How To Reduce Math

Introduction to reduce in math

In math, reduction or reduce refers to the process of rewriting an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator an integer) is called "reduce a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reduce a radical". (Source: From Wikipedia). Here we will see some example problems to how to reduce a fraction or a radical expression in math.


Example problems to reduce fractions in math


Here we will see some example problems to learn how to reduce a fraction in math.

Example 1

Reduce the fraction `25/365` to simplest form.

Solution

The given fraction `25/365` is not the simplest form, because the numerator and denominator of the fraction has some common factors. By finding the common factors between the numerator and denominator, we can reduce the fraction further into simplest form.

To find the common factors of the numerator and denominator, the prime factorization is given as,

25 = 5 * 5

365 = 5 * 73

So the fraction `25/365` can be written as, `((5)(5))/((5)(73))`

So the simplest form or reduced form of the fraction `25/365` is `5/73`

Example 2

Reduce the fraction `28/118`

Solution

The prime factorization of 28 = 2 * 2 * 7

The prime factorization of 118 = 2 * 59

So, the fraction `28/118` can be written as `((2)(2)(7))/((2)(59))`

So the reduced form of the fraction `28/118` is `14/59`


Example problems to reduce radical expressions in math


Here we will see some example problems to learn how to reduce a radical expression in math.

Example 1

Reduce the radical expression, `sqrt(856)`

Solution

The prime factorization of 856 = 2 * 2 * 2 * 107

So the expression `sqrt856` can be written as, `sqrt((2)(2)(2)(107))`

= 2`sqrt214`

2`sqrt214` is the reduced form of `sqrt856`

Example 2

Reduce the radical expression `sqrt250` into simplest form

Solution

The prime factorization of 250 = 2 * 5 * 5 * 5

So, `sqrt250` = `sqrt((2)(5)(5)(5))`

= `5sqrt((2)(5))`

= `5sqrt10`