3. Now let us see what happens when we divide any number by 0. Work with a friend once more and do the following with the aid of your calculator:
3.1 6 ÷ 0 = ................................... 3.2 38 ÷ 0 = ..............................
3.3 438 ÷ 0 = ............................... 3.4 1 679 ÷ 0 = .........................
- 63 827 ÷ 0 = .........................
4. Why does the calculator give these answers?
DO YOU STILL REMEMBER?
Division by 0 is not allowed. We say it is undefined .
BRAIN-TEASER!
I think of a number. If I subtract 3 and then divide the number by 6, the quotient will be 7. What is the number? ..................
I think of another number. If I halve it and then divide it by 12, the quotient will be 9. What is the number? ..................
Activity 4:
To describe and illustrate other cultures' ways of writing [lo 1.2]
DID YOU KNOW?
The Chinese write either from top to bottom or from left to right. Some of their numbers look like these:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
100.
1.1 Can you write the following in Chinese? Then give the answer in our number system.
| a) | 10 ÷ 1 = | |
| b) | 100 ÷ 10 = | |
| c) | 9 ÷ 3 = | |
| d) | 100 ÷ 4 = | |
| e) | 100 ÷ 5 = | |
| f) | 100 ÷ 7 = |
Division by 10, 100 and 1 000
Activity 5:
To describe observed patterns and rules in own terms [lo 2.2]
1. In Mathematics certain rules enable us to calculate answers quickly. However, we must be able to "spot" or "deduce" the rule first before we can apply it. Work with a friend and complete the table.
| Number | 20 | 50 | 90 | 120 | 360 | 1 470 | 2 560 | 14 380 | 26 520 |
| ÷ 10 | ............ | ............ | ............ | ............ | ............ | ............ | ............ | ............ | ............ |
What do you notice when you look at the answer?
2. Complete the following also:
| Number | 300 | 800 | 1 200 | 2 600 | 14 700 | 32 500 |
| ÷ 100 | ................. | ................. | ................. | ................. | ................. | ................. |
Can you also write down the answers to the following?
3. Can you also write down the answers to the following?
| Number | 5 000 | 7 000 | 13 000 | 45 000 | 126 000 | 382 000 |
| ÷ 1 000 | .................. | .................. | .................. | .................. | .................. | .................. |
What happens when we divide by 1 000?
Division by multiples of 10 and 100:
Activity 6:
To calculate by using selected computations [lo 1.8.4]
1. You have now discovered rules for division by 10, 100 and 1 000. Now let us look at division by multiples of 10 and 100. Work through the following calculations with a friend:
| 1.1 180 ÷ 20 = (180 ÷ 10) ÷ 2 = 18 ÷ 2 = 9 | 1.2 4 200 ÷ 60 = (4 200 ÷ 10) ÷ 6 = 420 ÷ 6 = 70 |
| 1.3 3 600 ÷ 400 = (3 600 ÷ 100) ÷ 4 = 36 ÷ 4 = 9 | 1.4 54 000 ÷ 900 = (54 000 ÷ 100) ÷ 9 = 540 ÷ 9 = 60 |
2. Complete the following on your own:
2.1 1 380 ÷ 60 = (1 380 ÷ 10) ÷ ..................
= .................. ÷ ..................
= ..................
2.2 32 840 ÷ 40 = (32 840 ÷ ..................) ÷ ..................
= ......................... ÷ ..................
= ..................
2.3 15 500 ÷ 500 = (15 500 ÷ 100) ÷ ..................
= .................. ÷ ..................
= ..................
2.4 312 300 ÷ 300 = (312 300 ÷ ..................) ÷ ..................