Reduce Fractions
2026-02-28 08:59 Diff
https://brightchamps.com/en-us/math/numbers/reduce-fractions

Variables are usually represented by letters like a, b, c, x, y, z, etc. They represent changeable or unknown values.

Step 1: Factor both the numerator and the denominator, including variables.

Step 2: Avoid all common factors from the numerator and the denominator.

Step 3: The resultant is in simple form.

An example will help us understand better: 

Find the simplest form of the fraction \(\frac{6x^2y}{3xy^2} \)

Step 1: Numerator = 6x2y


The prime factorization of 6 is \(2 × 3\). 


Therefore, \(6 = 2 × 3\)


Similarly, the prime factorization of x2 is x × x 


So,\( x^2 = x × x \)


y can be written as it is.


In other words, \(6x^2y = 2 × 3 × x × x × y.\)

Let’s do the same in the denominator.


Denominator = 3xy2

Since 3 is a prime number, it cannot be factorized further. So write 3 as it is. 

\(x = x\)


\(y^2 = y × y \)


So \(3xy^2 = 3 × x × y × y\)

Step 2: Let’s rewrite the fraction and then cancel out the common factors.

\(6x^2y = 2 × 3 × x × x × y\) and \(3xy^2 = 3 × x × y × y \)


Therefore, the fraction is \(\frac{2 \times 3 \times x \times x \times y}{3 \times x \times y \times y} \)


Now, canceling out common factors (x, y, 3)


x → \(\frac{2 \times x \times y}{y \times y} \)


y → \(\frac{2x}{y} \), we get: 


\(\frac{2x}{y} \).