100 × 2 700 = .........................
- Write a rule for multiplying any number by 100:
Does your rule “work” for 0,2 × 100?
Activity 7:
To recognise and use the characteristics of multiplication with whole numbers [lo 1.12.3]
1. In our previous module we looked at the associative and commutative characteristics of addition – do you remember this? There are similar characteristics of multiplication. Do you want to know how it works? Fill in the missing factors to balance the equasions:
8 x 6 = 6 x ____
23 x ____ = 13 x 23
124 x 85 = ____ x 124
2. Is the following true or false?
2.1 6 × 3 × 4 = 3 × 4 × 6 = 4 × 6 × 3 ..................................................
2.2 (2 × 4) × 5 = (5 × 4) × 2 = 4 × (2 × 5) ..................................................
3. What do you realise from the above examples?
Activity 8:
To estimate and calculate by means of rounding off [lo 1.8.1]
1. To be able to estimate answers is an important skill. If you are good at estimating, it will be easier for you to realise that you may have made a mistake in your calculations. Round off the following numbers first and in this way you will be able to estimate what the product of each of the following will be:
SUM | ESTIMATE | CALCULATOR | DIFFERENCE |
E.g. 19 × 21 | 400 | 399 | 1 |
a) 38 × 27 | ......................... | ......................... | ......................... |
b) 99 × 146 | ......................... | ......................... | ......................... |
c) 45 × 69 | ......................... | ......................... | ......................... |
d) 998 × 78 | ......................... | ......................... | ......................... |
e) 409 × 18 | ......................... | ......................... | ......................... |
BRAIN-TEASERS!
a) Which two numbers, smaller than 10, have 3 factors each?
......................... and .........................
b) Colour in the correct block:
The product of 2 uneven numbers is always an | EVEN | UNEVEN | number. |
c) Which two numbers have a product of 48 and a sum of 16?
......................... and .........................
Activity 9 :
- To be able to solve problems in context [LO 1.6.1]
- To be able to use a series of techniques to do calculations [LO 1.10]
Let’s do some brainstorming now. Your teacher will give you the necessary paper.
1. Split up into groups of three and, as quickly as possible, make a list of all the means of transportation that exist in our country.
2. Which of the above-mentioned would you choose if you had to travel? Why?
3. Where is your favourite seat in:
- a car
- a school bus
- a boat
- an aeroplane
4. Now see whether you are able to solve the following problems:
Messrs Slobo, Mugathle and Sisula have each bought a brand new taxi with which to transport passengers. For their first trip their plans are the following:
Owner | Amount per person | Number of passengers | km travelled |
Slobo | R15,80 | 13 | 76 |
Mugathle | R14,60 | 14 | 84 |
Sisula | R16,25 | 12 | 59 |
- Who made the most money with the first trip?
- If the petrol cost R1,05 for every kilometre that was travelled, how much did Mr Mugathle’s petrol account come to?
- If all the passengers in Mr Slobo’s taxi were athletes and they had to run back, how far did they run altogether?
- Explain to the rest of the class how your group calculated the answers.
- Compare your methods. How do your methods differ?
- Check the answers, using a pocket calculator.