Basic Math Examples

$\frac{p - 4}{3} - \frac{p - 3}{4} = \frac{p - 5}{5} + 1$

Step 1

Simplify $\frac{p - 4}{3} - \frac{p - 3}{4}$ .

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Step 1.1

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

$\frac{p - 4}{3} \cdot \frac{4}{4} - \frac{p - 3}{4} = \frac{p - 5}{5} + 1$

Step 1.2

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

$\frac{p - 4}{3} \cdot \frac{4}{4} - \frac{p - 3}{4} \cdot \frac{3}{3} = \frac{p - 5}{5} + 1$

Step 1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{p - 4}{3}$ by $\frac{4}{4}$ .

$\frac{(p - 4) \cdot 4}{3 \cdot 4} - \frac{p - 3}{4} \cdot \frac{3}{3} = \frac{p - 5}{5} + 1$

Step 1.3.2

Multiply $3$ by $4$ .

$\frac{(p - 4) \cdot 4}{12} - \frac{p - 3}{4} \cdot \frac{3}{3} = \frac{p - 5}{5} + 1$

Step 1.3.3

Multiply $\frac{p - 3}{4}$ by $\frac{3}{3}$ .

$\frac{(p - 4) \cdot 4}{12} - \frac{(p - 3) \cdot 3}{4 \cdot 3} = \frac{p - 5}{5} + 1$

Step 1.3.4

Multiply $4$ by $3$ .

$\frac{(p - 4) \cdot 4}{12} - \frac{(p - 3) \cdot 3}{12} = \frac{p - 5}{5} + 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(p - 4) \cdot 4 - (p - 3) \cdot 3}{12} = \frac{p - 5}{5} + 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{p \cdot 4 - 4 \cdot 4 - (p - 3) \cdot 3}{12} = \frac{p - 5}{5} + 1$

Step 1.5.2

Move $4$ to the left of $p$ .

$\frac{4 \cdot p - 4 \cdot 4 - (p - 3) \cdot 3}{12} = \frac{p - 5}{5} + 1$

Step 1.5.3

Multiply $- 4$ by $4$ .

$\frac{4 \cdot p - 16 - (p - 3) \cdot 3}{12} = \frac{p - 5}{5} + 1$

Step 1.5.4

Apply the distributive property.

$\frac{4 p - 16 + (- p - - 3) \cdot 3}{12} = \frac{p - 5}{5} + 1$

Step 1.5.5

Multiply $- 1$ by $- 3$ .

$\frac{4 p - 16 + (- p + 3) \cdot 3}{12} = \frac{p - 5}{5} + 1$

Step 1.5.6

Apply the distributive property.

$\frac{4 p - 16 - p \cdot 3 + 3 \cdot 3}{12} = \frac{p - 5}{5} + 1$

Step 1.5.7

Multiply $3$ by $- 1$ .

$\frac{4 p - 16 - 3 p + 3 \cdot 3}{12} = \frac{p - 5}{5} + 1$

Step 1.5.8

Multiply $3$ by $3$ .

$\frac{4 p - 16 - 3 p + 9}{12} = \frac{p - 5}{5} + 1$

Step 1.5.9

Subtract $3 p$ from $4 p$ .

$\frac{p - 16 + 9}{12} = \frac{p - 5}{5} + 1$

Step 1.5.10

Add $- 16$ and $9$ .

$\frac{p - 7}{12} = \frac{p - 5}{5} + 1$

Step 2

Simplify $\frac{p - 5}{5} + 1$ .

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Step 2.1

Combine into one fraction.

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Step 2.1.1

Write $1$ as a fraction with a common denominator.

$\frac{p - 7}{12} = \frac{p - 5}{5} + \frac{5}{5}$

Step 2.1.2

Combine the numerators over the common denominator.

$\frac{p - 7}{12} = \frac{p - 5 + 5}{5}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Add $- 5$ and $5$ .

$\frac{p - 7}{12} = \frac{p + 0}{5}$

Step 2.2.2

Add $p$ and $0$ .

$\frac{p - 7}{12} = \frac{p}{5}$

Step 3

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

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Step 3.1

Subtract $\frac{p}{5}$ from both sides of the equation.

