Basic Math Examples

$10 - \frac{2}{3 p} = 52$

Step 1

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

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Step 1.1

Subtract $10$ from both sides of the equation.

$- \frac{2}{3 p} = 52 - 10$

Step 1.2

Subtract $10$ from $52$ .

$- \frac{2}{3 p} = 42$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 p, 1$

Step 2.2

The LCM of one and any expression is the expression.

$3 p$

Step 3

Multiply each term in $- \frac{2}{3 p} = 42$ by $3 p$ to eliminate the fractions.

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Step 3.1

Multiply each term in $- \frac{2}{3 p} = 42$ by $3 p$ .

$- \frac{2}{3 p} (3 p) = 42 (3 p)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3 p$ .

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Step 3.2.1.1

Move the leading negative in $- \frac{2}{3 p}$ into the numerator.

$\frac{- 2}{3 p} (3 p) = 42 (3 p)$

Step 3.2.1.2

Cancel the common factor.

$\frac{- 2}{3 p} (3 p) = 42 (3 p)$

Step 3.2.1.3

Rewrite the expression.

$- 2 = 42 (3 p)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $3$ by $42$ .

$- 2 = 126 p$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $126 p = - 2$ .

$126 p = - 2$

Step 4.2

Divide each term in $126 p = - 2$ by $126$ and simplify.

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Step 4.2.1

Divide each term in $126 p = - 2$ by $126$ .

$\frac{126 p}{126} = \frac{- 2}{126}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $126$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{126 p}{126} = \frac{- 2}{126}$

Step 4.2.2.1.2

Divide $p$ by $1$ .

$p = \frac{- 2}{126}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $- 2$ and $126$ .

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Step 4.2.3.1.1

Factor $2$ out of $- 2$ .

$p = \frac{2 (- 1)}{126}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $2$ out of $126$ .

$p = \frac{2 \cdot - 1}{2 \cdot 63}$

Step 4.2.3.1.2.2

Cancel the common factor.

$p = \frac{2 \cdot - 1}{2 \cdot 63}$

Step 4.2.3.1.2.3

Rewrite the expression.

$p = \frac{- 1}{63}$

Step 4.2.3.2

Move the negative in front of the fraction.

$p = - \frac{1}{63}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{1}{63}$

Decimal Form:

$p = - 0.\overline{015873}$