# Fractions?

11th October 2017 Off By star worksheetFractions is a very important concept in maths.It is defined as part of a whole thing.For example half of a cake or a quarter of a pizza.It is represented in the form of 1/2.In 1/2, 1 is called the numerator while 2 is called denominator.Numerator is used to describe the part of the entity which is in discussion while denominator is used to represent the total number of parts.

## Classifying Fractions.

**Proper Fraction.**

A proper fraction has a numerator that is smaller than its denominator, for example 3/7.Proper fraction is always less than 1.e.g 4/5,6/7 etc.

**Improper Fraction.**

An improper fraction has a numerator that is bigger than its denominator, for example 10/7.Improper fraction is always greater than 1. e.g 16/7,13/9 etc.*If numerator is equal to denominator then the fraction is equal to 1.These *are also called improper fractions e.g. 5/5=1,4/4=1 etc.

### Mixed Fraction.

A fraction which is represented as 2 1/4 is called a mixed fraction because it has a whole number and a fraction together.

## Comparing Fractions

**Common fractions.**

A fraction in which numerator and denominator both are integers is called common fraction.e.g. 5/7 is a common fraction while 1/2/3/5 is not common fraction here numerator and denominator are also a fraction i.e 1/2 and 3/5.

**Equivalent Fractions.**

Some fractions may look different, but are really the same,so these are called equivalent fractions. for example:

^{4}/_{8} |
= | ^{2}/_{4} |
= | ^{1}/_{2} |

(Four-Eighths) | (Two-Quarters) | (One-Half) |

It is always desirable to show an answer in its simplest possible way. In this above examples it is 1/2.This process is called ** simplifying or reducing a fraction**.

#### 1 Least Common Denominators(LCD).

In Maths, the lowest common denominator or **least common denominator** (abbreviated **LCD**) is the least common multiple of the denominators of a set of fractions.LCD of a set of fraction is the lowest number which we can use in the denominators to convert these fractions into equivalent fractions that have the same denominators.

e.g

1/3 and 4/5 are two fractions.In order to create the same denominator of both fractions,we convert them into their equivalent fractions in such a way that both of them have a common denominator.We find the LCD of fractions to find equivalent fractions. In the above example, 5/15 and 12/15 are equivalent of 1/3 and 4/5. if we find their Least Common Multiplication (LCM) which became their LCD and it is used to create the Equivalent Fractions.

#### 2.Least Common Multiplication (LCM).

A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, .... The **least common multiple** (**LCM**) of two numbers is the smallest number (not zero) that is a multiple of both.So the LCM of 3 and 4 is 12.

## Basic Math Operations.

**Addition**.

1-**With Common Denominator**:We add the numerators and then simply it at the end to get the addition e.g

A)2/7+4/7+5?7=11/7.

B) 5/8+1/8=6/8=3/4. (divide by 2 to simplify it.)

Addition of fractions with common denominators can be practiced here using our worksheets for year 4.

All our worksheets are designed on the basis of latest national curriculum.

2-**With different Denominators**:If denominators of the fractions are different then we use the following method.

e.g. 3/8+1/4=??

Method:We must *somehow* make the denominators the same.

In this case it is easy, because we know that ^{1}/_{4} is the same as ^{2}/_{8} :

^{3}/_{8} |
+ | ^{2}/_{8} |
= | ^{5}/_{8} |

If we cannot find the suitable equivalent fraction we have to use following method to find the common denominators and then add them later.

#### How to Find Addition of fractions by LCD method?

- First,convert all the integer and mixed numbers into proper fractions.
- Then for all the denominators, find the LCM(Least Common Multiplication).
- This LCM number will be LCD of set of fractions.
- Now divide the LCD found in step 3 by each of the denominators.
- After that multiply both the numerator and denominator by the number found in step 4.
- In the end,add the numerators of the newly found fractions from step three but keep the same denominators.
- This will give the result of addition of set of fractions.

*Example.*

Question 1.Add the following .

4/5+ 6/7=?

Answer.

- First find the LCM of both denominators which is 35.
- Now Use this LCM to make LCD and divide 35 by 5 and get 7.Then divide 35 by 7 and get 5.
- After that multiply both numerator and denominator separately by their respective number. In this case,multiply 7 by 4 and then by 5 e.g. 4*7/5*7=28/35.Similarly 6*5/7*5=30/35.
- Add the new numerators of both fractions by keeping the denominators same to get the result. i.e 28/35+30/35=
**58/35**.answer.

### Subtraction.

The method of subtracting the fractions is same like addition.If denominators are same then subtract the numerators like simple subtraction e.g. 5/4-3/4=2/4=1/2.

If denominators are not equal then first make them equivalent fraction using LCD method of equivalent fractions.

### Multiplication .

Division.

This is a very useful description of fractions in a BBC website.