Grouping of Numbers (Addition)ft.Shriranchini S#Ganitaprakash#NCERT#Grade6#Grade7#Grade8#Mathematics

Added: 2026-05-10

[00:00:02]Hello mathletes, welcome to the math route by Shiranjani. So today's topic is all going to be grouping of numbers. So when it comes under addition, we always add the numbers be it natural or whole numbers. What if a negative sign is included? That is when we use the concept of grouping.

[00:00:23]Watch the full video to know more about grouping. So what is grouping?

[00:00:28]Rearranging numbers to make calculations easier. So it basically means rearranging without changing the sum. So it can be arranged in any order but the final result is the same. So in the first method we have grouped the first two numbers minus2 and 10. Whereas in the second method the second and the third numbers are grouped and solved whereas the result is the plus4. So the key takeaway is the same answer in different groupings. You can arrange or group numbers in any way. The final result is always the same. It does not change the sum. Answer remains the same. The golden rule.

[00:01:11]The two major properties of addition are commutative property and associative property under grouping of numbers. So the commutative property is more like a communication between two persons. So it involves only two numbers where a and b are two numbers and the rule is a + b is equal to b + a. The order can change.

[00:01:34]This means that we can change the order of the numbers while adding it. The sum will remain the same. Let us take two numbers 3 and 5. 3 + 5 gives you 8. Vice versa 5 + 3 gives you 8.

[00:01:48]No matter how we change the order, the sum is the same. This is the commutative property of addition under grouping of numbers.

[00:01:57]Next comes the associative property.

[00:01:59]Associative is a slight extension of commutative involving more than two people at once.

[00:02:07]So basic association is a good example.

[00:02:10]And let us take three numbers here for associative property. A, B and C. So first a + b + c is equal to a + b + c.

[00:02:21]This is how we read the rule. So grouping can change. In the first time we group a and b whereas in the rhs we group b and c together. So 2 + 3 + 4 is equal to 2 + 3 + 4. We solve the brackets or the grouping first and then add the next number. The result is the same. Again, pair the numbers wisely and combine positives and negatives is the smart strategy behind the associative property. This grouping of numbers helps solving longer problems in seconds. So here the pattern example is provided. 2 - 4 + 6 - 8 + 10 - 12. So when we group it as pairs, each pair yield the answer minus2. So five pairs of -2 is obtained.

[00:03:10]So 5 into -2 gives you -10. The first solving technique helps you solve aptitude quickly.

[00:03:20]Anything with a real life application seems interesting, right? So here we go with the real life application. Climb eight steps up and then go three steps down. Look at the picture from the ground level. So what happened? Climb eight steps up. So up is a positive word and with the rule of integers we get plus eight steps went three steps down.

[00:03:44]So from eight steps he has gone three steps down. So down is a negative word and it represents -3 steps. So the net steps will be or where he will land is + 8 plus of -3. So one positive and one negative. So he'll be landing in the fifth step applying the rule of difference sign. So difference sign subtract the numbers and put the greater number sign. So he'll be five steps above the ground level. This is how you apply grouping of numbers in real life applications.

[00:04:23]So let's recap today's session. So what did we learn about the grouping of numbers under addition? So rearranging numbers or terms to make the calculations easier without changing the sum. The key idea behind is grouping does not change the sum. The two properties used where commutative property and associative property.

[00:04:43]Commutative property deals with two numbers whereas associative property deals with three numbers. How to group smartly? You will look at the positive and negative numbers. Make pairs wisely and then combine and solve step by step.

[00:04:58]I have also discussed the real life example using a ladder problem negative and positive words applying the rules of integers. So the takeaway is you can rearrange numbers in any order but the final result will always remain the same. Group smartly, calculate easily, answer remains the same. Hope this video was useful and informative. Thanks for watching. Grouping saves time and reduces error. Solve this using grouping. Comment your answer in the comment section below. Like, share and subscribe at the math routt. Thank you.

[00:05:29]See you in the next video.