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How to Compare Fractions with the Same Numerator | Free PDF with Answer Key

Hello young people!! Do you ever think the fractions in your real life? Do you know how to compare fractions easily? Do you enjoy solving mathematical and logical problems? If the answer is yes, this article is for you. Let’s compare fractions with the same numerator with some basic activities.

As you can see, I am mentioning a new term here which is called the numerator. Some terminologies are there for fractions. A fraction is a technique to express a quantity that represents a portion of a total in mathematics.

The numerators and denominators are the basic portions of fractions. If you want to have some mathematical jobs to do with fractions, you need to know the numerators and denominators. Stay with us in this article to have a firm knowledge about all of these.

two children comparing fractions with the same numerator          


Introduction to Numerator of a Fraction

A fraction consists of two numbers printed one above the other and separated by a fraction bar, which is a horizontal line. The numerator is the number above the fraction bar, while the denominator is the number below the fraction bar.

The top number in a fraction, or numerator, denotes the portion of the entire that is being tallied or measured. It shows how many factors are being taken into account. A fraction’s denominator, which indicates the entire or the whole number of pieces, is the lowest number in the fraction. It specifies the number of equally sized sections that make up the whole.

For instance, if you take a fraction a/b, a is the numerator and b is the denominator. If we take the numbers as nominators and denominators like- ⅘ then 5 is the denominator and 4 is the nominator here. Let’s consider a cake of which you need to make 5 pieces.

Then you give the 4 pieces of the cake to your younger sister. Here the 5 pieces are whole numbers of the cake called the denominator and the 4 pieces are the portion you have to give to your sister is the numerator.

Numerator of a fraction

 


5 Ways to Compare Fractions with the Same Numerator

Here, we are going to describe 5 easy ways to compare fractions with the same numerator. This is a very basic mathematical operation regarding fractions. This will help you guys to increase your mathematical sense as well as number sense. You may improve your fraction skills here. Follow the activities carefully and practice them in the worksheets.


Comparing Fractions with Like Numerators in Ascending Order

Ascending order is a method of ordering numbers from smaller to bigger. Ascending means increasing. If you have a set of numbers 2, 3, 5, 9, 6, and 1, the ascending order for the numbers will be 1<2<3<5<6<9. If you have some fractions with the same numerator and need to make an ascending order, it is quite an easy task. The main idea of this activity: the larger the denominator, the smaller the fraction.

Example: Write the numbers in ascending order: 1/35, 1/33,  1/41, 1/15, 1/120

Solution: As you know, the larger the denominator, the smaller the fraction. So, 120>41>35>33>15 So, the ascending order of the fractions: 1/120<1/41<1/35<1/33<1/15.

Compare fractions with the same numerators in ascending order

Let’s practice the above method in the following worksheet.

 

 


Comparing Fractions with the Same Numerators in Descending Order

Descending order is a method of ordering numbers from bigger to smaller. Ascending means decreasing. If you have a set of numbers 4, 3, 5, 6, 9, and 7, the descending order for the numbers will be 9>7>6>5>4>3. If you have some fractions with the same numerator and need to make a descending order, it is quite an easy task. The main idea of this activity: the smaller the denominator, the larger the fraction.

Example: Write the numbers in ascending order: 1/35, 1/33,  1/41, 1/15, 1/120

Solution: As you know, the larger the denominator, the smaller the fraction. So, 15<33<35<41<120 So, the ascending order of the fractions: 1/15>1/33>1/35>1/41>1/120

Compare fractions with the same numerators in descending order

Try out the aforementioned technique using the worksheet that follows.

 


Using Different Types of Visual Elements to Compare Fractions with Same Numerator

In this portion, I will use different types of visual elements to compare fractions. We can use squares, rectangles, circles, and triangles to represent fractions. Let’s see an example of visual elements to compare fractions.

Example: Find which is a greater fraction between ⅙ and 1/7.

Solution: You can see the numerators of the fractions are the same. Now, look at the elements. Here you can see a rectangle divided into 6 areas and one of the areas is shaded. This rectangle represents ⅙. Again another rectangle is found which is divided into 7 areas and 1 area is shaded. This rectangle is representing 1/7. Now as you can see, the shaded area of ⅙ is greater than 1/7. So, ⅙ is greater than 1/7.

Different Elements to Compare Fractions with the Same Numerator

Try out the technique mentioned above using the worksheet that follows.

 


Comparing Fractions with the Same Numerator by Using Decimal Method

By using decimal procedures, you may compare fractions. Here, we contrast fractions’ decimal values. In this case, the fraction is transformed into decimals by dividing the numerator by the denominator. The decimal values are then contrasted.

Example: Let us compare 1/10 and ⅕.

Solution: Convert 1/10 and ⅕ into decimals. The decimals will be: 1/10 = 0.1 and ⅕ = 0.2 Then compare the decimal values 0.1 and 0.2. As 0.2 is greater than 0.1, ⅕ is greater than 1/10. Therefore, ⅕>1/10.

Using Decimal Methods for comparing fractions with the same numerator

Let’s follow the following worksheet to practice more.

 


Using Cross Multiplication to Compare Fractions with the Same Numerator

We multiply the numerator of one fraction by the denominator of the second fraction to compare fractions using cross multiplication. Let’s use an illustration to better grasp this. Compared to 1/4, 1/6. See the illustration below for a clearer explanation of this.

  • First, cross-multiply the numbers in the numerator in the first fraction and the denominator in the second fraction. You will find product 6. Write down the product under ¼.
  • Then, cross-multiply the numerator in the second fraction and the denominator in the first fraction. You will find the product: 4. Write down the product under 1/6.
  • Now compare the products. Here you will find 6 is greater than 4. Here, the number representing ¼ is 6, and 4 is representing ⅙. So, the greater fraction is ¼.

Using Cross Multiplication to compare fractions with the same numerator

Try out the aforementioned technique using the worksheet that follows.

 


Comparing Fractions with the Same Numerator and Denominator

We have discussed how to compare fractions with the same numerator in the former sections of this article. Now I will show how to compare fractions with the same denominators. Let’s take two fractions ¼ and ¾ as examples. Here, you should bear in mind that for the same denominator, the greater the numerator, the greater the fractions. As in the given fraction, 3>1. Then ¾>¼.

Comparing Fractions with the Same Numerator and Denominator

Follow the procedure and practice in the worksheet attached with the article.

 


Download the Free Worksheet PDF

In this article, I have discussed 5 interesting ways to compare fractions with the same numerator. Moreover, if you become an enthusiast, you will find the paragraph about how to compare fractions with the same denominator. A worksheet is added to this article for your practice. Write in the comment section if you have any questions or anything to recommend.

Enjoy!

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