Properties of AdditionCommutative

e.g. 4 + 2 = 2 + 4

We can picture this as follows:

1. Show that the answers for each of these questions are the samea) 10 + 13 + 7 + 9b) 13 + 9 + 7 + 10c) 7 + 10 + 9 + 13

2. Which of these sums will not have the same answer as the rest?a) 12 + 20 + 42 + 18b) 20 + 12 + 18 + 42c) 42 + 20 + 18 + 20d) 18 + 12 + 20 + 42

3. Fill in the gaps to make these statements true :

a) 22 + 11 + 9 + 3 = 11 + 9 + ___ + 22 = ___ + 11 + 3 + 22

b) 14 + 4 + 2 + 16 = 16 + 4 + 14 + ___ = 4 + 2 + 16 + ___

Does the same work for subtraction? Try it and see if you can find things that work.

Rearranging to make questions more manageable: You can use the associative property of addition to make questions much easier to handle. For example:

49 + 17 + 12 + 3 + 1 = (49 + 1) + (17 + 3) + 12 = 82.

See if you can solve these easily by rearranging:

4. 36 + 21 + 17 + 4 + 13

5. 83 + 18 + 6 + 27 + 14

6. 40 + 68 + 14 + 22 + 6

7. 402 + 205 + 66 + 2 + 15

8. 191 + 72 + 66 + 2 + 18 + 2

Summing Up!In this lesson, you’ll practice how to make addition and subtraction easier by breaking down numbers. It’s much easier to aim for ‘easy numbers’ such as the nearest ten, fifty, hundred, thousand etc rather than going straight for the ‘goal’.

Q: How much do I need to add to 42 to get to 180?

Step 1: Add 8 (to get to the nearest 10 – in this case 50 (five tens)). Step 2: Add 50 (to get to the nearest hundred)Step 3: Add 80 (to get to 180).

So in total, I added 8 + 50 + 80 – which is (80 + 20) + (30 + 8) = 138

Getting to 180 (useful for angles)

Getting to 360 (useful for angles and pie

charts)

b = 146o

next ten : +____

180: +____

TOTAL _____

a = 38o

next ten : +____

next hundred: +____

180: +____

TOTAL _____

b = 123o

next ten : +____

180: +____

TOTAL _____

b

a = 62o

next ten : +_8_

next hundred: +_30_

180: +_80_

TOTAL _____

a

a = 308o

next ten : +____

360: +____

TOTAL _____

a = 102o

next ten : +____

next hundred: +____

360: +____

TOTAL _____

Getting to 60 (useful for time)

Getting to 24 (useful for time)Find the amount of hours needed to get to midnight from each of the following:

to 13:30 : +_8 _

to nearest hour: +_30_

TOTAL _____

to next ten : +____

to next hour: +____

TOTAL _____

to next ten : +____

to next hour: +____

TOTAL _____

to next ten : +____

to next hour: +____

TOTAL _____

to next ten : +____

to next hour: +____

TOTAL _____

to next ten : +____

to next hour: +____

TOTAL _____

to 04:00 : +____

to 24:00: +____

TOTAL _____

to 14: 00 +____

to 24:00: +____

TOTAL _____

b = 53o

next ten : +____

next hundred: +____

360: +____

TOTAL _____

b = 76o

next ten : +____

next hundred: +____

360: +____

TOTAL _____