Quickie maths question....(13 Posts)
What is 3/5 + 1/2 ?
and how is it worked out?
Cheers....ashamed of my maths ability!
Change them both into 10ths
then add them together
6/10+5/10= 11/10 (improper fraction ) or 1 and 1/10 (mixed numebr)
3/5 = 6/10
6/10 + 5/10 =11/10
Yes, find the lowest common denominator, which is tenths, because 10 is a multiple of both of the numbers at the bottom of the fraction (5 and 2).
Change so they have same denominator,so
6/10 and 5/10
So it would be 11/10 or
Start with thinking about the denominators
5 & 2 - what number is a factor of both of these numbers (which are prime numbers by the way).
you should get 10
so for 3/5th - you need to multiply 5 by 2 to get 10
so the rule is with multiplying you must do the same to the numerator (number above the line - or upper number) as the denominator (number below the line or lower number)
so you will also need to multiply 3 by 2
so you should get 3/5th = 6/ 10th
now with 1/2 do the same thing:
multiply denominator by 5 and numerator by 5 (remembering 5/5 = 1)
so 1/2 = 5/ 10ths.
Now you can add the two fractions to 10th together
so 6/10th + 5/ 10ths = 11/ 10 (tenths)
Now 10 can go into 11 once with a remainder of 1
So you can write the fraction as 1 (effectively = 10/10) & 1/10
The above are all good ways of solving the problem, Doowrah, but, if you are trying to get a child to understand how it works rather than just learning a procedure, why not represent the problem in concrete terms.
If you draw an orange (a circle) and divide it into five equal parts and shade three of them, you can see immediately how much of the 'orange' three fifths is - self evidently, more than half. If you now divide all the fifths in half, you'll see that the shaded three fifths is six tenths. Now take another 'orange' and split it into two halves. Again divide the halves into tenths, which shows graphically that there are five tenths in a half.
With each circle sitting side by side, you can see that five tenths plus six tenths makes eleven tenths. As there are (you can see this from your circles divided into tenths) ten tenths in one whole 'orange', you have one whole 'orange' plus one tenth of an 'orange'.
Learning how to do things in maths procedurally will, if you follow the correct procedures, give you the right answers to questions. The problem is that not everyone understands how and why we use the procedures and then they can't apply their knowledge to other similar problems. So, you should always teach conceptual understanding with the procedures.
surely if they are adding these fractions, they have already done the pizza slices?
"surely if they are adding these fractions, they have already done the pizza slices?"
You would hope so, Sausagesandwich, but it's worth remembering that conceptual understanding grows with the presentation of mathematical as well as other problems in different concrete forms repeatedly. Concepts learned in one context may not have been learned sufficiently for them to be applied in another.
As Vivian Paley put it: "The adult should not underestimate the young child's tendency to revert to earlier thinking: new concepts have not been 'learned' but are only in temporary custody. They are glimpsed and tried out but are not in permanent possession."
Paley, V.G., (1981) Wally's Stories, London, Harvard University Press.
For your own understanding try Khan Academy www.khanacademy.org/math/arithmetic/fractions
It's really good and he explains it really well.
The most important concept in the teaching of fractions is that of equivalent fractions. This is not a topic that should be taught in isolation, but a fundamental concept on which virtually all fraction work is based.
Beginning with a fraction such as 30/40 we can cancel the fraction by any common factor of 30 and 40 such as 5, so 30/40 = 6/8. We can then cancel by 2 to get 3/4. Of course we could go straight from 30/40 to 3/4 by cancelling by 10. There are two important facts to understand: a) whichever way we wish to cancel, the answer will always come to the same in the end (in this case 3/4), and b) cancelling is not the same as dividing since dividing actually changes the value of the fraction. Cancelling keeps the value the same but the numerator (top number) and the denominator (bottom number) are changed.
The opposite of cancelling is lecnacing (reverse the letters of cancel to indicate the reverse process). So we can lecnac 30/40 by 2 to get 60/80 or lecnac 30/40 by 7 to get 210/280 etc.
All the fractions we have so far obtained (3/4, 6/8, 30/40, 60/80 and 210/280) are EQUIVALENT FRACTIONS, i.e. fractions which look different, but actually have the same value.
By continuing to cancel and lecnac fractions by different numbers we could obtain a chain of an infinite number of fractions, all of which are equivalent to all the others in the chain. This concept really needs to be understood before fractions are added, subtracted, multiplied or divided.
Now we can see why the explanations others have given above work:
Lecnac 3/5 by 2 to get 6/10 and lecnac 1/2 by 5 to get 6/10 and the rest is easy. Notice by the way that when we say 11/10 = 1 1/10, we are using the fact that 10/10 is EQUIVALENT to 1/1, i.e just 1 (One whole one, that is).
Hope this helps.
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