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Maths

Using formulae

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Changing the subject of a formula

The formula for finding the circumference of a circle is C = 2πr. So it is easy to find the circumference if we know the radius.

What happens, though, if we know the circumference but want to know the radius?

In this case we can rearrange to make r the subject of the formula.

C = 2πr, so we divide both sides by 2π

C over 2pi = r

or

r = C over 2pi

Question

The equation of a straight line is y = mx + c

Rearrange the formula to make 'c' the subject.

toggle answer

Answer

y - mx = c

or

c = y - mx

[To work this out: y = mx + c, so subtract mx from both sides.]

Question

The formula connecting °C and °F is:

C = 5 (F - 32) over 9

Rearrange the formula to make 'F' the subject.

toggle answer

Answer

C = 5 (F - 32) over 9

[Multiply by 9] 9C = 5(F − 32)

[Divide by 5]  9C over 5 = F − 32

[Add 32] 9C over 5 + 32 = F

So F = 9C over 5 + 32

Note: (9c + 160) over 5 is also correct.

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