Proportion

June 18, 2024•2 min read

Proportion can be a pain to get your head around initially!

On a basic level a direct proportion question maybe something like this: If 3 books cost £15, how much would 5 books cost?

The equation that you need to use is y=kx

The k is the amount that never varies, the y in this instance is the total cost, and the x is the number of books.

So, if we substitute in what we know: 15=k3

The first thing we must do is work out the value of k so divide both sides by 3.

15/3 = £5

One book cost us £5.

Now we know the cost/book, we can multiply it by the number of books we want to buy which in this instance was 5:

£5(our k or cost/ book) x 5 (the number of books we want to buy)= £25

An Indirect (or Inverse) Proportion Question might take the line:

If 4 workers can complete a task in 12 days, how long would it take 6 workers to complete the same task, assuming they work at the same rate?

This time the equation we must use is y=k/x This time the y is the number of days, and the x is the number of workers.

So, again if we substitute in the numbers that we have: 4 = k/12 To find the time it would take one worker (our k) we need to multiply12 by 4. Meaning 1 worker will take 48 days.

Now if we want to know how long it will take 6 workers, we go back to the original formula but substitute 48 for the k, and 6 for the x (number of workers) Y = 48/6

Which means y = 48/6 = 8 It will take 6 workers 8 days to complete the job.

I hope this makes sense. Good luck with your maths!

Dawn Strachan

For the past 20+ years I have been a firm believer that learning should be an enjoyable experience. I appreciate that traditionally education has revolved around worksheets, textbooks, listening to teachers. But a grounding in early years and working with children who had a variety of learning styles from I learned that it is an individual activity that is personal to all of us. We don’t all learn in the same way. Our influences, our experiences, our capabilities all influence how we retain information. But through it all, I believe that if we can make it enjoyable and engaging, they will want to participate. With participation comes practice which in turn boosts skill and confidence. With an increase in skill and confidence comes a willingness to have a go. This in turn leads to more practice which leads to a positive spiral of success. The moral, we need to make learning fun, engaging, use a range of techniques.

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