m}{12} \cdot \frac{2}{2}$

Step 9

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{2 - m}{12}$ by $\frac{2}{2}$ .

$\frac{m (2 - m)}{24} - \frac{(2 - m) \cdot 2}{12 \cdot 2}$

Step 9.2

Multiply $12$ by $2$ .

$\frac{m (2 - m)}{24} - \frac{(2 - m) \cdot 2}{24}$

Step 10

Combine the numerators over the common denominator.

$\frac{m (2 - m) - (2 - m) \cdot 2}{24}$

Step 11

Simplify the numerator.

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Step 11.1

Factor $2 - m$ out of $m (2 - m) - (2 - m) \cdot 2$ .

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Step 11.1.1

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

$\frac{(2 - m) m - (2 - m) \cdot 2}{24}$

Step 11.1.2

Factor $2 - m$ out of $- (2 - m) \cdot 2$ .

$\frac{(2 - m) m + (2 - m) (- 1 \cdot 2)}{24}$

Step 11.1.3

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

$\frac{(2 - m) (m - 1 \cdot 2)}{24}$

Step 11.2

Multiply $- 1$ by $2$ .

$\frac{(2 - m) (m - 2)}{24}$

Step 12

Simplify the numerator.

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Step 12.1

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{(- 1 (- 2) - m) (m - 2)}{24}$

Step 12.2

Factor $- 1$ out of $- m$ .

$\frac{(- 1 (- 2) - (m)) (m - 2)}{24}$

Step 12.3

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

$\frac{- 1 (- 2 + m) (m - 2)}{24}$

Step 12.4

Reorder terms.

$\frac{- 1 (m - 2) (m - 2)}{24}$

Step 12.5

Raise $m - 2$ to the power of $1$ .

$\frac{- 1 ({(m - 2)}^{1} (m - 2))}{24}$

Step 12.6

Raise $m - 2$ to the power of $1$ .

$\frac{- 1 ({(m - 2)}^{1} {(m - 2)}^{1})}{24}$

Step 12.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 1 {(m - 2)}^{1 + 1}}{24}$

Step 12.8

Add $1$ and $1$ .

$\frac{- 1 {(m - 2)}^{2}}{24}$

Step 13

Move the negative in front of the fraction.

$- \frac{{(m - 2)}^{2}}{24}$

Step 14

Rewrite ${(m - 2)}^{2}$ as $(m - 2) (m - 2)$ .

$- \frac{(m - 2) (m - 2)}{24}$

Step 15

Expand $(m - 2) (m - 2)$ using the FOIL Method.

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Step 15.1

Apply the distributive property.

$- \frac{m (m - 2) - 2 (m - 2)}{24}$

Step 15.2

Apply the distributive property.

$- \frac{m \cdot m + m \cdot - 2 - 2 (m - 2)}{24}$

Step 15.3

Apply the distributive property.

$- \frac{m \cdot m + m \cdot - 2 - 2 m - 2 \cdot - 2}{24}$

Step 16

Simplify and combine like terms.

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Step 16.1

Simplify each term.

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Step 16.1.1

Multiply $m$ by $m$ .

$- \frac{m^{2} + m \cdot - 2 - 2 m - 2 \cdot - 2}{24}$

Step 16.1.2

Move $- 2$ to the left of $m$ .

$- \frac{m^{2} - 2 \cdot m - 2 m - 2 \cdot - 2}{24}$

Step 16.1.3

Multiply $- 2$ by $- 2$ .

$- \frac{m^{2} - 2 m - 2 m + 4}{24}$

Step 16.2

Subtract $2 m$ from $- 2 m$ .

$- \frac{m^{2} - 4 m + 4}{24}$

Step 17

Split the fraction $\frac{m^{2} - 4 m + 4}{24}$ into two fractions.

$- (\frac{m^{2} - 4 m}{24} + \frac{4}{24})$

Step 18

Split the fraction $\frac{m^{2} - 4 m}{24}$ into two fractions.

$- (\frac{m^{2}}{24} + \frac{- 4 m}{24} + \frac{4}{24})$

Step 19

Cancel the common factor of $- 4$ and $24$ .

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Step 19.1

Factor $4$ out of $- 4 m$ .

$- (\frac{m^{2}}{24} + \frac{4 (- m)}{24} + \frac{4}{24})$

Step 19.2

Cancel the common factors.

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Step 19.2.1

Factor $4$ out of $24$ .

$- (\frac{m^{2}}{24} + \frac{4 (- m)}{4 (6)} + \frac{4}{24})$

Step 19.2.2

Cancel the common factor.

$- (\frac{m^{2}}{24} + \frac{4 (- m)}{4 \cdot 6} + \frac{4}{24})$

Step 19.2.3

Rewrite the expression.

$- (\frac{m^{2}}{24} + \frac{- m}{6} + \frac{4}{24})$

Step 20

Move the negative in front of the fraction.

$- (\frac{m^{2}}{24} - \frac{m}{6} + \frac{4}{24})$

Step 21

Cancel the common factor of $4$ and $24$ .

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Step 21.1

Factor $4$ out of $4$ .

$- (\frac{m^{2}}{24} - \frac{m}{6} + \frac{4 (1)}{24})$

Step 21.2

Cancel the common factors.

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Step 21.2.1

Factor $4$ out of $24$ .

$- (\frac{m^{2}}{24} - \frac{m}{6} + \frac{4 \cdot 1}{4 \cdot 6})$

Step 21.2.2

Cancel the common factor.

$- (\frac{m^{2}}{24} - \frac{m}{6} + \frac{4 \cdot 1}{4 \cdot 6})$

Step 21.2.3

Rewrite the expression.

$- (\frac{m^{2}}{24} - \frac{m}{6} + \frac{1}{6})$