Fractions are numbers in the form of \dfrac{a}{b} where a and b are whole numbers and b ≠ 0. Fractions are divided into different types depending on the numbers above and below the fraction line ( i.e., numerators and denominators).
- The numerator shows the quantity of parts being considered,
- The denominator indicates the total number of parts in the whole.
There are 7 kinds of fractions which we will discuss below:
Proper Fraction
Proper Fractions are those Fractions in which the numerator is smaller than the denominator. In other words, when the number on top of a fraction (numerator) is smaller than the number at the bottom (denominator), then the fraction is called a Proper Fraction. The value of a proper fraction is always less than 1
Examples of Proper Fractions: 2/3, 4/5, 6/19, 7/9, 13/45 etc.
Example: Take a delicious pizza that Lily wants to share with her friends. The pizza gets sliced into 8 equal parts. Lily takes 2 of those slices for herself while sharing the rest with her friends. Now Lily's portion is represented as 2/8. Which is a proper fraction because 2 is smaller than 8.
Proper Fraction as Numerator < DenominatorImproper Fraction
Improper fraction is a fraction where the numerator is greater than the denominator. It means the fraction is equal to or greater than a whole. In other words, when the number on top of a fraction (numerator) is greater than the number at the bottom (denominator), then the fraction is called an Improper Fraction.
Examples of Improper Fractions: 19/13, 129/20, 45/6, 17/8 etc.
Example: If you have 10 slices from a pie that was originally cut into 8 slices, you have more than one whole pie. The fraction is: 10/8
Improper fraction as Denominator > Numerator
This is an improper fraction because 10 (numerator) is greater than 8 (denominator), meaning you have more than one full pie.
Like Fractions
Fractions are fractions that have the same denominators. This means the bottom number (denominator) in these fractions is the same. For instance, 2/5, 3/5, and 4/5 are like fractions.
Example of Like Fraction: 1/5, 3/5, and 5/9, 7/9 etc.
It is simple to add or subtract these types of fractions because there is no need to change the denominator, as it is the same '5' in all fractions. For example, while adding 2/5, 3/5, and 4/5, it gives (2+3+4)/5 = 9/5.
Unlike Fractions
Unlike fractions are fractions with different denominators. In other words, the bottom numbers (denominators) of these fractions are not the same.
Example of Unlike Fraction: 1/4, 1/3, and 1/6 etc.
➣ Check: Like and Unlike Fractions
Mixed Fraction
Mixed fractions are fractions that show a whole part and a smaller part together. All the improper fractions can be converted to mixed fractions, and the value of mixed fractions is always greater than or equal to one.
Mixed Fraction: 2 \frac{1}{4}, 5 \frac{3}{7},3 \frac{1}{9},3 \frac{2}{5} etc.
Example: Suppose from a pizza you have eaten 2 whole pizzas and some part from another pizza that has 4 slices, you can say you've eaten "2 and 1/4" Pizza. This is a mixed fraction, i.e.2 \frac{1}{4}. The "2" represents the whole pizza you ate, and the "1/4" shows the extra part of another pizza you ate. So, you've had a bit more than 2 whole pizzas.
Equivalent Fractions
Equivalent fractions are different fractions that represent the same portion of the whole. They may look different, but they have the same value.
Equivalent Fraction: 1/5 and 2/10, 10/18 and 5/9 etc.
Examplesthe 2/3 and 4/6, 3/8 and 6/16,are equivalent because when simplified, they both represent the same amount or the same portion of something.
Unit Fractions
A unit fraction is a type of fraction where the numerator is 1, and the denominator can be any whole number other than 0. In other words, a unit fraction is always written as 1 over something.
Unit Fractions: 1/3, 1/4, 1/2, 1/5 etc.
Unit fractions represent one part of a whole, and they are called units because they refer to a single, indivisible unit or piece. For example, 1/2 represents one-half of something, 1/3 represents one-third, and 1/4 represents one-fourth. They are essential in understanding parts and fractions of objects or quantities.
Improper Fraction and Mixed Fraction Conversion
Since, in an improper fraction, the numerator is greater than the denominator, we can convert it into a combination of a whole number and a proper fraction. The mixed fraction so obtained can also be converted into an improper fraction.
Improper Fraction to Mixed Fraction
By solving the improper fraction using the division method, it can be transformed into a mixed fraction. Divide the numerator by the denominator, then the remainder from this division will become the numerator, the number of times the denominator divides the numerator becomes the whole number, and the denominator stays unchanged.
Let's take an example of an improper fraction 7/3, to convert this fraction into a mixed follow the steps below:
Steps to convert Improper Fraction to Mixed Fraction :
- Step 1: Divide the numerator 7 by the denominator 3
- Step 2: This division will give 2 as the quotient and 1 as the remainder.
- Step 3: express the fraction into mixed fraction as 2\frac{1}{3}.
Conversion: Improper fraction into Mixed fractionMixed Fraction to Improper Fraction
A combination of a whole number and a proper fraction is called a mixed fraction. To change a mixed fraction into an improper fraction, it is required to multiply the whole number part by the denominator and then add the numerator. The outcome becomes the new numerator, while the denominator stays unchanged.
For example, let's convert the mixed fraction 2\frac{1}{3}to an improper fraction.
Steps to convert Mixed Fraction to Improper Fraction:
- Step 1: Multiply the whole number 2 by the denominator 3 , which will become 6.
- Step 2: Add the numerator 1 to the result obtained from step 1 ; 1 + 6 = 7
- Step 3: The result of step 2 is the new numerator and the denominator stays unchanged. Therefore the improper fractions is 7/3
Conversion: Mixed fraction into Improper fraction.Chart: Types of Fractions
As discussed above, there are seven types of fractions in mathematics, which are shown in the image below:
7 types of fractions
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