Pre-Algebra Examples

$\frac{7 x - 21}{3} \div \frac{3 x - 9}{5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{7 x - 21}{3} \cdot \frac{5}{3 x - 9}$

Step 2

Factor $7$ out of $7 x - 21$ .

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Step 2.1

Factor $7$ out of $7 x$ .

$\frac{7 (x) - 21}{3} \cdot \frac{5}{3 x - 9}$

Step 2.2

Factor $7$ out of $- 21$ .

$\frac{7 x + 7 \cdot - 3}{3} \cdot \frac{5}{3 x - 9}$

Step 2.3

Factor $7$ out of $7 x + 7 \cdot - 3$ .

$\frac{7 (x - 3)}{3} \cdot \frac{5}{3 x - 9}$

Step 3

Factor $3$ out of $3 x - 9$ .

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Step 3.1

Factor $3$ out of $3 x$ .

$\frac{7 (x - 3)}{3} \cdot \frac{5}{3 (x) - 9}$

Step 3.2

Factor $3$ out of $- 9$ .

$\frac{7 (x - 3)}{3} \cdot \frac{5}{3 x + 3 \cdot - 3}$

Step 3.3

Factor $3$ out of $3 x + 3 \cdot - 3$ .

$\frac{7 (x - 3)}{3} \cdot \frac{5}{3 (x - 3)}$

Step 4

Cancel the common factor of $x - 3$ .

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Step 4.1

Factor $x - 3$ out of $7 (x - 3)$ .

$\frac{(x - 3) \cdot 7}{3} \cdot \frac{5}{3 (x - 3)}$

Step 4.2

Factor $x - 3$ out of $3 (x - 3)$ .

$\frac{(x - 3) \cdot 7}{3} \cdot \frac{5}{(x - 3) \cdot 3}$

Step 4.3

Cancel the common factor.

$\frac{(x - 3) \cdot 7}{3} \cdot \frac{5}{(x - 3) \cdot 3}$

Step 4.4

Rewrite the expression.

$\frac{7}{3} \cdot \frac{5}{3}$

Step 5

Multiply $\frac{7}{3}$ by $\frac{5}{3}$ .

$\frac{7 \cdot 5}{3 \cdot 3}$

Step 6

Multiply.

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Step 6.1

Multiply $7$ by $5$ .

$\frac{35}{3 \cdot 3}$

Step 6.2

Multiply $3$ by $3$ .

$\frac{35}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{9}$

Decimal Form:

$3.\overline{8}$

Mixed Number Form:

$3 \frac{8}{9}$