Definition and example of fraction
A fraction is a number which represents a part of a whole.
Fractions in Maths helps us to measure how many parts are there and the size of each part of an object.
Let’s see how to read fractions with examples.
Example 1
511
This is read as five – elevenths.
Example 2
38
means 3 parts are taken from equally
divided 8 parts of whole.
Fractions are always positive, that means numerator and denominator are positive integers.
The Denominator can never be zero in a fraction.
Which are 10 types of fractions?
There are many types of fractions but the commonly used ten types of fractions are:
- Unit fraction
- Like fractions
- Unlike fractions
- Simple fraction
- Complex fraction
- Decimal fraction
- Vulgar fraction
- Proper fraction
- Improper fraction
- Mixed fraction
1. Unit fraction
A fraction whose numerator is one and denominator can be any positive integer is called a Unit fraction.
14 ,
17 ,
161 etc.
In 14 , the numerator is 1 and
denominator 4 which is a positive integer.
2. Like fractions
The fractions which have the same denominator are called Like fractions.
19 ,
29 ,
79 etc.
So, the above fractions
19 ,
29 and
79
have the same denominator i.e.
9, so they are like fractions.
3. Unlike fractions
The fractions which have different denominators are called Unlike fractions.
79 ,
14 ,
611 ,
58 etc.
So, the above fractions
79 ,
14 ,
611 and
58
have different denominators i.e. 9, 4, 11 and 8 respectively, so they are Unlike fractions.
4. Simple fraction
A fraction whose both terms are integers is called a simple fraction.
47 , 35 etc.
5. Complex fraction
A fraction whose one or both terms are fractional numbers is called complex fraction
2 57 , 7 5 6 7 etc.
6. Decimal fraction
Fractions whose denominators are 10, 100, 1000 etc. are decimal fractions.
310 , 111000 etc.
7. Vulgar fraction
Fractions whose denominators are not 10, 100, 1000 etc. are called vulgar fractions.
15 , 715 etc.
8. Proper fraction
A fraction whose numerator is positive and also less than its denominator is called proper fraction.
712 , 1921 etc.
9. Improper fraction
A fraction whose numerator is greater than its denominator is called improper fraction.
115 , 8521 etc.
10. Mixed fraction
A fraction which is expressed as a combination of integer and a proper fraction is called mixed fraction.
235 here 2 represents integer part and 35 represents proper fraction.
What is an equivalent fraction?
The two or more than two fractions are said to be equivalent when multiplying the numerator and denominator by a same non zero positive number results in the original fraction.
Let’s take an example of 13 and
39.
Multiply both numerator and denominator by 1:
13 ×
11 =
13
Multiply both numerator and denominator by 2:
13 ×
22 =
26
Multiply both numerator and denominator by 3:
13 ×
33 =
39
Here 13 becomes equal to
39 when multiplied by 3.
Hence, 13 and
39 are equivalent fractions.
Fractions with shaded diagram
Fractions can be shown with shaded area in a diagram also. The numerator in a fraction is shown as shaded area and the denominator is the total number of cut pieces in the diagram.
In general, a fraction can be changed into the shaded diagram with the following method.
Fraction =
numeratordenominator =
shaded parttotal number of parts
Let’s see with examples how to shade the area for fractions.
Example 1. Fraction 12
The fraction 12
can be shown like in the next diagram.
The numerator 1 of fraction 12
is represented by the shaded box. The denominator 2 is the total number of equal boxes to be drawn in the diagram.
So, the above diagram refers the 1 part out of 2 equal parts.
Example 2. Fraction 13
The numerator 1 of fraction 13
is represented by the shaded box. The denominator 3 is the total number of equal boxes to be drawn in the diagram.
So, the above diagram refers the 1 part out of 3 equal parts.
Example 3. Fraction 24
Fractions can also be represented with a circle and dividing it into equal sectors, equal to
denominator of the fraction and number of shaded sectors equal to the numerator of the fraction.
So, here, total number of sectors in the circle = 4
and number of shaded sectors in the circle = 2
So, the above diagram refers the 2 part out of 4 equal parts.
Example 4. Fraction 03
Total number of boxes = 3
and number of shaded boxes = 0
So, the above diagram refers the 0 part out of 3 equal parts.
Example 5. Fraction 33
Total number of boxes = 3
and number of shaded boxes = 3
So, the above diagram refers the 3 part out of 3 equal parts.
Example 6. Fraction 410
Total number of boxes = 10
and number of shaded boxes = 4
So, the above diagram refers the 4 part out of 10 equal parts.
Real life example of fractions
A pizza bought from market and sharing with 8 friends equally is a real life example of fractions. The pizza is going to be divided into eight equal pieces assuming that everyone will share one equal piece.
So, a pizza has been cut into total equal pieces of 8 to divide among 8 friends. We can write the one piece of pizza in fractions as 18 , where 1 in the numerator denotes one piece and 8 in the denominator denotes the total number of pieces.
In fractions we can say one friend is sharing 18th (read as one eighth) part of pizza. As, everybody share equal piece of pizza, so we can also say everyone has shared 18 fraction of pizza.
What we have learnt about fractions from above is that a fraction has a numerator and a denominator. The denominator keeps the value of the total number of parts and numerator holds the value of a part of the whole object.
Hence, we can write in fractions 18 fraction of a whole pizza is shared to each person.
How the fraction is written, if one person is absent out of 8, eventually any one friend will get an opportunity to have 2 pieces of it. So finally we have 7 friends and 8 cut pieces of pizza.
The friend who will get 2 pieces of pizza, in fractions it can be written as
28 piece of pizza. Again,
the denominator has a total number of pieces i.e. 8 and the numerator value is 2.
The remaining 6 friends share 1 piece, so their fraction of pizza shared still remains as
18.
