Learn that terms can be added in any order (Commutative) and grouped in any way (Associative) without changing the value.
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Formal term for swapping.
Introducing the commutative property of addition.
Imagine Madhu is flying a drone from a terrace. The drone goes up and then down.
We can write an expression for its height: .
Visualizing the swap and grouping properties solidifies abstract algebraic manipulation.
Adding terms in any order always results in the same final value.
Worked example showing swapping with three terms.
Problem. Evaluate the expression .
Faded practice utilizing swapping.
Let's evaluate the expression by swapping terms to make the math easier.
First, we rewrite all subtractions as additions of negative numbers: . Next, we use the commutative property to group the positive numbers together: .
Then, we group the negative numbers together: . Adding the positives gives , and adding the negatives gives .
Finally, adding these two sums together gives our final answer: .
MCQ identifying which expressions are equal via swapping.
Which of the following expressions does NOT have the same value as ?
Introducing the associative property of addition.
Just like swapping the order of terms doesn't change their value, grouping does not change the sum.
In mathematics, this is called the associative property of addition. Whether you add the first two terms together first, or the last two terms together first, you will get the exact same result.