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Common and decimal fractions

Common fractions

Educator section



The learning programme for grade six consists of five modules:

1. Number concept, Addition and Subtraction

2. Multiplication and Division

3. Fractions and Decimal fractions

4. Measurement and Time

5. Geometry; Data handling and Probability

  • It is important that educators complete the modules in the above sequence, as the learners will require the knowledge and skills acquired through a previous module to be able to do the work in any subsequent module.



  • This module continues the work dealt with in grade 5. Addition and subtraction of fractions are extended and calculation of a fraction of a particular amount is revised.
  • Check whether the learners know the correct terminology and are able to use the correct strategies for doing the above correctly.
  • Critical outcome 5 (Communicating effectively by using visual, symbolic and /or language skills in a variety of ways) is addressed.
  • It should be possible to work through the module in 3 weeks.
  • ** Activity 17 is designed as a portfolio task. It is a very simple task, but learners should do it neatly and accurately. They must be informed in advance of how the educator will be assessing the work.
  • This module extends the work that was done in grade 5. Learners should be able to do rounding of decimal fractions to the nearest tenth, hundredth and thousandth. Emphasise the use of the correct method (vertical) for addition and subtraction. Also spend sufficient time on the multiplication and division of decimal fractions.
  • As learners usually have difficulty with the latter, you could allow 3 to 4 weeks for this section of the work.
  • ** Activity 19 is a task for the portfolio. The assignment is fairly simple, but learners should complete it neatly and accurately. They must be informed in advance of how the educator will be assessing the work.

1.1 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}

1.2 13 20 size 12{ { { size 8{"13"} } over { size 8{"20"} } } } {}

1.3 5 8 size 12{ { { size 8{5} } over { size 8{8} } } } {}

1.4 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}

Leaner section


Activity: to recognise equivalent forms of numbers to recognise equivalent forms of numbers [lo 1.5.1]

If you know how to simplify and to apply it correctly, you will soon realise that it is a helpful aid when calculating with fractions. It can help you multiply, divide, add and subtract more easily (and quickly). You will also find it easier to fill in relationship signs. Let’s have a look at how you manage.

1. Simplify the following:

1.1 10 15 size 12{ { {"10"} over {"15"} } } {}

1.2 26 40 size 12{ { {"26"} over {"40"} } } {}

1.3 45 72 size 12{ { {"45"} over {"72"} } } {}

1.4 42 63 size 12{ { {"42"} over {"63"} } } {}


You'll need a partner and two dice.

  • Roll both dice and write the numbers that are on top as a proper fraction.
  • Simplify the fraction, if this is possible.
  • Your friend has to do the same.
  • Decide whose fraction is larger.
  • The one with the larger fraction claims 2 points.
  • The winner is the one who gains the most points!

Do you remember this?

When we wish to do addition with fractions, the denominators have to be made similar.

Eg. 1 3 size 12{ { {1} over {3} } } {} + 3 6 size 12{ { {3} over {6} } } {}

1 3 size 12{ { {1} over {3} } } {} = 2 6 size 12{ { {2} over {6} } } {}

( 2 6 ) size 12{ \( { {2} over {6} } \) } {} 1 3 size 12{ { {1} over {3} } } {} + 3 6 size 12{ { {3} over {6} } } {} = 5 6 size 12{ { {5} over {6} } } {}

What you know about determining equivalent fractions will be useful when you do this.

Note the following!

When the sum of two fractions is calculated, only the numerators are added together. The denominator is retained as it is.

Also remember!

If the answer is an improper fraction, you have to convert it to a mixed number.


Learning Outcome 1: Die leerder is in staat om getalle en die verwantskappe daarvan te herken, te beskryf en voor te stel, en om tydens probleemoplossing bevoeg en met selfvertroue te tel, te skat, te bereken en te kontroleer.

Assessment Standard 1.5: We know this when the learner recognises and uses equivalent forms of the numbers listed above, including:

1.5.1 common fractions with 1-digit or 2-digit denominators.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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what is nano technology
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preparation of nanomaterial
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
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what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 6. OpenStax CNX. Sep 10, 2009 Download for free at http://cnx.org/content/col11030/1.1
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