CHAPTER 6
PERCENTAGES AND RATIOS
Percentages and ratios are common in shopping and cooking, so are needed by learners regardless of examination curricula
In percentages ‘of’ and ‘off’ are particularly problematic for all learners because they look similar but are very different in calculations
Ratios use a semi colon, : , in the UK, but this is the division symbol to many ESOL learners
Inclusions of alcohol in making cocktails can be culturally sensitive and are best avoided. Use squash instead!
Introduction
Ratios and percentages come into the Adult Core Curriculum for Numeracy at Level 1 and above, but you may find, as I have, that when teaching shopping or making drinks, even at lower levels of ESOL classes, percentages and ratios often come up and learners want to be able to understand them.
This is an example of how teachers are sometimes pulled in two different directions- the needs and requirements of the learners are often different from the demands of the exam system, and as teachers we have to reconcile the two. In my case this means I end up teaching language and topics way above the maths levels in English of my learners, but as they need them for their lives, they are clearly important. The maths levels in English can be very different from learners’ maths levels in their first languages, of course.
Interestingly, these are two topics that native English speakers can also find very challenging, so any resources produced for either group are likely to be useful for everyone.
Percentages
‘Per cent’ is Latin for ‘out of 100’, which means that rather than trying to compare portions of large amounts to see how they relate in terms of the size, if the percentages are used the comparison of both is out of 100. This makes it much easier.
For instance, A has 46 items out of 250, and B has 96 items out of 600. Who has the proportionally larger amount? The calculations look like this: 46/250 x 100 = 18.4%; 96/600 x 100 = 16%. Thus, A has a larger proportion of their total than B.
The main confusion when teaching percentages used in shopping scenarios are two small words and they can cause mayhem! They are ‘off’ and ‘of’. For instance, ‘What is 20% of £40?’ and ‘What is 20% off £40?’ See what I mean? This is tricky and I suggest you teach ‘of’ first and ‘off’ second and keep them discrete. If I teach them together this seems to add to the confusion. When learners have practised both, then I try the mixed worksheet and see if they have really got it. Native speakers of English also use these worksheets in my classes, and it cheers the ESOL learners up to know they are not alone!
Percentages are often used in shopping, such as ‘All stock 25% off’. If an item is £30, then 25% of 30 is: 25/100 x 30 = £7.50, so the new price is 30 – 7.50 = £22.50.
To get back to an original price from a discounted price causes much confusion. The calculation looks like this: 100 – 25 = 75, so the new price is 75% of the original one. Now divide the new price by 0.75: 22.50/ 0.75 = £30, or 22.50/75 x 100 = £30. I love maths!
Any discussion of percentages in my classes always includes a discussion on what, for instance, 25% APR on credit cards means in terms of the amount of money you will pay, if you do not pay off credit card bills at the end of each month. Learners are often astonished!
Ratios
Ratios do not seem to exist in all cultures, so if your learners are progressing to Level 1 or above in maths you will need to teach this topic from first principles. It is worth starting with some practical examples of written ratios, such as the ones found on such products as squash bottles or hair dye packets, and working from there. The colon, :, seems very unfamiliar used in the ratio context to most of the ESOL learners I have taught, as it is the symbol for division in many other countries.
Ratios are commonly seen on bottles of squash, in the form of how much squash to how much water. An example is ‘Dilute the squash in the ration 1 part of squash to 3 parts of water’. This can be written as squash: water, 1:3. The order is important and should not be changed- 3 parts of squash to one of water will not taste the same!
On exam papers ratio questions can come in the form of money to be divided up between 3 people, A, B and C. If I share £60 out in the ratio A: B: C of 2: 3: 1, then I must firstly add up the shares: 2 + 3 + 1= 6; then find one part: 60/ 6 = 10. Now, A gets two parts, so 2 x 10 = £20, B gets 3 parts, so 3 x 10 = £30, and C gets one share, £10.
Beware the use of some of the ratio material in the public domain, often much beloved by some native English speakers, as it is based around making alcoholic cocktails which may not be acceptable to some of our learners. I avoid any references to alcohol in the Maths sessions, although in Citizenship classes the minimum age for various activities in the UK is covered, including the minimum age for alcohol consumption.
JMS 2026