Basic Math Examples

$10 (1 - p) \div 3 = - 4 \div 3$

Step 1

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

$10 (1 - p) = - 4$

Step 2

Divide each term in $10 (1 - p) = - 4$ by $10$ and simplify.

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Step 2.1

Divide each term in $10 (1 - p) = - 4$ by $10$ .

$\frac{10 (1 - p)}{10} = \frac{- 4}{10}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $10$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{10 (1 - p)}{10} = \frac{- 4}{10}$

Step 2.2.1.2

Divide $1 - p$ by $1$ .

$1 - p = \frac{- 4}{10}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $- 4$ and $10$ .

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Step 2.3.1.1

Factor $2$ out of $- 4$ .

$1 - p = \frac{2 (- 2)}{10}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $10$ .

$1 - p = \frac{2 \cdot - 2}{2 \cdot 5}$

Step 2.3.1.2.2

Cancel the common factor.

$1 - p = \frac{2 \cdot - 2}{2 \cdot 5}$

Step 2.3.1.2.3

Rewrite the expression.

$1 - p = \frac{- 2}{5}$

Step 2.3.2

Move the negative in front of the fraction.

$1 - p = - \frac{2}{5}$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$- p = - \frac{2}{5} - 1$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- p = - \frac{2}{5} - 1 \cdot \frac{5}{5}$

Step 3.3

Combine $- 1$ and $\frac{5}{5}$ .

$- p = - \frac{2}{5} + \frac{- 1 \cdot 5}{5}$

Step 3.4

Combine the numerators over the common denominator.

$- p = \frac{- 2 - 1 \cdot 5}{5}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $5$ .

$- p = \frac{- 2 - 5}{5}$

Step 3.5.2

Subtract $5$ from $- 2$ .

$- p = \frac{- 7}{5}$

Step 3.6

Move the negative in front of the fraction.

$- p = - \frac{7}{5}$

Step 4

Divide each term in $- p = - \frac{7}{5}$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- p = - \frac{7}{5}$ by $- 1$ .

$\frac{- p}{- 1} = \frac{- \frac{7}{5}}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{p}{1} = \frac{- \frac{7}{5}}{- 1}$

Step 4.2.2

Divide $p$ by $1$ .

$p = \frac{- \frac{7}{5}}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$p = \frac{\frac{7}{5}}{1}$

Step 4.3.2

Divide $\frac{7}{5}$ by $1$ .

$p = \frac{7}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = \frac{7}{5}$

Decimal Form:

$p = 1.4$

Mixed Number Form:

$p = 1 \frac{2}{5}$