Comparing Fractions

Fractions are an integral part of mathematics. Learning about the comparison of fractions by cross multiplication can teach us a lot about the quantity of any object and how much of any object is included or excluded. Fractions can be understood by imagining real-life experiences like you are cutting a birthday cake into some number of slices. These slices are nothing but a fraction or part of the cake (whole). The actual meaning of fractions is broken, even though we will learn fractions from a mathematical point of view. “/” is the symbol of fractions. For example, 3/7 means 3 is the numerator (upper part) and 7 is the denominator (lower part). In this article, tricks of comparison of fractions have been given at the end. 

What Are Like Fractions?

A fraction is made up of two sections. The numeric value at the top is known as a numerator, which gives us an idea about how many equal divisions of a whole object or complete value are taken. The numeric value at the bottom is known as the denominator, which gives us an idea of the total number of parts that are divisible from the whole and thus possible. 

Like fraction is a mathematical term used for those fractions whose value of denominators are the same or in the same ratio. Comparison of like fractions is easier than the comparison of unlike fractions whose denominators are different.

Comparison Of Like Fractions

Like Fractions are easy to manage and students often find them easier to apply and use in problems. The reason is that since the denominators of both the fraction are the same and denominators are the backbone of a fraction. They decide the total number of parts that are divisible from the whole. If the denominators are the same, it makes the comparison of like fractions easy.

Let’s understand the comparison of like fractions by an example,

Comparing 9/11 and 5/11. 

Step 1. Comparing the denominators only of both the like fractions. 

Both 9/11 and 5/11 are like fractions as we can see that the denominators of 9/11 are 11 and 5/11 is also 11.

Step 2. Secondly, you should compare numerators of both fractions.

Here,  9 > 5.

Step 3. The fraction which possesses the larger numerator is going to be the larger fraction.

Therefore, 9/11 is a greater fraction in comparison to 5/11.

Comparing Unlike Fractions

Unlike fraction is a mathematical term used for those fractions whose value of denominators are not the same or in the same ratio. The comparison of unlike fractions is more complex than the comparison of like fractions whose denominators are the same.

To compare unlike fractions, there is no direct formula or function to apply. 

Let us compare two unlike fractions 1/3 and 3/7.

Step 1. Convert the different denominators into the same denominators by any method. Here, 3 is not equal to 7. 

Step 2. Calculating the least common multiple (LCM) of both the denominators, in this case, we have to obtain the LCM of 7 and 3.

LCM of (3, 7) is 21.

Step 3. Converting both the fractions so that they can get the same denominators.

Multiplying 1/3 * 7/7= 7/21.

Multiplying 3/7 * 3/3 = 9/21.

Step 4. Now, we can compare both the fractions just like we use to do in the case of like fractions because 7/21 and 9/21 are like fractions.

We can easily compare 7/21 and 9/21 and therefore, 9/21 > 7/21.

Hence, 3/7 is greater than 1/3.

#Note:- If there are two fractions such as 6/11 and 6/15. The numerators are equal i.e. 6 but the denominators are different i.e 11 and 15. Then in such cases, we should ignore the numerator as it is the same, and focus on the denominators. The fraction with the larger denominator is going to be the smaller fraction overall. Thus, 6/11 > 6/15. 

Comparing Fractions by Decimal Method

In this method, we will compare two fractions doesn’t matter if they are like fractions or unlike fractions by converting them into decimal format.

For example, let’s compare 3/10 and 7/12.

Writing 3/10 and 7/12 in decimal form.

3/10 = 0.3 and 7/12 = 0.5

Hence, we can conclude that 0.5 is greater than 0.3, therefore, 7/12 is greater than 3/10.

Comparison Of Fraction By Cross Multiplication

Cross Multiplication is a great substitute method to compare fractions. Cross-multiplication is the method where the numerator of one fraction is multiplied by the denominator of another fraction and similarly, the denominator of the other fraction is multiplied by the numerator of the first fraction.  

Let’s understand the comparison of fractions by cross multiplication by an example.

1/6 and 3/4.

1*4 = 4 and writing this on the left-hand side of the equation.

3*6 = 18 and writing this on the right-hand side of the equation.

The last step involves you comparing the product on both ends.

4 < 18.

Equating the sides with original fractions.

3/4 > 1/6.

Conclusion

A fraction is made up of two sections. The numeric value at the top is known as a numerator, which gives us an idea about how many equal divisions of a whole object or complete value are taken. The numeric value at the bottom is known as the denominator, which gives us an idea of the total number of parts that are divisible from the whole and thus possible. Learning about the comparison of fractions by cross multiplication can teach us a lot about the quantity of any object and how much of any object is included or excluded.