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Commutative Property
Overview
Commutative Law may sound very scary, but it simply means that we can switch numbers in a situation and always end up with the same answer.
The commutative law applies to both addition and multiplication, but for this grade level we are only going to discuss how commutative law applies for addition problems.
Take a look at the following picture below.
We are given the addition problem 2 + 1 = 3
When we ADD 2 plus 1, we have 3 in all.
We say: TWO plus ONE equals THREE.
We write it like this: 2 + 1 = 3
HOWEVER, we can add the same groups in a different order too.
Instead of adding 2 + 1, we can add 1 + 2. We simply switched the numbers and it gives us the same answer.
2 + 1 = 3 and 1 + 2 = 3.
Each time, we get the same sum. This is the commutative law. We can add groups in any order and still get the correct sum.
Time for another example!
In this problem, we are joining together two groups of airplanes.
We are working with the problem 8 + 3 = 11
When we ADD 8 plus 3, we have 11 in all.
Let’s use the commutative law and switch the two numbers. Instead of 8 + 3, we will write 3 + 8.
Notice that 3 + 8 is also equal so 11.
That’s the commutative law in action! You can confidently switch numbers in addition problems and end up with the same answer.
Ready to try another problem?
In this problem, we are joining together two groups of diamonds.
We are working with the problem 9 + 4 = 13
When we ADD 9 plus 4, we have 13 in all.
We can also add the groups like this:
4 + 9 = 13
We know that we can add the groups in any order and the sum is still the same!
9 + 4 = 13 and 4 + 9 = 13
Let’s try a word-problem question before trying the practice questions.
In the problem, the pencils are being joined together. The key words are AND as well as ALTOGETHER. This helps tell us that we need to ADD.
ONE yellow pencil is joined with THREE orange pencils and this will give us the correct SUM.
1 + 3 = 4 pencils
We can also add the groups like this: 3 + 1 = 4 pencils
We get the same sum both times because we can add the groups in any order and will get the correct sum. This is the commutative law of addition.
You are officially an expert in understanding the commutative law!
Practice Question 1
Write the addition sentences and solve the problem below.
Count the apples to help find the correct sum!
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Practice Question 2
Write two addition sentences and solve.
Practice Question 3
Let’s try another! Write two addition sentences and solve.
TIP: Count the hearts to help find the correct sum!
Practice Question 4
Let’s try another! Write two addition sentences and solve.
TIP: Count the flowers to help find the correct sum!
Practice Question 5
Look at the groups below.
How many are there in all?
Write two addition sentences and solve.
The commutative law allows us to switch numbers in an addition problem and get the same answer. We can apply this law to make our life easier when adding numbers. For example, what does 10 + 42 equal? The fastest way to solve this problem is if we switch the two numbers and write what is 42 + 10 = ? All we need to do here is count up by 10 from the number 42, which would get us to the answer 52. Commutative law ROCKS!
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