Basic Math Examples

$(\frac{1}{7} - 1) (2^{- 3})$

Step 1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(\frac{1}{7} - 1 \cdot \frac{7}{7}) \cdot 2^{- 3}$

Step 2

Combine $- 1$ and $\frac{7}{7}$ .

$(\frac{1}{7} + \frac{- 1 \cdot 7}{7}) \cdot 2^{- 3}$

Step 3

Combine the numerators over the common denominator.

$\frac{1 - 1 \cdot 7}{7} \cdot 2^{- 3}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 1$ by $7$ .

$\frac{1 - 7}{7} \cdot 2^{- 3}$

Step 4.2

Subtract $7$ from $1$ .

$\frac{- 6}{7} \cdot 2^{- 3}$

Step 5

Move the negative in front of the fraction.

$- \frac{6}{7} \cdot 2^{- 3}$

Step 6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{6}{7} \cdot \frac{1}{2^{3}}$

Step 7

Raise $2$ to the power of $3$ .

$- \frac{6}{7} \cdot \frac{1}{8}$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Move the leading negative in $- \frac{6}{7}$ into the numerator.

$\frac{- 6}{7} \cdot \frac{1}{8}$

Step 8.2

Factor $2$ out of $- 6$ .

$\frac{2 (- 3)}{7} \cdot \frac{1}{8}$

Step 8.3

Factor $2$ out of $8$ .

$\frac{2 \cdot - 3}{7} \cdot \frac{1}{2 \cdot 4}$

Step 8.4

Cancel the common factor.

$\frac{2 \cdot - 3}{7} \cdot \frac{1}{2 \cdot 4}$

Step 8.5

Rewrite the expression.

$\frac{- 3}{7} \cdot \frac{1}{4}$

Step 9

Multiply $\frac{- 3}{7}$ by $\frac{1}{4}$ .

$\frac{- 3}{7 \cdot 4}$

Step 10

Simplify the expression.

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Step 10.1

Multiply $7$ by $4$ .

$\frac{- 3}{28}$

Step 10.2

Move the negative in front of the fraction.

$- \frac{3}{28}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{28}$

Decimal Form:

$- 0.10714285 \dots$