Simplify (26x*20)/30

Solution:

Simplification Process

Step 1:
Identify and remove common factors between the numerator and the denominator.

Step 1.1:
Extract the factor of $2$ from the numerator $26x\cdot 20$ to get $\frac{2(13x\cdot 20)}{30}$.

Step 1.2:
Eliminate common factors between numerator and denominator.

Step 1.2.1:
Extract the factor of $2$ from the denominator $30$ to get $\frac{2(13x\cdot 20)}{2\cdot 15}$.

Step 1.2.2:
Remove the common factor of $2$ to simplify $\frac{\cancel{2}(13x\cdot 20)}{\cancel{2}\cdot 15}$.

Step 1.2.3:
Rewrite the simplified expression as $\frac{13x\cdot 20}{15}$.

Step 2:
Further simplify by canceling out common factors between the new numerator and denominator.

Step 2.1:
Factor out $5$ from the numerator $13x\cdot 20$ to get $\frac{5(13x\cdot 4)}{15}$.

Step 2.2:
Proceed to cancel out common factors.

Step 2.2.1:
Factor out $5$ from the denominator $15$ to get $\frac{5(13x\cdot 4)}{5\cdot 3}$.

Step 2.2.2:
Remove the common factor of $5$ to simplify $\frac{\cancel{5}(13x\cdot 4)}{\cancel{5}\cdot 3}$.

Step 2.2.3:
Rewrite the simplified expression as $\frac{13x\cdot 4}{3}$.

Step 3:
Perform the multiplication in the numerator to find the final simplified form $\frac{52x}{3}$.

Knowledge Notes:

To simplify a fraction, we follow these steps:

1. Factorization: Break down both the numerator and the denominator into their prime factors or common factors.

2. Cancellation: If there are common factors in both the numerator and the denominator, they can be canceled out. This is based on the property that $\frac{a\cdot c}{b\cdot c}=\frac{a}{b}$ when $c\ne 0$.

3. Simplification: After canceling out common factors, rewrite the fraction to reflect the simplified form.

4. Multiplication: If there are any multiplications left in the numerator or denominator, carry them out to get the final simplified expression.

In the given problem, we used these principles to simplify the expression $(26x\cdot 20)/30$. We factored out common factors of $2$ and $5$ from the numerator and denominator, canceled them, and then performed the remaining multiplication to arrive at the simplified expression $\frac{52x}{3}$.