Fractions, Types of Fractions

Fractions, Types of Fractions


fraction represents a part of the whole. In a fraction, the top number is called the numerator and the bottom number is called the denominator. In ¾, 3 is the numerator and 4 is the denominator.
Remember that the numerator tells us the number of parts taken while the denominator tells us the total number of parts that the whole number is divided into.

Types of Fractions

There are mainly three types of fractions:
1.      Proper fractions
2.      Improper fractions
3.      Mixed fractions

We have two other types of fractions as follows:
1.      Like fractions

2.      Unlike fractions

Proper Fractions

Fractions in which the numerator is smaller than the denominator are called the proper fractions. A proper fraction is a part of a whole. For example, 1, 351113 

Improper Fractions

Fractions in which the numerator is greater than the denominator are called the improper fractions. They are greater than a whole. For example, 75 , 95

Mixed Fractions 

When we combine a whole number and a proper fraction together, we get a mixed fraction. For example, 21, 53

Converting Improper Fractions into Mixed Fractions

To convert 75 into mixed fraction, divide the numerator by the denominator. Write the quotient as the whole number, remainder as the numerator and divider as the denominator. Thus, 75  = 125

Converting Mixed Fractions into Improper Fractions

To convert 75 into improper fraction, multiply the denominator with the whole number and add the product with numerator and write the denominator as it is.
Thus, 21= (2 × 2 + 1)/2 = 5/2

Like Fractions

All those fractions whose denominators are the same are called like fractions. For example, 1/7, 3/7, 4/7, 6/7, etc. are all like fractions.

Unlike Fractions

All those fractions whose denominators are not the same are called unlike fractions. For example, 1/2, 5/8, 3/4, 9/16, etc. are all unlike fractions.

Converting Unlike Fractions into Like Fractions

To convert 1/2, 5/8, 3/4, 9/16, in like fractions, we first find the LCM of the denominators of all the unlike fractions, i.e., 2, 8, 4 and 16.
LCM of 2, 8, 4 and 16 = 16

Now, find the equivalent fractions for all the fractions with denominator 16.
1/2 = 1 × 8 / 2 × 8 = 8/16
5/8 = 5 × 2 / 8 × 2 = 10/16
3/4 = 3 × 4 / 4 × 4 = 12/16
9/16 = 9 × 1 / 16 × 1 = 9/16
Thus, 8/16, 10/16, 12/16 and 9/16 are like fractions.

Equivalent Fractions

Two or more than two fractions are said to be equivalent if both have the same value after simplification. Let us say, a/b and c/d are two fractions, if after simplification they both result in equal fraction, say e/f, then they are equivalent to each other.
For example, 1/3 and 5/15 are the equivalent fractions, because if we simplify 5/15, its value is the same as 1/3. Similarly, 1/2 and 2/4 are also the equivalent fractions.

The biggest question here can be, why do they have equal values in spite of having different number?
The answer to this question is that, as the numerator and denominator are not co-prime numbers, therefore they have a common multiple which on division gives an exactly the same value.
Take for an example:
1/2 = 2/4 = 4/8
But, it is clearly seen that the above fractions have different numbers as numerators and denominators.
Dividing both numerator and denominator by their common factor, we have:
4/8 = 4÷4 / 8÷= 1/2
In the same way, if we simplify 2/4, we again get 1/2.
2/4 = 2÷2 / 4÷= 1/2

Here’s an example of equivalent fractions.

How to find equivalent fractions?

By multiplying the numerator and the denominator of a fraction by the same non-zero whole number, we can get an equivalent fraction. But it will not change its value. Equivalent fractions may look different, but they have the same value. Let's look at some more examples of equivalent fractions.

For example:  to find equivalent fraction of 2/3, we multiply both the numerator and the denominator by 2, then we get equivalent fraction 4/6.
Again to find one more equivalent fraction of 2/3, we multiply both the numerator and the denominator by 3, then we get equivalent fraction 6/9.

Similarly, we can multiply both the numerator and the denominator by 2, 3, 4, 5, 6, etc. to get equivalent fractions of a given fraction.

How to check two or more fractions are equivalent fractions?

Simplify all fractions. If they reduce to be the same fraction, then the fractions are equivalent.

For example: Check the fractions 6/15 and 10/50 are equivalent or not.
We will simplify both the fractions-
6÷3 / 15÷3 = 2/5
10÷10 / 50÷10 = 1/5

The fractions 2/5 and 1/5 are not the same, hence fractions are not equivalent.

Use cross-multiplication to check two fractions are equivalent or not

The products are equal. Therefore, the fractions are equivalent.

Lowest Form of a Fraction

A fraction is said to be in its lowest form if the only common factor of the numerator and the denominator is 1.
For example, /3, 2/5, 3/7, 4/9, etc. are in their lowest forms.

Reducing a Fraction to its Lowest Form

A fraction can be reduced to its lowest form by dividing both the numerator and the denominator by a common factor.

Example: Reduce 45/75 to its lowest form.
(45 ÷ 3)/(75 ÷ 3) = 15/25
But 15/25 is not in its lowest form, so repeat the process till the numerator and the denominator have no common factor except 1.
15/25 = (15 ÷ 5)/(25 ÷ 5) = 3/5

Therefore, the lowest form of 45/75 is 3/5 .

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