Math Is Fun Forum

What is the difference between, say, 10 and 2?

Seems obvious to me. 10-2=8. The difference is 8.

What is the difference between 2 and 10?

Seems obvious to me, at first, i.e, 8 again. But then I’m wondering why I shouldn’t be calculating 2-10=-8 this time, given that the 2 appears first in the question this time.

Q. Can you have a difference of -8? Can you have a difference of negative anything?

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When I Googled it I was pointed to the number line.

When I then wrote out the 1 to 10 section of the number line, and circled 2 and 10, it showed that there were 7 numbers in between them (3 4 5 6 7 8 9).

This puzzled me further.

Any thoughts?

I was asked to draw THE LOCUS OF ALL POINTS 3cm from a line.

I measured 3cm above and below the line, and drew two parallel lines there. Then drew two semi-circles with radii 3cm out from either end of the line to complete the locus, the shape(which Google tells me is a stadium).

But is the question imprecise?

Regards the lines above and below the line; shouldn’t it specify that the distance of 3cm is perpendicular?
There are many points 3cm from the line INSIDE THE STADIUM, no? (If you measure at an angle).
E.g. Draw a 3cm line perpendicular to the line, and north of the line. Then from the base of that line, draw another 3cm line at an angle of 45 degrees to the line. The point where this new line ends will be more than 1cm inside the stadium.

Doesn’t that mean that your original shape, your stadium, doesn’t actually cover THE LOCUS OF ALL POINTS 3CM FROM THE LINE?

Fearne invests £5600 in a savings account.
She gets 2% per annum compound interest.
After n years, Fearne has £6061.62 in her account.
Work out the value of n.

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I found finding the value of n one way straightforward. I put 5600 into my calculator, pressed equal then pressed ANS to store it. Then put the multiplier (1.02, for the 2% interest) next to ANS in brackets. Then pressed = repeatedly until I got my answer of 6061.62. As I had to press it 4 times this told me n=4.

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But before doing that I wrote out the following equation;
5600(1.02)^n=6061.62
(1.02)^n=6061.62/5600
(1.02)^n=1.082432143
1.02=nth root of 1.082432143
Nb; I wasn’t sure of this last step but it seemed to check out re;
2^2=4
Therefore;
Sqrt4=2
And then I substituted the 4 (from my first answer using the calculator) for the n and that checked out;
1.02=4th root of 1.082432143

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My question;

How do I get the nth root from the second method, once I’ve got to the stage;
1.02=nth root of 1.082432143 ?
Is there a way, other than putting the 5600 into the calculator and multiplying it by 1.02 repeatedly?

Why does the prime factors/Venn diagram system work for this?

Example.
Find the HCF of 42 and 56
Prime factors of 42; 2,3,7.
Prime factors of 56; 2,2,2,7.

The intersection of the Venn diagram contains 2 and 7, so the HCF is 14, which checks out when you use the simple method of listing all factors of 42 and 56 and look for the HCF that way.

But why does this work?

All I can glean from the 2 and the 7 in the intersection (imagining I didn’t know what the 2 original numbers were, that I didn’t know they were 42 and 56) is that both numbers must be at least 14; and that one of them must be at least 28.
They must be at least 14 because both have 2 and 7 as factors.
One must be at least 28 because its circle in the diagram must contain at least one other prime factor (beyond the intersection) and the lowest of these is 2.

But I can’t work out why the 2 and the 7 produce the HCF.