Addition and subtraction are inverse operations.
Addition is commutative. Is subtraction commutative?
Use an example to show your answer.
Multiplication and division are inverse operations.
Multiplication is commutative. Is division commutative?
Use an example to show your answer.
well a+b = b+a
but does a - b = b - a ?????
a * b = b*a
but
a/b is not b/a
Subtraction is not commutative. In terms of addition and subtraction being inverse operations, it means that adding a number and then subtracting the same number will give you the original number back. However, the order in which the subtraction is performed does matter.
Let's take an example to illustrate this:
Consider the numbers 5 and 3. If we add 5 and then subtract 3, we get:
(5 + 3) - 3 = 8 - 3 = 5
Now, let's reverse the order and subtract 3 first, and then add 5:
5 - (3 - 5) = 5 - (-2) = 5 + 2 = 7
As you can see, when we reversed the order of subtraction, we got a different result. Therefore, subtraction is not commutative.
Moving on to multiplication and division, multiplication is commutative, but division is not commutative. The concept of multiplication and division being inverse operations means that multiplying a number and then dividing by the same number will give you the original number back. However, similar to subtraction, the order in which the division is performed matters.
Let's use an example to demonstrate this:
Consider the numbers 6 and 2. If we multiply 6 and then divide by 2, we get:
(6 x 2) ÷ 2 = 12 ÷ 2 = 6
Now, let's reverse the order and divide by 2 first, and then multiply by 6:
6 ÷ (2 ÷ 6) = 6 ÷ (1/3) = 6 x 3 = 18
As you can see, when we reversed the order of division, we got a different result. Therefore, division is not commutative.