Algebra Examples

$\frac{5}{3} (\frac{4}{3} a + 9 b + \frac{2}{3} a)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{4}{3}$ and $a$ .

$\frac{5}{3} \cdot (\frac{4 a}{3} + 9 b + \frac{2}{3} a)$

Step 1.2

Combine $\frac{2}{3}$ and $a$ .

$\frac{5}{3} \cdot (\frac{4 a}{3} + 9 b + \frac{2 a}{3})$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{5}{3} \cdot (9 b + \frac{4 a + 2 a}{3})$

Step 2.2

Add $4 a$ and $2 a$ .

$\frac{5}{3} \cdot (9 b + \frac{6 a}{3})$

Step 2.3

Cancel the common factor of $6$ and $3$ .

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Step 2.3.1

Factor $3$ out of $6 a$ .

$\frac{5}{3} \cdot (9 b + \frac{3 (2 a)}{3})$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $3$ out of $3$ .

$\frac{5}{3} \cdot (9 b + \frac{3 (2 a)}{3 (1)})$

Step 2.3.2.2

Cancel the common factor.

$\frac{5}{3} \cdot (9 b + \frac{3 (2 a)}{3 \cdot 1})$

Step 2.3.2.3

Rewrite the expression.

$\frac{5}{3} \cdot (9 b + \frac{2 a}{1})$

Step 2.3.2.4

Divide $2 a$ by $1$ .

$\frac{5}{3} \cdot (9 b + 2 a)$

Step 2.4

Apply the distributive property.

$\frac{5}{3} (9 b) + \frac{5}{3} (2 a)$

Step 2.5

Cancel the common factor of $3$ .

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Step 2.5.1

Factor $3$ out of $9 b$ .

$\frac{5}{3} (3 (3 b)) + \frac{5}{3} (2 a)$

Step 2.5.2

Cancel the common factor.

$\frac{5}{3} (3 (3 b)) + \frac{5}{3} (2 a)$

Step 2.5.3

Rewrite the expression.

$5 (3 b) + \frac{5}{3} (2 a)$

Step 2.6

Multiply $3$ by $5$ .

$15 b + \frac{5}{3} (2 a)$

Step 3

Multiply $\frac{5}{3} (2 a)$ .

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Step 3.1

Combine $2$ and $\frac{5}{3}$ .

$15 b + \frac{2 \cdot 5}{3} a$

Step 3.2

Multiply $2$ by $5$ .

$15 b + \frac{10}{3} a$

Step 3.3

Combine $\frac{10}{3}$ and $a$ .

$15 b + \frac{10 a}{3}$