Pre-Algebra Examples

$\frac{\frac{10 - 5 t}{3}}{\frac{t - 2}{12 t}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{10 - 5 t}{3} \cdot \frac{12 t}{t - 2}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Factor $3$ out of $12 t$ .

$\frac{10 - 5 t}{3} \cdot \frac{3 (4 t)}{t - 2}$

Step 2.1.2

Cancel the common factor.

$\frac{10 - 5 t}{3} \cdot \frac{3 (4 t)}{t - 2}$

Step 2.1.3

Rewrite the expression.

$(10 - 5 t) \frac{4 t}{t - 2}$

$(10 - 5 t) \frac{4 t}{t - 2}$

Step 2.2

Multiply $10 - 5 t$ by $\frac{4 t}{t - 2}$ .

$\frac{(10 - 5 t) (4 t)}{t - 2}$

$\frac{(10 - 5 t) (4 t)}{t - 2}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $5$ out of $10 - 5 t$ .

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Step 3.1.1

Factor $5$ out of $10$ .

$\frac{(5 (2) - 5 t) \cdot 4 t}{t - 2}$

Step 3.1.2

Factor $5$ out of $- 5 t$ .

$\frac{(5 (2) + 5 (- t)) \cdot 4 t}{t - 2}$

Step 3.1.3

Factor $5$ out of $5 (2) + 5 (- t)$ .

$\frac{5 (2 - t) \cdot 4 t}{t - 2}$

$\frac{5 (2 - t) \cdot 4 t}{t - 2}$

Step 3.2

Multiply $4$ by $5$ .

$\frac{20 (2 - t) t}{t - 2}$

$\frac{20 (2 - t) t}{t - 2}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $2 - t$ and $t - 2$ .

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Step 4.1.1

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{20 (- 1 (- 2) - t) t}{t - 2}$

Step 4.1.2

Factor $- 1$ out of $- t$ .

$\frac{20 (- 1 (- 2) - (t)) t}{t - 2}$

Step 4.1.3

Factor $- 1$ out of $- 1 (- 2) - (t)$ .

$\frac{20 (- 1 (- 2 + t)) t}{t - 2}$

Step 4.1.4

Reorder terms.

$\frac{20 (- 1 (t - 2)) t}{t - 2}$

Step 4.1.5

Cancel the common factor.

$\frac{20 (- 1 (t - 2)) t}{t - 2}$

Step 4.1.6

Divide $20 \cdot (- 1) t$ by $1$ .

$20 \cdot (- 1) t$

$20 \cdot (- 1) t$

Step 4.2

Multiply $20$ by $- 1$ .

$- 20 t$

$- 20 t$

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