Could someone help me explain how to do this sum? (6 is 2/3 of ?)

[TizzyDongue]

DS 10, up to this year he had a difficult time at school (academically) which resulted in a lot of anxiety.

We changed school this year and things have improved no end, and a happy and confident boy is emerging. But we do come up against things now and again with homework which cause a bit of a wobble.

The question is 'What is 6 2/3 of'.

Now I know the answer but I want to be able explain it simply to him - he's not done it in class the year (highly possible it was covered earlier years and he missed out).

Could someone explain the method used to work this out please? I don't want to tell him my way in case its not the way.

Is it the number (6) divided by the numerator, then multiplied by the dominator?

If two thirds is 6 then what is one third? "3"

And how many thirds in a whole? "3"

So three lots of three would make the whole number "9"

To be honest it's a confusing question I think. Could you use a visual aid like pennies to help?

Divide 6 by two and then multiply by three

Divide 6 by 2 (or whatever upper figure you have)

Multiply the result by 3 (or whatever lower figure you have)

I would add I would try not to teach that it's divide by numerator, multiply by denominator purely because that doesn't teach for understanding, like what is actually going on. And it could lead to confusion when asked to find 2/3 of a number (in which case u would have to do the opposite- divide by denominator and multiply by numerator)

holy crap I got the answer totally wrong until I read all your replies..I hated math at school & still can't do it, I just have a blank with it, I hope my dd asks her dad (maths wizard) when she gets to needing help with homework

Hmmm I would say ok, we have to find the 'destination' number, how do we do that? Let's divide 3 by 2 which gives 1.5 we then multiple by 6 to get 9 (the answer).

To proof this let's make 9 dots and number them 1-9, group the dots in to chunks of 3 (our denominator) and then add up two (our numerator) of these chunks. What does that give you? Our original 6!

Sorry, not that great at explaining with out pen and paper

Thanks.

No I wont use any technical wording, I will do it visually.

I'd do it as an equation.

6=? X 2/3

Then do the same to both sides (multiply by 3, then divide by 2). But not sure if that is appropriate for a 10 year old.

6=? X 2/3
18=?X2
?=9

If 6 is two thirds then you divide by two to find one third.

Then multiply by three to find 3 thirds or one whole.

(9 btw)

I would say that as 6 is 2/3, you first need to find half of 6, because that will tell you what 1/3 is. So you could do that visually with 6 pennies (or apples, pencils, whatever) split the pennies to make 2 groups of 3 pennies. So 1/3 is 3 and 2/3 is 6, if you add another third to make 3/3, what number do you get? Then you could add another three pennies to make 3 groups of 3 and then count them to make 9.

No idea if that is the "correct" way, but it is the most logical way to me.

As last poster

Find 1/3(divide by 2), then 3/3(x3)

The equation method is more yr9 up

Draw a circle. Mark it as near as you can into thirds. Get six counters. Put three in one third and 3 in another third. Show him that there are three in one third, six in 2 thirds. As how many there would be in 3 thirds.
Try it with circles divided into halves or quarters. Start by putting the counters on then move on to giving him the counters to put on himself so that they are equal in the fractions you specify. So if you give him six counters and tell him that is three quarters, he needs to put two on each of three of the quarters. Move on to him seeing he is dividing by the numerator (top number) and multiplying by the denominator. (bottom number).