Pre-Algebra Examples

$a - \frac{5}{10} = 2 a - \frac{3}{5}$

Step 1

Cancel the common factor of $5$ and $10$ .

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Step 1.1

Factor $5$ out of $5$ .

$a - \frac{5 (1)}{10} = 2 a - \frac{3}{5}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $10$ .

$a - \frac{5 \cdot 1}{5 \cdot 2} = 2 a - \frac{3}{5}$

Step 1.2.2

Cancel the common factor.

$a - \frac{5 \cdot 1}{5 \cdot 2} = 2 a - \frac{3}{5}$

Step 1.2.3

Rewrite the expression.

$a - \frac{1}{2} = 2 a - \frac{3}{5}$

Step 2

Move all terms containing $a$ to the left side of the equation.

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Step 2.1

Subtract $2 a$ from both sides of the equation.

$a - \frac{1}{2} - 2 a = - \frac{3}{5}$

Step 2.2

Subtract $2 a$ from $a$ .

$- a - \frac{1}{2} = - \frac{3}{5}$

Step 3

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

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Step 3.1

Add $\frac{1}{2}$ to both sides of the equation.

$- a = - \frac{3}{5} + \frac{1}{2}$

Step 3.2

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

$- a = - \frac{3}{5} \cdot \frac{2}{2} + \frac{1}{2}$

Step 3.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- a = - \frac{3}{5} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 3.4

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

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Step 3.4.1

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

$- a = - \frac{3 \cdot 2}{5 \cdot 2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 3.4.2

Multiply $5$ by $2$ .

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

Step 3.4.3

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

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

Step 3.4.4

Multiply $2$ by $5$ .

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

Step 3.5

Combine the numerators over the common denominator.

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

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 3$ by $2$ .

$- a = \frac{- 6 + 5}{10}$

Step 3.6.2

Add $- 6$ and $5$ .

$- a = \frac{- 1}{10}$

Step 3.7

Move the negative in front of the fraction.

$- a = - \frac{1}{10}$

Step 4

Divide each term in $- a = - \frac{1}{10}$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- a = - \frac{1}{10}$ by $- 1$ .

$\frac{- a}{- 1} = \frac{- \frac{1}{10}}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{- \frac{1}{10}}{- 1}$

Step 4.2.2

Divide $a$ by $1$ .

$a = \frac{- \frac{1}{10}}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$a = \frac{\frac{1}{10}}{1}$

Step 4.3.2

Divide $\frac{1}{10}$ by $1$ .

$a = \frac{1}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1}{10}$

Decimal Form:

$a = 0.1$