22 May, 2012 at 15:05 #1656
Count in 6’s: 6, 12, 18, 24, 30, 36, 42, …
Then count in 9’s: 9, 18, 27, 36, 45, …
Learners need lots and lots of practice in counting like this until they know all the multiples of 1 to 10 up to 12 times each number.
Can you see now that the smallest number that is in BOTH of the 2 lists above is the Least Common Multiple of 6 and 9?
23 May, 2012 at 05:15 #1658
Zet Zet ZozoParticipant
Common factor is the issue in this approach. It means simplify your answer after the process if it is necessary.
N1 for numerator one and D1 for denominator One. N1/D1 + N2/D2 – N3/D3 =(N1.D2.D3 +N2.D1.D3 – N3.D1.D2)Ã· D1.D2.D3. Example 1: 5/6 + 4/9 = (5×9 + 4×6)Ã·(6×9) =69/54 then simplify the fraction, it means your answer is 23/18. Example 2: 13/5 +23/6 – 9/7 = (13.6.7 +23.5.7 – 9.6.5)Ã·(5.6.7) =(546 +805 -270)Ã·210 = 1081/210 this fraction simple.
23 May, 2012 at 08:51 #1661
Zet Zet is giving a method but he is not answering the question which was about least common multiples.
We must avoid teaching a rule or a method when the learners do not understand why the method works.
Learners find fractions difficult because their teacher has only told them the rules and not taught them so that they can understand what they are doing.
Ntombonzi is right.
To understand addition of fractions you need to understand that the fractions are expressed as equivalent fractions with the SAME denominator. The most efficient way is to use the smallest denominator and not to multiply all the denominators together.
So in Ntombonzi’s example use 36 as the common denominator not 54. The fractions are then 30/36 and 16/36 adding up to 46/36 which simplifies to 23/18.
Zet Zet’s method is not the best method because it does not use the least common multiple. Zet Zet’s rule is not the most efficient method. This may not matter when the fractions are just numbers but the process may be dauntingly complicated when it is applied to algebraic fractions.
26 May, 2012 at 17:32 #1672
The problem that I encounter with addition of fractions is that the learners have a difficulty in finding the common factor especially with algebraic fractions
28 May, 2012 at 09:56 #1674
I find it helpful when teaching algebraic fractions,to start off by revising addition of numerical fractions.This reminds the learners of how to find a common denominator before adding the fractions.You can then move on to trying addition of algebraic fractions with numerical denominators. Once they have an understanding of the process involved they should then be able to progress to more complicated algebraic fractions.See the attachment for the sort of examples i would use to help them to understand what they are doing.Hope you find this helpful.
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