Algebra Examples

$\frac{7}{3} a - \frac{8}{5} a + \frac{4}{15} a$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{7}{3}$ and $a$ .

$\frac{7 a}{3} - \frac{8}{5} a + \frac{4}{15} a$

Step 1.2

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

$\frac{7 a}{3} - \frac{a \cdot 8}{5} + \frac{4}{15} a$

Step 1.3

Move $8$ to the left of $a$ .

$\frac{7 a}{3} - \frac{8 \cdot a}{5} + \frac{4}{15} a$

Step 1.4

Combine $\frac{4}{15}$ and $a$ .

$\frac{7 a}{3} - \frac{8 a}{5} + \frac{4 a}{15}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{7 a}{3}$ by $\frac{5}{5}$ .

$\frac{7 a}{3} \cdot \frac{5}{5} - \frac{8 a}{5} + \frac{4 a}{15}$

Step 2.2

Multiply $\frac{7 a}{3}$ by $\frac{5}{5}$ .

$\frac{7 a \cdot 5}{3 \cdot 5} - \frac{8 a}{5} + \frac{4 a}{15}$

Step 2.3

Multiply $\frac{8 a}{5}$ by $\frac{3}{3}$ .

$\frac{7 a \cdot 5}{3 \cdot 5} - (\frac{8 a}{5} \cdot \frac{3}{3}) + \frac{4 a}{15}$

Step 2.4

Multiply $\frac{8 a}{5}$ by $\frac{3}{3}$ .

$\frac{7 a \cdot 5}{3 \cdot 5} - \frac{8 a \cdot 3}{5 \cdot 3} + \frac{4 a}{15}$

Step 2.5

Multiply $3$ by $5$ .

$\frac{7 a \cdot 5}{15} - \frac{8 a \cdot 3}{5 \cdot 3} + \frac{4 a}{15}$

Step 2.6

Reorder the factors of $5 \cdot 3$ .

$\frac{7 a \cdot 5}{15} - \frac{8 a \cdot 3}{3 \cdot 5} + \frac{4 a}{15}$

Step 2.7

Multiply $3$ by $5$ .

$\frac{7 a \cdot 5}{15} - \frac{8 a \cdot 3}{15} + \frac{4 a}{15}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 a \cdot 5 - 8 a \cdot 3 + 4 a}{15}$

Step 4

Simplify each term.

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Step 4.1

Multiply $5$ by $7$ .

$\frac{35 a - 8 a \cdot 3 + 4 a}{15}$

Step 4.2

Multiply $3$ by $- 8$ .

$\frac{35 a - 24 a + 4 a}{15}$

Step 5

Simplify terms.

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Step 5.1

Subtract $24 a$ from $35 a$ .

$\frac{11 a + 4 a}{15}$

Step 5.2

Add $11 a$ and $4 a$ .

$\frac{15 a}{15}$

Step 5.3

Cancel the common factor of $15$ .

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Step 5.3.1

Cancel the common factor.

$\frac{15 a}{15}$

Step 5.3.2

Divide $a$ by $1$ .

$a$