Calculate Indirect Proportion Using Formal Notation

In this activity, we will use indirect (sometimes called inverse) proportion to find a formula connecting two unknowns.

Recap

y is directly proportional to x

This means 'as x goes up, y goes up'

A Typical Question

A is directly proportional to B

When A = 8, B = 2

Find a formula for A in terms of B

Answer

We write A is directly proportional to B like this:

The letter in the middle is the Greek letter alpha and it means 'proportional to' here.

Now, we know they both go up proportionally but we do not know the multiplier (or exchange rate if it was currency exchange).

A = KB

Where K is just a letter used for the multiplier because we are unsure what it is at the minute.

To find K (the multiplier) we use the values given in the question:

A = 8 when B = 2

A = KB

8 =  2K

Divide through by 2:

K = 8 ÷ 2

K = 4

We can now write the formula as we know the multiplier K

A = 4B

Now we can use this to find any missing value of A or B.

When something is indirectly or inversely proportional it means 'as one goes up, the other one goes down'

We write it like this:

Let's do a question.

Example

A is indirectly proportional to B

When A = 3, B = 4

Find a formula for A in terms of B.

Answer

A is indirectly proportional to B so we write:

1) Find K, the multiplier:

A = K ÷ B

2) Use the values given in the question to find K:

A = K ÷ B

When A = 3 and B = 4

3 = K ÷ 4

Multiply through by 4:

K = 3 x 4

K = 12

3) Rewrite the formula with K = 12:

A = 12 ÷ B

We will do the first question together to help! 

It will get easier!