Ben thinks of a number - he adds half of the number to a quarter of the number the result is 60 what was the number

[LardLizard]

Ok, I realise the answer is 80, but how do I explain the process of working it out town right year old please

My child can work out similar questions with more info, such as ben thinks of a number multiplies by three then add 7 the answer is such and such, what is the number
My dc can do this be reversing the operation
Then double checking

But hasn't a clue where to start with. The above question

Please help, wise ones

Start by calling the number "x"

This is a great introduction to algebra.

Add 1/2 x to 1/4 x to make 3/4 x which you know is 60 so write that out in a maths way:

3/4 x = 60 (but set it out better with the 3 and the x on the same line etc)

Then divide both sides by 3 giving:

1/4 x = 20

Multiply both sides by 4: x = 20 x 4
= 80

What age if your child?

"is" not if

Split 60 into thirds. Each of these represent a quarter of the answer (half and a quarter). Add on another quarter (20) to make the whole number.?

Got something to do with realising that a half plus a quarter is three quarters, and then working out the whole by knowing that 3/4=60. Which makes sense to me, but I think I've explained it really badly.

A half and a quarter is three quarters in total.

So three quarters of the number is 60

So one quarter of the number is 20 ( a third of 60)

So four quarters ( ie the whole) is 4 x20 which is 80

It's fractions. Add half and a quarter gives you three quarters, which equals 60. If 60 is three quarters then one quarter is 60/3 - so then to get a whole you need to multiply that by 4.

Perhaps best to start with a question like if 3/4 is 15 what is the whole and then build up. X

0.25x + 0.5x = 60
0.75x = 60
X = 60 / 0.75
X = 80

60 = 1/2+1/4=3/4
60/3=1/4=20
4/4=20x4=80

My dc struggling with this is 8 years old

a bit random, but my lot seemed to get the hang of fractions and the like by applying it to cake or biscuits

so instead of saying X you say cake

so half a cake plus a quarter of a cake is 60 pieces so it'd be 80 pieces in a whole cake. :o

Trial and improvement.
Choose a number eg 100
Half of the number is 50
A quarter of the number is 25
50 add 25 = 75 too big
Need to try a smaller number. Keep going till you guess the right one.

Is this type of question usually aimed at 8 year olds ?

I usually find the 'cake' method described above very useful in teaching basic fractions.

So for this one, draw a big circle (cake) - that represents the number ben is thinking of. (the number is the number of slices the cake has)

He eats half the cake (shade half)
then he eats a quarter (shade a quarter)
He's eaten now eaten 60 slices

Sometimes easier then (until they get the hang of it) - to look at how the half is two quarters. - so he's eaten three quarters

if three quarters is 60 slices, how many in one quarter

then if one quarter is 20 slices, how many in four quarters (the whole cake).

Also works well using lego - 2-spud piece is a quarter, 4-spud piece is a half and so on

The maths isn't hard but I think the algebraic approach is hard for an 8 year old. My 9 year old hasn't tackled anything like this yet.

Pictures. Draw pictures.

You can get a number - show it in 4 bits - quarters.

Then - add 2 of the quarters to 1 of the quarters - you've got 3 'bits' which make 60.

What must each 'bit' be worth?

I do it by seeing the half and quarter as three chunks of equal size, then 60 divided by 3 is 20. So one chunk is 20. As one chunk is a quarter of the answer, 20 x 4 = 80.

One half plus one quarter makes three quarters. Make this clear by going over it with sketches of pies or cakes.

Three quarters in this case is 60. So One quarter is 60 ÷3. That's 20.

So the original, four quarters is 20 × 4 = 80.

Singapore maths is good for this - visualisation of abstract problems

www.bbc.co.uk/skillswise/0/24925787

Do simple examples where you know the number is a multiple of 2 and 4.

Start with 8. So DD, what is half of 8, what is quarter of 8. Let's add them... 4+2=6. OK, that's not the correct answer for the question.

Let's do 12. What is half of 12 and what's quarter of 12? Hmmmm, 6+3=9. Still not the winner.

Etc. Etc.

You don't have to do every single multiple of 2 and 4 either. Encourage her to skip a few because the answers are way too low and we know the answer needs to be 60.

If she's having trouble with fractions, use objects and separate into 2 groups and then 4 groups.

Just saw that honking said the same. This methid/approach is appropriate for an 8 year old. Umless she's capable, keep algebra for when she's older.

First get her to work out how many quarters one half is (2). Then count how many quarters she has (3). So 3 quarters is 60. Divide by 3 to find one quarter: 60÷3=20. Multiply by 4 (or just add 4 times) to get a whole: 20+20+20+20=80.