Maths

[Kiera]

my daughter is doing her maths homework. She has four 2`s ie 2,2,2,2 and she has to make sums to total 5,7,9 and 11. she can do the even numbers but is stuck with the odd numbers

eg (2x2x2)/2=4

Can anyone please help with the sums?

Kiera

[gen2]

2 + 2 + ( 2 / 2 ) = 5

[Kiera]

Excellent

Thank you very much.

Still need help with the other numbers as I cannot work them out myself either.

[gen2]

Is this a trick question?
If it has to total 5,7,9 and 11, then that comes to 32.
I can make 32 with the four 2's like this:

(( 2 x 2) ^ 2 ) x 2 = 4 squared x 2 = 32

[Kiera]

no this is not a trick question.

The sums are separate.

The sum that totals 5 is correct so she needs a similiar sum to total 7 then another sum to total 9 etc.  but using only four 2`s.

She has just told me she also has four 3`s and i am at the moment trying to work these out as well. if i get stuck I will have to ask for more help.

Thanks

Kiera

[GarryD39b]

2divided by 2 +2+2=5

[smouse]

Have you got to use all the 2s

22/2 = 11

[smouse]

(2 + 2/2) to the power 2 (ie squared) = 9

[kempie]

... which gives us the 9 =(22/2) -2

or does each 2 have to be treated separately i.e. you cannot have 22 as a number?

[gen2]

You don't say what operations we are allowed to use.
Suppose I could use a square root (sqr)
Suppose I could use a recurring decimal which would be written as .2 with a bar over the two, but since I cannot type that I shall write .2r

Then:

2 + 2 + sqr ( 2 / .2r ) = 7

[Kiera]

Thanks for the answers.

2 has to be treated separately.

It can be any operations but for a 12year old to understand, she cannot understand the recurring decimal but square root is fine.

The sum to the answer seven is fine but is too difficult.

Kiera

[Kiera]

sorry you also have to use all the 2`s

[gen2]

That's a pity because I had just made 11 by
2 + ( sqr ( 2 + 2 ) / .2r ) = 11

[Kiera]

Sorry about the recurring decimal.

the sum for the 11 sorry can not do it this way because no numbers allowed, only 4 2`s in the sum.

[ringer]

9 = (2/2 + 2)^2 where ^ means "to the power"

[smouse]

I certainly dont think its possible especially for a 12 year old

[gen2]

Does a 12 year old know about factorials?
If so then here is an answer for 11

(( 2 + 2 ) ! - 2 ) / 2 = 11

that is 4 factorial -2 all divided by 2

[Kiera]

No it is not a wind up. It is her maths homework.  I told perhaps it can`t be done so to tell the teacher she could not do it.  She said no, her teacher will be annoyed if the maths is not done.

[gen2]

Hi Kiera,
I have just been out for a pint (or 2) and mentioned your problem to a teacher.  He thinks that the homework may have been phrased as "CAN you make the following totals using four 2's".  Here in Scotland there is an emphasis on Problem Solving he he thought that your daughter's teacher may be looking for an appropriate method being applied, that is how your daughter approaches the solution.  i.e. With only even numbers, the only way of getting an odd number is to add or subtract 1 (obtained from 2/2) or to divide a number by 2.  She would then have to show that she could, or couldn't make the required target using the remaining 2's.
I hope this helps alleviate your daughter's worries about not being able to find a solution to all the target totals.