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Gcse maths: Direct and inverse proportions

Hi,

I'm trying to learn direct and inverse proportions for GCSE Maths, however I can't get my head around it, it confuses me so much. Can anyone help me with it or direct me to a website which can, I've tried mathswatch and it doesn't make sense. Please help its annoying me! Thanks.

Here's an example question.

DIRECT PROPORTION

The time, T seconds, it takes a water heater to boil is directly proportional to the mass of water, m kg, in the water heater.

When M = 250, then T = 400.

Find T when M = 300.
Firstly, always use the formula

T M

this can be put into the formula:

T = k x M

First off you need to find k. To do this:

- Substitute given figures into the formula

400 = k x 250

- Rearrange the formula so that you have k =

k = 400 / 250

- Work out the equation

k = 1.6

- Substitute k in:

T = 1.6 x M

- Substitute the figure given for M then work out the sum

T = 1.6 x 300

T = 480
Reply 2
Avatar for ChowSultan
ChowSultan
OP
Thanks, It took me 15 minutes to get my head around it, it's just the fact that K comes out of nowhere to me which made it confusing and all the formulas and rearranging, but its definitely helped thanks., but now there is Inverse proportion can you help me with this if you can please.

Example

The time, T seconds, it takes a water heater to boil is inversely proportional to the mass of water, m kg, in the water heater.

When M = 250, then T = 400.

Find T when M = 300.

(replaced direct with inversely if that still makes it valid?)
Reply 3
Avatar for Zen-Ali
Zen-Ali
8
Original post by ChowSultan
Thanks, It took me 15 minutes to get my head around it, it's just the fact that K comes out of nowhere to me which made it confusing and all the formulas and rearranging, but its definitely helped thanks., but now there is Inverse proportion can you help me with this if you can please.

Example

The time, T seconds, it takes a water heater to boil is inversely proportional to the mass of water, m kg, in the water heater.

When M = 250, then T = 400.

Find T when M = 300.

(replaced direct with inversely if that still makes it valid?)


kk is just a constant. Consider:

A A 02b6d397e015e480420f59701c1a1d26.png r2r^2   ⟹  A=πr2\implies A = \pi r^2

For inverse proportion...

tt 02b6d397e015e480420f59701c1a1d26.png 1m\dfrac{1}{m}   ⟹  t=km\implies t = \dfrac{k}{m}

Use the same method you used previously; rearrange to find kk, then use it.
(edited 10 years ago)
Original post by ChowSultan
can you help me with this if you can please.


Of course.

All right so for inverse proportion the formula is:

T 1/M

which can be:

T = k/M

- Again, find k: (which is always involved in proportion of this sort)

400 = k / 250

- Rearrange so it's k=

k = 400 x 250

k = 100000

- Substitute into formula:

T = 100000 / M

- Substitute in for the given value for M:

T = 100000 / 300

T = 333
Reply 5
Avatar for ChowSultan
ChowSultan
OP
Original post by Lokiofasgard
Of course.

All right so for inverse proportion the formula is:

T 1/M

which can be:

T = k/M

- Again, find k: (which is always involved in proportion of this sort)

400 = k / 250

- Rearrange so it's k=

k = 400 x 250

k = 100000

- Substitute into formula:

T = 100000 / M

- Substitute in for the given value for M:

T = 100000 / 300

T = 333


So with direct proportion, its multiplying with k (T = K x M)
and with inverse proportion its dividing with k (T = K / M) ?
Is it like this all the time for every question?
Original post by ChowSultan
So with direct proportion, its multiplying with k (T = K x M)
and with inverse proportion its dividing with k (T = K / M) ?
Is it like this all the time for every question?


Yes it is. Just use the formulas and you should be fine.

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