Pre-Algebra Examples

$- \frac{1}{10} = x - \frac{3}{8}$

Step 1

Rewrite the equation as $x - \frac{3}{8} = - \frac{1}{10}$ .

$x - \frac{3}{8} = - \frac{1}{10}$

Step 2

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

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Step 2.1

Add $\frac{3}{8}$ to both sides of the equation.

$x = - \frac{1}{10} + \frac{3}{8}$

Step 2.2

To write $- \frac{1}{10}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = - \frac{1}{10} \cdot \frac{4}{4} + \frac{3}{8}$

Step 2.3

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = - \frac{1}{10} \cdot \frac{4}{4} + \frac{3}{8} \cdot \frac{5}{5}$

Step 2.4

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{10}$ by $\frac{4}{4}$ .

$x = - \frac{4}{10 \cdot 4} + \frac{3}{8} \cdot \frac{5}{5}$

Step 2.4.2

Multiply $10$ by $4$ .

$x = - \frac{4}{40} + \frac{3}{8} \cdot \frac{5}{5}$

Step 2.4.3

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

$x = - \frac{4}{40} + \frac{3 \cdot 5}{8 \cdot 5}$

Step 2.4.4

Multiply $8$ by $5$ .

$x = - \frac{4}{40} + \frac{3 \cdot 5}{40}$

Step 2.5

Combine the numerators over the common denominator.

$x = \frac{- 4 + 3 \cdot 5}{40}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $3$ by $5$ .

$x = \frac{- 4 + 15}{40}$

Step 2.6.2

Add $- 4$ and $15$ .

$x = \frac{11}{40}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{40}$

Decimal Form:

$x = 0.275$