Algebra Examples

$3 \frac{1}{9} p + 5 - \frac{1}{3} p$

Step 1

Convert $3 \frac{1}{9}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(3 + \frac{1}{9}) p + 5 - \frac{1}{3} p$

Step 1.2

Add $3$ and $\frac{1}{9}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$(3 \cdot \frac{9}{9} + \frac{1}{9}) p + 5 - \frac{1}{3} p$

Step 1.2.2

Combine $3$ and $\frac{9}{9}$ .

$(\frac{3 \cdot 9}{9} + \frac{1}{9}) p + 5 - \frac{1}{3} p$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 9 + 1}{9} p + 5 - \frac{1}{3} p$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $9$ .

$\frac{27 + 1}{9} p + 5 - \frac{1}{3} p$

Step 1.2.4.2

Add $27$ and $1$ .

$\frac{28}{9} p + 5 - \frac{1}{3} p$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{28}{9}$ and $p$ .

$\frac{28 p}{9} + 5 - \frac{1}{3} p$

Step 2.2

Combine $p$ and $\frac{1}{3}$ .

$\frac{28 p}{9} + 5 - \frac{p}{3}$

Step 3

Find the common denominator.

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Step 3.1

Write $5$ as a fraction with denominator $1$ .

$\frac{28 p}{9} + \frac{5}{1} - \frac{p}{3}$

Step 3.2

Multiply $\frac{5}{1}$ by $\frac{9}{9}$ .

$\frac{28 p}{9} + \frac{5}{1} \cdot \frac{9}{9} - \frac{p}{3}$

Step 3.3

Multiply $\frac{5}{1}$ by $\frac{9}{9}$ .

$\frac{28 p}{9} + \frac{5 \cdot 9}{9} - \frac{p}{3}$

Step 3.4

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

$\frac{28 p}{9} + \frac{5 \cdot 9}{9} - (\frac{p}{3} \cdot \frac{3}{3})$

Step 3.5

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

$\frac{28 p}{9} + \frac{5 \cdot 9}{9} - \frac{p \cdot 3}{3 \cdot 3}$

Step 3.6

Multiply $3$ by $3$ .

$\frac{28 p}{9} + \frac{5 \cdot 9}{9} - \frac{p \cdot 3}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{28 p + 5 \cdot 9 - p \cdot 3}{9}$

Step 5

Simplify each term.

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Step 5.1

Multiply $5$ by $9$ .

$\frac{28 p + 45 - p \cdot 3}{9}$

Step 5.2

Multiply $3$ by $- 1$ .

$\frac{28 p + 45 - 3 p}{9}$

Step 6

Simplify terms.

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Step 6.1

Subtract $3 p$ from $28 p$ .

$\frac{25 p + 45}{9}$

Step 6.2

Factor $5$ out of $25 p + 45$ .

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Step 6.2.1

Factor $5$ out of $25 p$ .

$\frac{5 (5 p) + 45}{9}$

Step 6.2.2

Factor $5$ out of $45$ .

$\frac{5 (5 p) + 5 (9)}{9}$

Step 6.2.3

Factor $5$ out of $5 (5 p) + 5 (9)$ .

$\frac{5 (5 p + 9)}{9}$