Basic Math Examples

$\frac{7 - 2}{b - a} \div \frac{49 - 8}{a - b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{7 - 2}{b - a} \cdot \frac{a - b}{49 - 8}$

Step 2

Simplify terms.

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Step 2.1

Subtract $2$ from $7$ .

$\frac{5}{b - a} \cdot \frac{a - b}{49 - 8}$

Step 2.2

Subtract $8$ from $49$ .

$\frac{5}{b - a} \cdot \frac{a - b}{41}$

Step 2.3

Multiply $\frac{5}{b - a}$ by $\frac{a - b}{41}$ .

$\frac{5 (a - b)}{(b - a) \cdot 41}$

Step 2.4

Cancel the common factor of $a - b$ and $b - a$ .

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Step 2.4.1

Factor $- 1$ out of $a$ .

$\frac{5 (- 1 (- a) - b)}{(b - a) \cdot 41}$

Step 2.4.2

Factor $- 1$ out of $- b$ .

$\frac{5 (- 1 (- a) - (b))}{(b - a) \cdot 41}$

Step 2.4.3

Factor $- 1$ out of $- 1 (- a) - (b)$ .

$\frac{5 (- 1 (- a + b))}{(b - a) \cdot 41}$

Step 2.4.4

Reorder terms.

$\frac{5 (- 1 (- a + b))}{(- a + b) \cdot 41}$

Step 2.4.5

Cancel the common factor.

$\frac{5 (- 1 (- a + b))}{(- a + b) \cdot 41}$

Step 2.4.6

Rewrite the expression.

$\frac{5 \cdot (- 1)}{41}$

$\frac{5 \cdot (- 1)}{41}$

$\frac{5 \cdot (- 1)}{41}$

Step 3

Multiply $5$ by $- 1$ .

$\frac{- 5}{41}$

Step 4

Move the negative in front of the fraction.

$- \frac{5}{41}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{41}$

Decimal Form:

$- 0.\overline{12195}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$