Have you ever done additions or subtractions of fractions? If yes, then you will have a wonderful revision today.
Fraction strips are rectangular pieces of distinct parts of a whole equal number. It comes in numerous colors, shapes, and sizes. One needs to take out a whole number or a definite value by addition or subtraction. As we all know, there are three types of fractions (proper, mixed, and improper), so the value of the fraction strip can be in any of the three forms. You have to carry forward your additions and subtractions accordingly.
How do you add and subtract fractions?
If you are well-versed with the correct method, it is very easy to carry out the addition and subtraction of fractions. There are myriads of ways to add two different fractions. While some try simplifying proper and improper fractions, some also try to convert the mixed fraction to proper or improper fractions. Here are two cases through which you can easily add or subtract fractions:
Case 1: Adding Like Fractions
Just like numbers, proper fractions can also be added or subtracted by following some easy steps.
Step 1: Keep the denominators of the fraction the same.
By keeping the denominator the same, all you would have to do is perform the maths operations on the numerator. You can divide the strips into four equal parts, each representing the fraction 1/4.
Step 2: Add the numerator.
When the denominator is the same, all you are left with is the numerator. In the example stated above, if you are given two fractions to add (like the one in the image), that is, you need to add 2/4 and 1/4, all you would need to do is take two strips of 1/4 fraction and add another strip of 1/4 fraction.
Step 3: Answer
By performing the mathematical operation, you will be able to get the answer to your proper fraction. In this case, You would now get the answer, which is 3/4.
Case 2: Subtracting Like Fractions
Step 1: Keep the denominators of the fraction the same.
Just like the addition, subtracting with the help of these strips is easy! In the example stated above, you need to divide the strips again in 4 equals, each depicting the fraction 1/4.
Step 2: Subtract the numerator.
When the denominator is the same, all you are left with is the numerator. In the example stated above, if you are given two fractions to subtract (like the one in the image), that is, you need to subtract 1/4 from 3/4, all you would have to do is take out the one strip from the first section, that is from the three strips in the first fraction (each depicting 1/4), taking out one strip would give us the answer to our question.
Step 3: Answer
By performing the mathematical operation, you will be able to get the answer to your like fraction. In this case, You would now get the answer, which is 2/4. You can also convert this fraction into a simpler form, which would be 1/2.
Case 3: Adding Unlike Fractions
While calculating like fractions might look like a cakewalk, calculating and performing addition in unlike fractions can be a little more complex. However, here are the steps to do the same:
Step 1: Calculate the Lowest Common Multiple (LCM) of the denominators.
Since with unlike fractions, the denominators are different; therefore, to calculate, we first have to land up on a common denominator so that the mathematical operation can be made easy. In this case, we would calculate the LCM of the denominators. For example, When adding 1/2 + 1/4 , we need to take the multiples of the denominators, which are 2,4,6,8,10,12,14,16,18,20 for 2. While, the multiples of 4 would be 4,8,12,16,20,24,28,32,36 and 40. Here, 4 and 8 are both multiples of the denominators 2 and 4, but 4 is the LCM (Lowest common multiple).
Using fraction strips, you can now again divide the strips into 4 equal parts, each of the strips representing the fraction 1/4.
Step 2: Multiply the denominator and numerator of the given fraction number to have LCM as its new denominator.
Now that we have an LCM, we would multiply both the denominator and numerator by a number so that we get 4 as the new denominator. Since 2X2=4, we would have to multiply the numerator also by 2.
The answer for the same would be 2/4.
Step 3: Add or subtract the numerator by keeping the same denominator.
Similarly, for the second fraction, we would keep it as it is, as the denominator is already 4. Now, we would calculate the new fraction (2/4) with ¼.
Step 4: Answer
By performing the mathematical operation, you will be able to get the answer to your unlike fraction. In this case, the answer to 2/4 + 1/4 would be 3/4 Using the fraction strips, you can simply add 3 of the strips together to get the answer, which is 3/4.
Case 4: Subtracting Unlike Fractions
Step 1: Calculate the Lowest Common Multiple (LCM) of the denominators.
Just like adding the, unlike fractions, to perform subtraction too, we first have to land up on a common denominator to make the mathematical operation easy. In this case, we would calculate the LCM of the denominators. In the image shown above, when subtracting ¼ from ½, we need to take the multiples of the denominators, which are 2,4,6,8,10,12,14,16,18,20 for 2. While, the multiples of 4 would be 4,8,12,16,20,24,28,32,36 and 40. Here, 4 and 8 are both multiples of the denominators 2 and 4, but 4 is the LCM (Lowest common multiple).
Using fraction strips, you can now again divide the strips into 4 equal parts, each of the strips representing the fraction ¼.
Step 2: Multiply the denominator and numerator of the given fraction number to have LCM as its new denominator.
Now that we have an LCM, we would multiply both the denominator and numerator by a number so that we get 4 as the new denominator. Since 2X2=4, we would have to multiply the numerator also by 2.
The answer for the same would be 2/4.
Step 3: Add or subtract the numerator by keeping the same denominator.
Similarly, for the second fraction, we would keep it as it is, as the denominator is already 4. Now, we would calculate the new fraction (2/4) with 1/4.
Step 4: Answer
By performing the mathematical operation, you will be able to get the answer to your unlike fraction. In this case, the answer to 1/2 – 1/4 would be 1/4. Using the fraction strips, you can simply subtract 1 strip, which represents the fraction 1/4. Doing so, you would be left with just 1 strip, which gives you your answer, 1/4.
Benefits of using fraction strips
Fraction strips, also referred to as fraction bars or tiles, aid students to envision and scrutinize fraction relationships. They help convey an abstract articulation of the problem. What’s more, they enable the learners to formulate a substantial insight of fractions and mixed numbers, analyse correspondence, compare and order fractions and examine number systems with fractions. Below are a few benefits of using fraction strips.
- Easy to visualise and understand Fractional problems
Fraction strips are a great tool to help you learn the concept of fractions easily. The steps are designed so that you can divide a number in fractions. Similarly, you can combine those fractions to make it a whole number. You will be able to do all this manually with the mere aid of fraction strips, and it helps you visualise properly. Thus, fraction strips allow you to build a proper visualisation and comprehend fractional problems.
- Great tool for modelling analogous fractions
The fraction strips allow the student to break the same ‘whole’ number into different equal sizes. When students pick up any strip and move it side by side, they can visualise that fraction amount. In the same way, with the help of different strips, students can add, multiply, divide, subtract. Due to all those reasons, fraction strips are considered the perfect tools for modelling tasks.
- It helps students to develop a deeper understanding of fraction
Students encounter a lot of difficulty in understanding maths concepts, especially in fractions. The Fraction Strip provides a conceptual representation of the questions and adds a different perspective towards mathematics. Fractions strips provide a fun way for students to learn something. Thus, it helps students develop a better understanding of the concept.
Conclusion
With this, we can conclude that fraction strips make any fractional addition or subtraction an easy job. Fraction strips help students scrutinise deeply the fraction concepts. It also allows them to clear their mathematical doubts as it gives them the advantage of a visual aspect. The games listed above can be rendered useful for the students; they can learn anything without getting bored. Students get to uncover the whole concept of fractions while playing games – and can develop a strong base in mathematics. This way students can make the most out of their time and their game-playing time will be spent in a good place!
An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,