Basic Math Examples

$- \frac{12029}{1470} + 11 p = \frac{1}{5} \cdot (- \frac{23}{6} p - \frac{5}{6})$

Step 1

Simplify $\frac{1}{5} \cdot (- \frac{23}{6} p - \frac{5}{6})$ .

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Step 1.1

Rewrite.

$- \frac{12029}{1470} + 11 p = 0 + 0 + \frac{1}{5} \cdot (- \frac{23}{6} p - \frac{5}{6})$

Step 1.2

Simplify by adding zeros.

$- \frac{12029}{1470} + 11 p = \frac{1}{5} \cdot (- \frac{23}{6} p - \frac{5}{6})$

Step 1.3

Simplify each term.

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Step 1.3.1

Combine $p$ and $\frac{23}{6}$ .

$- \frac{12029}{1470} + 11 p = \frac{1}{5} \cdot (- \frac{p \cdot 23}{6} - \frac{5}{6})$

Step 1.3.2

Move $23$ to the left of $p$ .

$- \frac{12029}{1470} + 11 p = \frac{1}{5} \cdot (- \frac{23 p}{6} - \frac{5}{6})$

Step 1.4

Apply the distributive property.

$- \frac{12029}{1470} + 11 p = \frac{1}{5} (- \frac{23 p}{6}) + \frac{1}{5} (- \frac{5}{6})$

Step 1.5

Multiply $\frac{1}{5} (- \frac{23 p}{6})$ .

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Step 1.5.1

Multiply $\frac{1}{5}$ by $\frac{23 p}{6}$ .

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{5 \cdot 6} + \frac{1}{5} (- \frac{5}{6})$

Step 1.5.2

Multiply $5$ by $6$ .

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{1}{5} (- \frac{5}{6})$

Step 1.6

Cancel the common factor of $5$ .

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Step 1.6.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{1}{5} \cdot \frac{- 5}{6}$

Step 1.6.2

Factor $5$ out of $- 5$ .

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{1}{5} \cdot \frac{5 (- 1)}{6}$

Step 1.6.3

Cancel the common factor.

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{1}{5} \cdot \frac{5 \cdot - 1}{6}$

Step 1.6.4

Rewrite the expression.

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{- 1}{6}$

Step 1.7

Move the negative in front of the fraction.

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} - \frac{1}{6}$

Step 2

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

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Step 2.1

Add $\frac{23 p}{30}$ to both sides of the equation.

$- \frac{12029}{1470} + 11 p + \frac{23 p}{30} = - \frac{1}{6}$

Step 2.2

To write $11 p$ as a fraction with a common denominator, multiply by $\frac{30}{30}$ .

$- \frac{12029}{1470} + 11 p \cdot \frac{30}{30} + \frac{23 p}{30} = - \frac{1}{6}$

Step 2.3

Combine $11 p$ and $\frac{30}{30}$ .

$- \frac{12029}{1470} + \frac{11 p \cdot 30}{30} + \frac{23 p}{30} = - \frac{1}{6}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{12029}{1470} + \frac{11 p \cdot 30 + 23 p}{30} = - \frac{1}{6}$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $p$ out of $11 p \cdot 30 + 23 p$ .

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Step 2.5.1.1.1

Factor $p$ out of $11 p \cdot 30$ .

$- \frac{12029}{1470} + \frac{p (11 \cdot 30) + 23 p}{30} = - \frac{1}{6}$

Step 2.5.1.1.2

Factor $p$ out of $23 p$ .

$- \frac{12029}{1470} + \frac{p (11 \cdot 30) + p \cdot 23}{30} = - \frac{1}{6}$

Step 2.5.1.1.3

Factor $p$ out of $p (11 \cdot 30) + p \cdot 23$ .

$- \frac{12029}{1470} + \frac{p (11 \cdot 30 + 23)}{30} = - \frac{1}{6}$

Step 2.5.1.2

Multiply $11$ by $30$ .

$- \frac{12029}{1470} + \frac{p (330 + 23)}{30} = - \frac{1}{6}$

Step 2.5.1.3

Add $330$ and $23$ .

