Basic Math Examples

$\frac{3}{4} - 9 p = - \frac{3}{5}$

Step 1

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

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Step 1.1

Subtract $\frac{3}{4}$ from both sides of the equation.

$- 9 p = - \frac{3}{5} - \frac{3}{4}$

Step 1.2

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 9 p = - \frac{3}{5} \cdot \frac{4}{4} - \frac{3}{4}$

Step 1.3

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 9 p = - \frac{3}{5} \cdot \frac{4}{4} - \frac{3}{4} \cdot \frac{5}{5}$

Step 1.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3}{5}$ by $\frac{4}{4}$ .

$- 9 p = - \frac{3 \cdot 4}{5 \cdot 4} - \frac{3}{4} \cdot \frac{5}{5}$

Step 1.4.2

Multiply $5$ by $4$ .

$- 9 p = - \frac{3 \cdot 4}{20} - \frac{3}{4} \cdot \frac{5}{5}$

Step 1.4.3

Multiply $\frac{3}{4}$ by $\frac{5}{5}$ .

$- 9 p = - \frac{3 \cdot 4}{20} - \frac{3 \cdot 5}{4 \cdot 5}$

Step 1.4.4

Multiply $4$ by $5$ .

$- 9 p = - \frac{3 \cdot 4}{20} - \frac{3 \cdot 5}{20}$

Step 1.5

Combine the numerators over the common denominator.

$- 9 p = \frac{- 3 \cdot 4 - 3 \cdot 5}{20}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 3$ by $4$ .

$- 9 p = \frac{- 12 - 3 \cdot 5}{20}$

Step 1.6.2

Multiply $- 3$ by $5$ .

$- 9 p = \frac{- 12 - 15}{20}$

Step 1.6.3

Subtract $15$ from $- 12$ .

$- 9 p = \frac{- 27}{20}$

Step 1.7

Move the negative in front of the fraction.

$- 9 p = - \frac{27}{20}$

Step 2

Divide each term in $- 9 p = - \frac{27}{20}$ by $- 9$ and simplify.

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Step 2.1

Divide each term in $- 9 p = - \frac{27}{20}$ by $- 9$ .

$\frac{- 9 p}{- 9} = \frac{- \frac{27}{20}}{- 9}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 9 p}{- 9} = \frac{- \frac{27}{20}}{- 9}$

Step 2.2.1.2

Divide $p$ by $1$ .

$p = \frac{- \frac{27}{20}}{- 9}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$p = - \frac{27}{20} \cdot \frac{1}{- 9}$

Step 2.3.2

Cancel the common factor of $9$ .

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Step 2.3.2.1

Move the leading negative in $- \frac{27}{20}$ into the numerator.

$p = \frac{- 27}{20} \cdot \frac{1}{- 9}$

Step 2.3.2.2

Factor $9$ out of $- 27$ .

$p = \frac{9 (- 3)}{20} \cdot \frac{1}{- 9}$

Step 2.3.2.3

Factor $9$ out of $- 9$ .

$p = \frac{9 \cdot - 3}{20} \cdot \frac{1}{9 \cdot - 1}$

Step 2.3.2.4

Cancel the common factor.

$p = \frac{9 \cdot - 3}{20} \cdot \frac{1}{9 \cdot - 1}$

Step 2.3.2.5

Rewrite the expression.

$p = \frac{- 3}{20} \cdot \frac{1}{- 1}$

Step 2.3.3

Multiply $\frac{- 3}{20}$ by $\frac{1}{- 1}$ .

$p = \frac{- 3}{20 \cdot - 1}$

Step 2.3.4

Multiply $20$ by $- 1$ .

$p = \frac{- 3}{- 20}$

Step 2.3.5

Dividing two negative values results in a positive value.

$p = \frac{3}{20}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$p = \frac{3}{20}$

Decimal Form:

$p = 0.15$