$\frac{p - 7}{12} - \frac{p}{5} = 0$

Step 3.2

To write $\frac{p - 7}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{p - 7}{12} \cdot \frac{5}{5} - \frac{p}{5} = 0$

Step 3.3

To write $- \frac{p}{5}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{p - 7}{12} \cdot \frac{5}{5} - \frac{p}{5} \cdot \frac{12}{12} = 0$

Step 3.4

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{p - 7}{12}$ by $\frac{5}{5}$ .

$\frac{(p - 7) \cdot 5}{12 \cdot 5} - \frac{p}{5} \cdot \frac{12}{12} = 0$

Step 3.4.2

Multiply $12$ by $5$ .

$\frac{(p - 7) \cdot 5}{60} - \frac{p}{5} \cdot \frac{12}{12} = 0$

Step 3.4.3

Multiply $\frac{p}{5}$ by $\frac{12}{12}$ .

$\frac{(p - 7) \cdot 5}{60} - \frac{p \cdot 12}{5 \cdot 12} = 0$

Step 3.4.4

Multiply $5$ by $12$ .

$\frac{(p - 7) \cdot 5}{60} - \frac{p \cdot 12}{60} = 0$

Step 3.5

Combine the numerators over the common denominator.

$\frac{(p - 7) \cdot 5 - p \cdot 12}{60} = 0$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Apply the distributive property.

$\frac{p \cdot 5 - 7 \cdot 5 - p \cdot 12}{60} = 0$

Step 3.6.2

Move $5$ to the left of $p$ .

$\frac{5 \cdot p - 7 \cdot 5 - p \cdot 12}{60} = 0$

Step 3.6.3

Multiply $- 7$ by $5$ .

$\frac{5 \cdot p - 35 - p \cdot 12}{60} = 0$

Step 3.6.4

Multiply $12$ by $- 1$ .

$\frac{5 p - 35 - 12 p}{60} = 0$

Step 3.6.5

Subtract $12 p$ from $5 p$ .

$\frac{- 7 p - 35}{60} = 0$

Step 3.6.6

Factor $7$ out of $- 7 p - 35$ .

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Step 3.6.6.1

Factor $7$ out of $- 7 p$ .

$\frac{7 (- p) - 35}{60} = 0$

Step 3.6.6.2

Factor $7$ out of $- 35$ .

$\frac{7 (- p) + 7 (- 5)}{60} = 0$

Step 3.6.6.3

Factor $7$ out of $7 (- p) + 7 (- 5)$ .

$\frac{7 (- p - 5)}{60} = 0$

Step 3.7

Factor $- 1$ out of $- p$ .

$\frac{7 (- (p) - 5)}{60} = 0$

Step 3.8

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{7 (- (p) - 1 (5))}{60} = 0$

Step 3.9

Factor $- 1$ out of $- (p) - 1 (5)$ .

$\frac{7 (- (p + 5))}{60} = 0$

Step 3.10

Rewrite $- (p + 5)$ as $- 1 (p + 5)$ .

$\frac{7 (- 1 (p + 5))}{60} = 0$

Step 3.11

Move the negative in front of the fraction.

$- \frac{7 (p + 5)}{60} = 0$

Step 4

Set the numerator equal to zero.

$7 (p + 5) = 0$

Step 5

Solve the equation for $p$ .

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Step 5.1

Divide each term in $7 (p + 5) = 0$ by $7$ and simplify.

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Step 5.1.1

Divide each term in $7 (p + 5) = 0$ by $7$ .

$\frac{7 (p + 5)}{7} = \frac{0}{7}$

Step 5.1.2

Simplify the left side.

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Step 5.1.2.1

Cancel the common factor of $7$ .

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Step 5.1.2.1.1

Cancel the common factor.

$\frac{7 (p + 5)}{7} = \frac{0}{7}$

Step 5.1.2.1.2

Divide $p + 5$ by $1$ .

$p + 5 = \frac{0}{7}$

Step 5.1.3

Simplify the right side.

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Step 5.1.3.1

Divide $0$ by $7$ .

$p + 5 = 0$

Step 5.2

Subtract $5$ from both sides of the equation.

$p = - 5$