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Examples of methods:

  • 7 × 18

Estimation: 7 × 20 = 140; the answer is about 140

7 × 10 + 7 × 8 i.e. 7 times all of 18

Other ways of finding the exact answer:

or: 18 + 18 + 18 + 18 + 18 +18 + 18

or: 7 × 20 - 14

There are other methods. Try to think of them.

  • 64 × 35

i.e. all of 64 × all of 35

Estimation: 60 × 40 =2 400

60 × 30 = 1 800

60 × 5 = 300 i.e. add all answers

4 × 30 = 120

4 × 5 = 20

2 240

When you are really comfortable with this method, you can proceed to the old traditional vertical method. Don’t try to get there too quickly; more haste, less speed.

2. Word sums.

2.1 Share 54 Smarties equally amongst 9 friends. What does each one receive?

2.2 54 learners have to be transported to an Athletics Meeting. The coach wants to hire vehicles that may take 8 passengers. How many vehicles will be needed?

2.3 A shopkeeper has 106 apples. He puts them on little trays to sell them in his shop. There are 6 apples on each tray. How many trays can he fill?

Some methods:

  • 9 + 9 + 9 + 9 + 9 + 9 (How many 9’s in 54?)

or: 54  9

9 × ? = 54

There are other methods

  • 54  8

6 × 8 = 48; 6 rem. 6, but they are people who have to get to the athletics meeting.

7 × 8 = 56

7 vehicles will be needed and there will be 2 empty seats on one of them.

  • 106  6

10 × 6 = 60

5 × 6 = 30

2 × 6 = 12


17 trays rem. 4 apples (The key word here is “fill”.)

There are other ways. Discuss them with your friends and find the way that you understand best.

3. Calculate the answer. Write down the steps of your calculations, explaining (in numbers) how you reached your solution. Then write down the steps which you used to check that your answer is reasonable.

3.1 The mass of a van after it has been loaded is 2 500 kg. If the mass of the load is 500 kg, what is the mass of the van when it is empty?

3.2 The mass of one bag of cement is 25 kg. How many bags of cement will there be if the mass of the whole load is 500 kg?

3.3 The petrol tank of the van can hold 55 litres of petrol when it is full. The van needs one litre of petrol to travel 13 km. The driver fills his tank with petrol. How far can he travel before he needs to fill his tank again?

3.4 When the van is used for short trips around the town, it only travels 11 km per litre of petrol. The driver fills his petrol tank, which holds 55 litres of petrol. How many kilometres can it travel in the town?

3.5 Your school soccer team has to travel from Cape Town to Grahamstown to take part in a soccer tournament. Your team can go by bus along the coast, a distance of 899 km, or you can go by train via De Aar. The distance between Cape Town and De Aar is 762 km. From De Aar to Grahamstown is 444 km.

How much further will you travel if you go by train?

3.6 A special tour to the Kruger National Park is arranged for 134 tourists from overseas. At the rest camp 8 people can sleep in a rondavel. How many rondavels are needed for the tourists?

3.7 There is a tourist shop at the rest camp in the Kruger Park. In this shop special torches called Bush Baby Lanterns are sold. Seven tourists buy a torch each and together they pay R273 for them. How much does one Bush Baby Lantern cost?

Questions & Answers

What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Berger describes sociologists as concerned with
Mueller Reply
Read about ancient clocks like_ hour glass, water clock and sun dial for a quiz and hand on Activity in the class
Neha Reply

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Source:  OpenStax, Mathematics grade 4. OpenStax CNX. Sep 18, 2009 Download for free at http://cnx.org/content/col11101/1.1
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