# Reducing Fractions

We have been studying the fractions from our elementary classes that they are represented in A /B form. Where, A and B or numerator and denominator respectively are the two parts of the fraction. For instance, 45 /59 represent a fraction with 45 as numerator and 59 as the denominator. reducing fractions by dividing the top and the bottom part by the same numbers is mathematically possible. It is always not possible to reduce the fraction. The reduced fraction represents the equivalent fraction of the original one. It is similar to writing a number in the form of its multiples. The same way we reduce a fraction by writing the numerator and the denominator of a fraction in the form of their multiples. The common multiples are cancelled from the top and the bottom to get the reduced fraction.

So, to reduce fractions means to write them in their lower terms.

For example, if we have a reducing fraction 1024 /5124, we can reduce it by either dividing each of the numerator and the denominator by their common multiple or by factorizing them. Let us factorize the two numbers 1024 and 5124. 1024 can be written as: 1024 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 and 5124 can be factorized as follows: 5124 = 2 * 2 * 3 * 7 * 61.

Replacing the numerator and the denominator by their respective factors we write the fraction as:

1024 / 5124 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 /2 * 2 * 3 * 7 * 61

Here we see that the Greatest common factor in the numerator and the denominator is 2 * 2 = 4. Removing it we get:

1024 / 5124 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 / 3 * 7 * 61 = 256 /1281

256 / 1281 is further not possible to be reduced. Also the fraction 256 /1281 represents the equivalent fraction of 1024 / 5124.

## Prime and Composite Numbers

There are different types of numbers and prime and composite number are one of them. Any number that is exactly divisible only by itself and one is known as prime number. According to definition of prime number we can say that remainder term is zero. So using definition of prime numbers, number 2 is only even prime number and rest are odd prime numbers. And als...Read More

## Least Common Multiple

Least common multiple is also known as lowest common multiple, it is also known as smallest common multiple. LCM of any set of numbers can also be defined as positive integer which is smallest and which is ...Read More

## Least Common Denominator

Denominator is the number in the bottom of fraction. The lowest common denominator is also called as least common denominator (LCD). LCD can be defined as least common multiple of denominators of a set o...Read More

## Simplifying Fractions

Fractions can be defined as part of the whole. For instance, If there are five mangoes and six people to take then each person will have some proportion in it. This part of the each person will be referred ...Read More

Math Topics