$- \frac{12029}{1470} + \frac{p \cdot 353}{30} = - \frac{1}{6}$

Step 2.5.2

Move $353$ to the left of $p$ .

$- \frac{12029}{1470} + \frac{353 p}{30} = - \frac{1}{6}$

Step 3

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

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Step 3.1

Add $\frac{12029}{1470}$ to both sides of the equation.

$\frac{353 p}{30} = - \frac{1}{6} + \frac{12029}{1470}$

Step 3.2

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{245}{245}$ .

$\frac{353 p}{30} = - \frac{1}{6} \cdot \frac{245}{245} + \frac{12029}{1470}$

Step 3.3

Write each expression with a common denominator of $1470$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{1}{6}$ by $\frac{245}{245}$ .

$\frac{353 p}{30} = - \frac{245}{6 \cdot 245} + \frac{12029}{1470}$

Step 3.3.2

Multiply $6$ by $245$ .

$\frac{353 p}{30} = - \frac{245}{1470} + \frac{12029}{1470}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{353 p}{30} = \frac{- 245 + 12029}{1470}$

Step 3.5

Add $- 245$ and $12029$ .

$\frac{353 p}{30} = \frac{11784}{1470}$

Step 3.6

Cancel the common factor of $11784$ and $1470$ .

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Step 3.6.1

Factor $6$ out of $11784$ .

$\frac{353 p}{30} = \frac{6 (1964)}{1470}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $6$ out of $1470$ .

$\frac{353 p}{30} = \frac{6 \cdot 1964}{6 \cdot 245}$

Step 3.6.2.2

Cancel the common factor.

$\frac{353 p}{30} = \frac{6 \cdot 1964}{6 \cdot 245}$

Step 3.6.2.3

Rewrite the expression.

$\frac{353 p}{30} = \frac{1964}{245}$

Step 4

Multiply both sides of the equation by $\frac{30}{353}$ .

$\frac{30}{353} \cdot \frac{353 p}{30} = \frac{30}{353} \cdot \frac{1964}{245}$

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 $\frac{30}{353} \cdot \frac{353 p}{30}$ .

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Step 5.1.1.1

Cancel the common factor of $30$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{30}{353} \cdot \frac{353 p}{30} = \frac{30}{353} \cdot \frac{1964}{245}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{353} (353 p) = \frac{30}{353} \cdot \frac{1964}{245}$

Step 5.1.1.2

Cancel the common factor of $353$ .

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Step 5.1.1.2.1

Factor $353$ out of $353 p$ .

$\frac{1}{353} (353 (p)) = \frac{30}{353} \cdot \frac{1964}{245}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{353} (353 p) = \frac{30}{353} \cdot \frac{1964}{245}$

Step 5.1.1.2.3

Rewrite the expression.

$p = \frac{30}{353} \cdot \frac{1964}{245}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{30}{353} \cdot \frac{1964}{245}$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Factor $5$ out of $30$ .

$p = \frac{5 (6)}{353} \cdot \frac{1964}{245}$

Step 5.2.1.1.2

Factor $5$ out of $245$ .

$p = \frac{5 \cdot 6}{353} \cdot \frac{1964}{5 \cdot 49}$

Step 5.2.1.1.3

Cancel the common factor.

$p = \frac{5 \cdot 6}{353} \cdot \frac{1964}{5 \cdot 49}$

Step 5.2.1.1.4

Rewrite the expression.

$p = \frac{6}{353} \cdot \frac{1964}{49}$

Step 5.2.1.2

Multiply $\frac{6}{353}$ by $\frac{1964}{49}$ .

$p = \frac{6 \cdot 1964}{353 \cdot 49}$

Step 5.2.1.3

Multiply.

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Step 5.2.1.3.1

Multiply $6$ by $1964$ .

$p = \frac{11784}{353 \cdot 49}$

Step 5.2.1.3.2

Multiply $353$ by $49$ .

$p = \frac{11784}{17297}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = \frac{11784}{17297}$

Decimal Form:

$p = 0.68127420 \dots$