Properties Of Addition And Subtraction

Student can apply properties like closure and commutativity to addition, and identify why subtraction lacks them.

4 lessons

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Concept

Mental Addition Tricks

Hook showing how grouping numbers makes addition faster.

Try to add $469 + 35 + 5 + 31$ quickly in your head.

Instead of reading left-to-right, try rearranging the numbers like this: $(469 + 31) + (35 + 5)$ .

Suddenly, the math is just $500 + 40 = 540$ ! This mental shortcut works because of the properties of addition.

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Whole Number Properties Breakdown

Grid comparing closure, commutative, and zero properties for + and -.

Addition Properties

Closure

Adding two whole numbers gives a whole number.

3 + 8 = 11

Commutative

Changing the order does not change the sum.

23 + 18 = 18 + 23

Associative

Changing the grouping does not change the sum.

11 + (18 + 25) = (11 + 18) + 25

Identity

Adding zero leaves the number unchanged.

7 + 0 = 7

Subtraction Properties

Not Closed

Subtracting whole numbers may not give a whole number.

4 - 5

is not a whole number

Not Commutative

Changing the order can change the answer.

5 - 4 \neq = 4 - 5

Not Associative

Changing the grouping can change the answer.

6 - (4 - 2) \neq = (6 - 4) - 2

Zero Property

Subtracting zero keeps the number same. A number minus itself is zero.

5 - 0 = 5

5 - 5 = 0

Main idea: addition is flexible, but subtraction depends on order.

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Property Matching

Fill missing values based on equality properties.

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The properties of addition allow us to change the order and grouping of addends without changing the final sum. This principle is very useful for simplifying numerical expressions involving brackets.

Let us balance the specific equation from the worksheet: $(200 + 1020) + 3303 =$ $+ (200 +$ $)$ .

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Subtraction Inverse Check

Subtract and verify via addition.

Subtract 75691 - 45512 and check your answer using the inverse operation.

Subtraction and addition are inverse operations.

Calculate:

$75691 - 45512$

Then check your answer using addition.

Step 1: Subtract*

Find the difference.

Step 2: Use the inverse operation*

Subtraction can be checked using addition.

Step 3: Check by adding*

Add your answer back to 45512.

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