Help....... I used to be good at maths, but my daughter has stumped me with this one:
x = 0.436 (with the 3 and 6 being recurring)
Prove algebraically that x can be written as 24/55
I might post some others.....working through them right now.
24 divided by 55 equals 0.43636363 which equals x therefore x equals 24/55?
Tegwin, I don't think that counts as an "algebraic proof"
Surely it can't be as simple as that, I think there needs to be some algebra in there somehow.
What a strange question.....
let x=0.436 recurring
multiply both side by 10 gives
10x= 4.36 recurring
multiply both side by 1000 gives
1000x= 436.36 recurring
therefore (1000x - 10x) = 436.36r -4.36r (this gets rid of the recurring decimal)
This gives
990x = 436-4
990x = 432
rearranging gives
x = 432/990
simplifies to
x= 24/55
24/55=0.436=x
24=0.436*55=55X
24= 23.98 = 55x
23.98/24 = 55X/24
23.98/4 CANCELS DOWN TO 1 (OR WOULD OF IF I HAD A PROPER CALCULATOR WITH RECURRING FUNCTION)
LEAVING 55X/24
REARANGED X =24/55
[Edited on 22/1/19 by wylliezx9r]
Nice, you boys are cleverer than you look. I think Liams' solution is right, I would not have come up with that.
What a great forum this is. Thanks both.
If you had asked this question 50 years ago I would have worked it out in my head.
What was the question?
I have similar difficulties helping my kids with their maths homework.
I didn't find maths difficult at school, but age has bitten and my brain power isn't what it used to be.
the answer is 42
How old is your daughter, that problem is far too difficult for GCSE. A-level maybe.
quote:
Originally posted by rusty nuts
If you had asked this question 50 years ago I would have worked it out in my head.
What was the question?
quote:
Originally posted by Slater
Nice, you boys are cleverer than you look. I think Liams' solution is right, I would not have come up with that.
What a great forum this is. Thanks both.
quote:
Originally posted by nick205
I have similar difficulties helping my kids with their maths homework.
I didn't find maths difficult at school, but age has bitten and my brain power isn't what it used to be.
quote:
Originally posted by wylliezx9r
quote:
Originally posted by Slater
Nice, you boys are cleverer than you look. I think Liams' solution is right, I would not have come up with that.
What a great forum this is. Thanks both.
I think you'll find both solutions are correct but just done in different ways. I haven't been able to show all the working with my method - it's very difficult to show the cross cancellation and re-arrangement but its very basic algebra probably A-level.
Im with Mr Whippy,
42
42 Spot on :-)
Hi, daughter is 15, doing GCSE Maths level 1. I took Maths O level age 15 and somehow got an A, but that question stumped me.
She says a big thank you to Liam, and that Mr Whippy must be a fool.
Obviously too young for HHGTTG.
I knew that maths degree would come in handy........one day
quote:
Originally posted by Angel Acevedo
quote:
Originally posted by rusty nuts
If you had asked this question 50 years ago I would have worked it out in my head.
What was the question?
No wonder there´s "rusty" on your forum name...
50 years ago I´d have mumbled "gu-gu-da-da"
quote:
Originally posted by Slater
Help....... I used to be good at maths, but my daughter has stumped me with this one:
x = 0.436 (with the 3 and 6 being recurring)
Prove algebraically that x can be written as 24/55
I might post some others.....working through them right now.
Was just helping my lad revise for his gcse, and recurring numbers came up, and I actually remembered this thread from 6 years ago! Crazy. Didn't help me solve it to be honest though. I did my maths gcse when I was 11, and I swear these things didn't come up.
With the prompt:
x = 0.436 (with the 3 and 6 being recurring)
Prove algebraically that x can be written as 24/55
ChatGPT gives:
To prove that x = 0.4363636... (where the digits 3 and 6 repeat can be written as 24/55 algebraically, let’s set up the problem and solve it
step-by-step.
1. Let x = 0.4363636...
2. Since the repeating part is "36," we’ll separate this into two parts: the non-repeating "4" and the repeating
"36."
3. Let x = 0.4 + 0.0363636...
4. Now let y = 0.0363636... , which is the repeating decimal part.
Then, we can write x = 0.4 + y
5. To express y as a fraction, set y = 0.0363636...
6. Multiply y by 100 (since "36" has two digits:
100y = 3.6363636...
7. Now, subtract y = 0.0363636... from 100y = 3.6363636... to eliminate the repeating decimal:
100y - y = 3.6363636... - 0.0363636...
99y = 3.6
8. Solve for y :
y = 3.6/99 = 36/990 = 4/110 = 2/55
9. Substitute y = 2/55 back into x = 0.4 + y :
x = 0.4 + 2/55
10. Rewrite 0.4 as a fraction:
0.4 = 4/10 = 22/55
11. Therefore:
x = 22/55 + 2/55 = 24/55
So, we have shown algebraically that: x = 24/55
[Edited on 29/10/24 by Rod Ends]
[Edited on 29/10/24 by Rod Ends]
I see questions like this and think... "I wonder what's on the TV".
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OU maths
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