[Maths Class Notes] on Comparing Fractions Pdf for Exam

Fractions are a part of a whole. Sometimes we have a whole divided into different number of parts. For example, three pizzas can be divided into 8 or 10 or 12 parts. In these cases, it might get difficult to understand how to compare fractions if we try to compare among all the pizzas. We need to compare fractions to find out which fraction is larger and which fraction is smaller. We use two methods to compare such fractions – Decimal method and Same Denominator method. However, before we learn what is comparing fractions, we need to know what a fraction is.

What Is A Fraction?

As mentioned before, fractions are a part of a whole. So, if you divide a whole cake into a number of equal parts, we call each part a fraction of the whole cake. It is represented by a/b where a is the numerator and b is the denominator. The numerator is the number of equal parts that are used while the denominator is the total number of equal parts in which the whole is divided. Suppose you have a pizza divided into 8 equal slices and you eat 1 slice, you can say you have ⅛ of the pizza and ⅞ is left.

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What Are Like And Unlike Fractions?

To understand how comparing fractions work, it is essential to first understand what like and unlike fractions are. Like fractions are those that have the same denominator. For example ⅖, ⅕, ⅗ is a group of like fractions. On the other hand, comparing unlike fractions is basically comparing fractions with different denominators. For example, ½, 4/7, ⅔, ⅗ are a group of unlike fractions. 

Comparing Fractions Using Decimal Method

We can compare fractions by converting fractions into decimals. Suppose we have different fractions – ½, ⅔, ¾ and ⅘ which we want to compare. In the decimal method, we convert each of them into a decimal.
½ = 0.5
⅔ = 0.66
¾ = 0.75
⅘ = 0.80
Here we can easily compare and say which one is bigger and which one is smaller.

Comparing Fractions Examples

Here are a few Comparing Fractions Questions:

EXAMPLE 1:
Which of the following fractions is larger: 3/7 or 5/9?

Solution:
3/7 = 0.42

5/9 = 0.56

Since 0.56 is greater than 0.42, we can conclude that 5/9 is greater than 3/7.

Comparing Fractions Using The Same Denominator Method

Comparing fractions is easier if the denominators of different fractions are the same. Hence, if there is a group of like fractions, they can be compared easily. For example, when you have to compare two fractions 21/50 and 37/50, you have to only compare the numerators. In this case, both fractions have the same denominator 50 and 37 is greater than 21. Hence, we can conclude that 37/50 is greater than 21/50. However, this method can only be used when the denominator of all the fractions in the group are the same.

Example:

Which of the following fractions is smaller: 90/90 or 80/90

Solution:
90/90 = 1

80/90 = 0.89

Since 1 is greater than 0.89, we can conclude that 80/90 is smaller than 90/90.

The above method can be used only when you are comparing fractions using the same denominator.

What happens if the denominators are different? What will you do when you are comparing fractions with unlike denominators and you do not want to convert them into decimals? Well, you can convert the unlike fractions into like fractions by multiplying them with a common multiple and converting them to the same denominators. Here is an example:

Example:

Which of the following fractions is larger: 7/9 or 4/7

Solution:
We convert 7/9 and 4/7 into the same denominators by finding out the LCM of the denominators. The LCM in this case is 63. So we multiply both 7 and 9 by 7 and get 49/63.

[frac{7 × 7}{9 × 7}] = [frac{49}{63}]

 Similarly, we multiply 4 and 7 with 9 and get 36/63. 

[frac{4 × 9}{7 × 9}] = [frac{36}{63}]

As numerator 49 is higher than numerator 36, 7/9 is higher than 4/7.