Everyday Maths for Real Life

The lessons at a glance

1. Percentages Without a Calculator

Percentages are everywhere: discounts, tips, VAT, exam grades, phone battery, interest rates. If you can find 10 percent and 1 percent in your head, you can build almost any percentage you will meet in daily life, and feel far more in control of your money.

• Find 10 percent by dividing by 10, 1 percent by dividing by 100, then build from there.
• Use multipliers: 1.15 for a 15 percent rise, 0.80 for a 20 percent fall.
• Percentage change always divides by the starting value.
• Percentage points and percent are not the same thing.
• Numeracy is a skill you build, not a talent you are born with.

2. Shopping Maths: Deals, Unit Prices and Shrinkflation

Shops are designed to make prices feel simple and deals feel generous. A few quick calculations show you what you are really paying, so you can choose calmly rather than react to a big red sign. (For budgeting and shopping habits, see the Money Basics module.)

• Stacked discounts multiply, so 20 percent then 10 percent is 28 percent off, not 30.
• 'Buy one get one free' is 50 percent off only if you use both.
• Compare unit prices, not pack prices.
• Shrinkflation is a hidden price rise; unit prices reveal it.

3. VAT and Tax on a Receipt

Every receipt in the UAE includes VAT, and when you travel or study abroad you will meet very different tax rates. Knowing how to add tax, and how to take it back out, helps you check bills, compare prices and claim refunds when you are eligible.

• UAE VAT is 5 percent; displayed prices should already include it.
• Add VAT by multiplying by 1.05; remove it by dividing by 1.05.
• The VAT inside a UAE price is the total divided by 21; inside a UK 20 percent price, the total divided by 6.
• Never take the VAT percentage of an inclusive price.

4. Splitting Bills and Tipping Fairly

Few things test a friendship like a shared bill. A little maths, agreed calmly before the bill arrives, keeps things fair and keeps friendships easy. (Flat bills are covered in Bills, Utilities and Household Paperwork; tipping customs around the world are in the etiquette modules.)

• Agree how to split before the bill arrives.
• Shared dishes split evenly; personal orders by item.
• Always check the shares add back up to the total.
• 10 percent: move the decimal point; 15 percent: add half again.
• Read the bill for a service charge before tipping.

5. Currency Conversion and Hidden Fees

Whether you are on holiday, studying abroad or buying online, currency conversion is where small, quiet fees add up. Understanding rates and margins helps you keep more of your money. (Bank transfers abroad are covered in the Banking, Cards and Credit module.)

• Multiply to convert one way, divide to convert back, and sense-check the direction.
• The gap between buy and sell rates is a cost, even when there is 'no commission'.
• Always pay in the local currency abroad.
• Small percentage fees add up over a whole trip.

6. Time, Speed, Distance and Running Costs

How long will it take, when should I leave, and what will it cost? The same three-part formula answers all of these, and it is useful whether you are planning a road trip, catching a train abroad or sharing fuel costs with friends.

• Time = distance / speed; then convert the decimal part of an hour by multiplying by 60.
• 1.4 hours is 1 hour 24 minutes, not 1 hour 40.
• Plan backwards from your arrival time and add a buffer.
• