Algebra Examples

$- 3 + \frac{4}{5} e = - 2 + \frac{3}{2} e + \frac{1}{10} e$

Step 1

Combine $\frac{4}{5}$ and $e$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3}{2} \cdot e + \frac{1}{10} \cdot e$

Step 2

Simplify each term.

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Step 2.1

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

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e}{2} + \frac{1}{10} \cdot e$

Step 2.2

Combine $\frac{1}{10}$ and $e$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e}{2} + \frac{e}{10}$

Step 3

To write $\frac{3 e}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e}{2} \cdot \frac{5}{5} + \frac{e}{10}$

Step 4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3 e}{2}$ by $\frac{5}{5}$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e \cdot 5}{2 \cdot 5} + \frac{e}{10}$

Step 4.2

Multiply $2$ by $5$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e \cdot 5}{10} + \frac{e}{10}$

Step 5

Combine the numerators over the common denominator.

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e \cdot 5 + e}{10}$

Step 6

Simplify each term.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Multiply $5$ by $3$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{15 e + e}{10}$

Step 6.1.2

Add $15 e$ and $e$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{16 e}{10}$

Step 6.2

Cancel the common factor of $16$ and $10$ .

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Step 6.2.1

Factor $2$ out of $16 e$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{2 (8 e)}{10}$

Step 6.2.2

Cancel the common factors.

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Step 6.2.2.1

Factor $2$ out of $10$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{2 (8 e)}{2 (5)}$

Step 6.2.2.2

Cancel the common factor.

$- 3 + \frac{4 e}{5} = - 2 + \frac{2 (8 e)}{2 \cdot 5}$

Step 6.2.2.3

Rewrite the expression.

$- 3 + \frac{4 e}{5} = - 2 + \frac{8 e}{5}$