The term ‘Fraction’ represents the parts of a whole object or collection of objects. Let us understand this concept using an example. A cake that is divided into 12 equal parts. Now, if you want to express one selected part of the cake, we can express it as 1⁄12 showing that out of 12 equal parts, we are referring to 1 part.
It can be read as
A fraction has two components. The number on the top of the line is called the numerator. It tells how many equal parts of the whole object or collection of objects are taken. The number below the line is called the denominator. It shows the total number of equal parts the whole object is divided into or the total number of the same objects in a collection. All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fractional bar.
For example, in the fraction 7⁄9, 7 is the numerator and 9 is the denominator.
Based on the values of the numerator and denominator, there are different types of fractions as mentioned below:
Proper Fractions
The fraction in which the numerator is less than its denominator is called Proper Fraction. For example, 6/7, 7/8, 4/5, etc are proper fractions.
Improper Fractions
The fraction in which the numerator is more than or equal to its denominator is called an Improper Fraction. It is always the same or greater than the whole. For example, 4/3, 7/2, 9/5, and so on.
Unit Fractions
The fraction in which the numerator is 1 is known as Unit Fraction. For example, 1/9, 1/17, 1/3, and so on.
Mixed Fractions
A mixture of a whole number and a proper fraction is known as Mixed Fraction. For example, 3 4⁄5, here 3 is the whole number and 4⁄5 is the proper fraction.
Like Fractions
The fractions having the same denominator are known as Like Fractions. For example, 5/7 and 4/7 are like fractions. Here, we have divided the whole into 7 equal parts.
Unlike Fractions
The fractions having different denominators are known as Unlike Fractions.
For example, 4⁄7 and 8⁄11 are unlike fractions.
Equivalent Fractions
The fractions that represent the same value after they are simplified are known as Equivalent Fractions. We can use the following method to find equivalent fractions of any given fraction:
Example: Find two fractions that are equivalent to 4⁄7.
Solution:
To find the first equivalent fraction, we multiply both the numerator and the denominator of
4⁄7 by 2 i.e., 4⁄7 = 4⁄7 × 2⁄2 = 8⁄14
To find the second equivalent fraction, we multiply both the numerator and the
denominator of 4⁄7 by 3 i.e., 4⁄7 = 4⁄7 × 3⁄3 = 12⁄21
Hence, 8⁄14, 12⁄21 and 4⁄7 are all equivalent fractions.
A number line is a straight line with numbers placed at equal intervals along its length. The fractions on a number line can be represented by making equal parts of a whole. For example, if we need to represent 1⁄10 on the number line, we need to mark 0 and 1 on the two ends and divide the number line into 10 equal parts. Then, the first interval can be marked as 1⁄10. Similarly, the next interval can be marked as 2⁄10, the next one can be marked as 3⁄10, and so on. It should be noted that the last interval represents 10⁄10 which means 1. Observe the following number line that represents these fractions on a number line.
Example: Convert 3 5⁄7 into an improper fraction.
Solution:
Example: Convert 25⁄8 into a mixed fraction.
Solution:
8 goes into 25 three times with one as the remainder.
25⁄8 = 3 1⁄8
Addition and Subtraction of Fractions:
Example: Find 3⁄5 + 1⁄5
Solution:
Since the denominators are the same, simply add the numerators: 3⁄5 + 1⁄5 = 3⁄5+1⁄5 = 4⁄5
Example: Find 2⁄3 - 1⁄7
Solution:
Find the LCM of the denominators : LCM of 3 and 7 is 21
Make 21 the common denominator : 2⁄3 × 7⁄7 = 14⁄21 and 1⁄7 × 3⁄3 = 3⁄21
Subtract the fractions : 14⁄21 - 3⁄21 = 14⁄21 - 3⁄21 = 11⁄21
Multiplication of Fractions:
Example: Find 3⁄5 × 6⁄7
Solution:
3⁄5 × 6⁄7 = 18⁄35
Division of Fractions:
Example: Workout 1⁄5 ÷ 4⁄5
Solution:
1⁄5 ÷ 4⁄5 = 1⁄5 × 5⁄4 = 1⁄4
Example: Calculate 5⁄8 of 200.
Solution:
Divide 200 by 8 and then multiply by 5.
5⁄8 of 200 = (200 ÷ 8) × 5
= 25 × 5
= 125
What counts as a "good" score will vary depending on the school you want to attend. The standardized 11 Plus test score average across the country is roughly 100. The highest average in some areas is 111. The lowest scores would often fall between 60 and 70, while the highest scores would normally fall between 130 and 140. To achieve excellent marks on 11+ Maths Exams, practice 11+ Maths topic-wise questions.
The best way to prepare for the 11+ Maths Exam is by practicing 11+ Maths topic-wise questions regularly.
Maths online subscriptions are “Non-Refundable“. No refunds can be issued for any reason. This is because of the nature of digital products.
You should, therefore, make sure that the Maths online subscriptions fulfil your needs before you subscribe.
As these are digital products, we advise parents to go through our Free Past Papers provided on our website and once decided they can buy subscriptions.
The majority of the 11 Plus Maths questions are mathematical problem-solving, where pupils need to understand and apply mathematical concepts. With regular practice of 11+ Maths Topic-wise questions, you will pass the 11-plus Maths Exam with a high score.
The children must master the following topics for the 11 plus exams
Get 10,000+ Topic-wise questions by subscribing to our 11+ Maths Topic-wise questions. These questions are collected from 180+ Maths past papers.
11 Plus Maths Past Papers Subscription
Any PiAcademy Memberships are for 1 year (366 days), We give Instant unlock to all exam Resources So that you can plan your 11+ Preparation according to your convenience and as per our Planner Spreadsheets.
Hurry! 11+ Exams are approaching in 6 months. High competition. Most parents fail to do structured planning for the 11+ Exam preparation.
Get a plan and strategy from 11+ Expert Tutors. Avoid the common mistakes that other parents make.
© 2014 - 2024 PiAcademy Limited, All Rights Reserved