Discover Mathematics P4: Term 1, Unit 2, Lessons 1–4
GoalUse the commutative, associative and identity properties of addition to add faster.
New words
commutative property · numbers can be added in any order: a + b = b + aassociative property · we can group the addends in different ways and the sum stays the sameidentity property · adding 0 to a number does not change itsum · the answer to an addition
Explanation
Addition has three useful rules. The commutative property says that changing the order does not change the sum: 47 + 86 = 86 + 47. The associative property says that changing the grouping does not change the sum: (36 + 14) + 27 = 36 + (14 + 27). The parentheses show what we add first. The identity property says that adding zero leaves a number the same: 4,380,000 + 0 = 4,380,000. We can use these rules to make a sum easy. Look for two numbers that make a round number such as 10, 100 or 1,000, add them first, and then add the last number. For example 25 + 68 + 75 is easy when we add 25 + 75 = 100 first.
Property
Example
Commutative
47 + 86 = 86 + 47
Associative
(36 + 14) + 27 = 36 + (14 + 27)
Identity
4,380,000 + 0 = 4,380,000
Worked examples
Karim adds 47 + 86 and gets 133. Salma adds 86 + 47. The order is different, but 86 + 47 is also 133. The commutative property tells us that both sums must be the same.
Grouping
Steps
Sum
(36 + 14) + 27
50 + 27
77
36 + (14 + 27)
36 + 41
77
Add (36 + 14) + 27. First 36 + 14 = 50. Then 50 + 27 = 77. Now group the other way: 36 + (14 + 27). First 14 + 27 = 41, then 36 + 41 = 77. Both groupings give 77, and the first one was easier because 36 + 14 made a ten.
Easy pair
Then
Sum
25 + 75 = 100
100 + 68
168
1,300 + 700 = 2,000
2,000 + 450
2,450
Add 25 + 68 + 75 in your head. Swap the order: 25 + 75 + 68. Then 25 + 75 = 100 and 100 + 68 = 168. Another one: 1,300 + 450 + 700 = (1,300 + 700) + 450 = 2,000 + 450 = 2,450.
Class activity
Easy pairs hunt. Write six numbers on paper, such as 35, 90, 65, 120, 10 and 80. Find pairs that make 100. Add the pairs first, then add what is left. Try to find the total in less than a minute, and then check it by adding in a different order.
Practice
1
Write the missing number: 58 + 42 = 42 + __.
58 (commutative property).
2
Add by making a hundred first: 64 + 38 + 36.
64 + 36 = 100, and 100 + 38 = 138.
3
What is 9,050,000 + 0? Which property helps?
9,050,000 (identity property).
4
Add 125 + 240 + 875 + 60 in your head.
125 + 875 = 1,000 and 240 + 60 = 300, so the sum is 1,300.
5
Mina says (8 + 5) + 2 = 8 + (5 + 2) but they give different sums. Is he right?
No. Both are 15. Changing the grouping does not change the sum (associative property).
