Algebra Examples

$\frac{5}{8} p - \frac{3}{4} = 4$

Step 1

Combine $\frac{5}{8}$ and $p$ .

$\frac{5 p}{8} - \frac{3}{4} = 4$

Step 2

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

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Step 2.1

Add $\frac{3}{4}$ to both sides of the equation.

$\frac{5 p}{8} = 4 + \frac{3}{4}$

Step 2.2

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

$\frac{5 p}{8} = 4 \cdot \frac{4}{4} + \frac{3}{4}$

Step 2.3

Combine $4$ and $\frac{4}{4}$ .

$\frac{5 p}{8} = \frac{4 \cdot 4}{4} + \frac{3}{4}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 p}{8} = \frac{4 \cdot 4 + 3}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $4$ .

$\frac{5 p}{8} = \frac{16 + 3}{4}$

Step 2.5.2

Add $16$ and $3$ .

$\frac{5 p}{8} = \frac{19}{4}$

Step 3

Multiply both sides of the equation by $\frac{8}{5}$ .

$\frac{8}{5} \cdot \frac{5 p}{8} = \frac{8}{5} \cdot \frac{19}{4}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{8}{5} \cdot \frac{5 p}{8}$ .

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Step 4.1.1.1

Cancel the common factor of $8$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{8}{5} \cdot \frac{5 p}{8} = \frac{8}{5} \cdot \frac{19}{4}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 p) = \frac{8}{5} \cdot \frac{19}{4}$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 p$ .

$\frac{1}{5} (5 (p)) = \frac{8}{5} \cdot \frac{19}{4}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 p) = \frac{8}{5} \cdot \frac{19}{4}$

Step 4.1.1.2.3

Rewrite the expression.

$p = \frac{8}{5} \cdot \frac{19}{4}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{8}{5} \cdot \frac{19}{4}$ .

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Step 4.2.1.1

Cancel the common factor of $4$ .

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Step 4.2.1.1.1

Factor $4$ out of $8$ .

$p = \frac{4 (2)}{5} \cdot \frac{19}{4}$

Step 4.2.1.1.2

Cancel the common factor.

$p = \frac{4 \cdot 2}{5} \cdot \frac{19}{4}$

Step 4.2.1.1.3

Rewrite the expression.

$p = \frac{2}{5} \cdot 19$

Step 4.2.1.2

Combine $\frac{2}{5}$ and $19$ .

$p = \frac{2 \cdot 19}{5}$

Step 4.2.1.3

Multiply $2$ by $19$ .

$p = \frac{38}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = \frac{38}{5}$

Decimal Form:

$p = 7.6$

Mixed Number Form:

$p = 7 \frac{3}{5}$