How To Compare Fractions?

Maths has not been the favorite of all kids. Many consider it one of the toughest subjects, so they seek some expert’s help and guidance. All parents are not in a position to dedicate their whole time to teach their kids. In such a scenario, a good tutor plays a significant role in easing the burden of the students by helping them learn the subject thoroughly.

At school, it often happens that all the students may not like the method of teaching, and because of time constraints, a teacher fails to cater to individual requirements. Cuemath is one such platform that efficiently meets the needs of all students. 

The questions that are frequently asked by the students are:

Can I take the help of different reference books for understanding how to solve fractions?

Is it mandatory to take the guidance of a tutor for clarity of concepts about fractions?

Is learning fractions complicated for beginners?

There may be many such endless questions popping up in your mind. In this article, we will clear such doubts and make it easy for you to compare and solve the different types of fractions.

Some basics about fractions:

What is a fraction?

A fraction is a part of some whole number, such as when 3 is divided into 9 equal parts, we write it as 3/9 or 1/3. It indicates the division of an integer into some parts. The lower part or denominator of a fraction is always a non zero number, and the upper or numerator is another number.

What are the types of fractions?

Fractions are broadly divided into the following types:

i.Proper function::

The absolute value of this fraction is less than one and higher than -1. In other words, the numerator is lower than the denominator. Example: 4/7, 2/3

1. Improper function:

The absolute value of this fraction is higher than 1. The numerators are greater than the denominators in this case.

Example: 8/3, 9/2

iii. Like fractions:

These are a group of fractions having the same denominator, such as 1/9, 3/9, 8/9

iv.Unlike fractions:

These are a group of fractions having different denominators, such as 2/5, 3/7, 4/9

1. Unit fractions:

The numerator in these fractions is always 1, such as 1/4, 1/9, 1/3.

vi.Mixed fractions:

This is a combination of a whole number and a proper fraction, such as 2 1/3, which is equal to 7/3. So a mixed fraction always reduces to an improper fraction or vice versa.

vii. Equivalent fractions:

When you simplify a fraction to get another fraction, both these fractions represent the same portion and are referred to as equivalent fractions. Let us see an example:

4/8 can be simplified to obtain 1/2. So both these are considered to be equivalent fractions.

Comparison of fractions:

This is categorized into two types:

1. For like fractions:

These are compared just like integers. Since their numerators are different but denominators are the same, you need to compare the numerators. Example:

4/9 > 2/9 > 1/9

1. Unlike fractions:

Unlike integers and like fractions, you can’t directly compare fractions. So, to do this, you need to follow either of the following two ways:

• Converting the fraction to decimals:

This method needs to be implemented when you have unlike fractions, i.e., those having different denominators.

When you have a set of fractions given, arrange in ascending or descending order, or find the least or maximum fraction, you need to convert each of them to a decimal number. Then you can easily identify which is the least and which one is the highest.

Example:

Which is greater among 2/9 and 5/7?

Now, 2 ÷ 9 = 0.222

and 5 ÷ 7 = 0.71

The decimal results clearly show which is the higher of the two, i.e., 5/7.

• Conversion of unlike fractions into like fractions:

As we have already seen at the beginning of this section, comparing fractions with the same denominators is very easy. Whenever you come across unlike fractions, try to make their denominators the same by multiplying the numerator and denominator of the fractions by a certain number. Let us see an example to clarify the process:

Consider two fractions 2/5 and 3/4

In such problems, the trick is to multiply the denominator of one fraction with the other fraction’s numerator and denominator. This will make both their denominators the same:

(2 x 4)/( 5 x 4) = 8/ 20

(3 x 3)/(4 x 5) = 9 / 20 

Now, we can see 9/20 > 8/20 which implies 3/4 > 2/5

What to do when there are more than two unlike fractions to be compared?

In such a case, find the LCM of the denominators and divide the resulting value with the denominator of all the given fractions to get a number for each fraction. Multiply this corresponding number with the numerator and denominator of each of the fractions to make their denominator the same. Let us see an example of this for better clarity:

2/3, 7/6 and 1/9

LCM of 3, 6, and 9 is 18

18 ÷ 3 = 6

So, (2 x 6)/( 3 x 6)= 12/18

18 ÷ 6 = 3

So, (7 x 3)/ (6×3)= 21/18

Similarly, 18 ÷ 9 = 2

So, (1 x 2) / (9 x 2)= 2/ 18

Now we can easily compare the three fractions: 21/18 > 12/18 > 2/18

7/6 > 2/3 > 1/9

Tips for solving problems related to fractions:

No matter which exam it is, you need to follow some tips for efficiently solving these number problems:

1. Learn all the basics with complete clarity and ask your mentor questions whenever you find something difficult.
2. Go through the previous years’ exam papers or sample question papers to know the pattern and number of marks expected from the fractions section.

iii. Since fractions are one of the simplest topics in maths you can easily score full marks in questions from this topic.

1. Keep on revising the techniques and practicing problems from various books and online websites to better grasp the subject and gain confidence in the main exam.
2. You can create a time table and fix sometime in a day for dedicating your time to focus on this topic.
3. Never hesitate to clarify your doubts with your tutor.

vii. Sometimes, in exams, you don’t get questions from the fractions section directly. This doesn’t mean that the chapter doesn’t have any importance as you will need to know how to solve them in other maths chapters as well. So it is like a basic concept that will always be helpful.

Importance of opting for the right mentor while learning fractions or any chapter in maths:

Though many books explain all the chapters in maths and online resources, a good mentor is needed to easily grasp the concept in the least possible time. Here are some important points you need to remember while choosing an online academy or mentor:

1. Tutor should communicate clearly:

No matter how skillful a person is in solving maths problems, an ideal tutor should be able to explain the concept to the student properly so that there is no doubt while solving any problems. He should identify the students’ weak points and focus on them to enhance their math skills instead of simply scolding them when they commit any mistake.

ii.Type of teaching:

Students need to see if individual tuition works best for them or are comfortable in group coaching. Also, since most classes are conducted online today, for safety, they need to start learning the etiquette for online classes besides learning how to use different tools for efficient communication. Teachers should be willing to guide the students in such cases. Based on this, they need to opt for online or offline classes to help them meet their goals.

iii. Check if the educational sites offer trial classes:

Trial classes will help you know if the quality of maths class you are expecting matches the one delivered online. So you can confidently opt for it or move on to the next.

Final words:

Fractions are one of the easiest chapters in maths, but it becomes even better for beginners when they get the right guidance from the right tutors either offline or online. We suggest you Explore Numbers with Cuemath for conceptual clarity along with complete guidance to excel in maths from skillful teachers online by staying at the comfort of your home.

When parents have invested their time and money in the right place, most of their stress is eliminated. This is because online tutorial websites like Cuemath take complete care of students to build their fundamentals and eliminate their fear for maths. This proves to be quite useful in the future when they appear for various competitive exams in government sectors or public sector units.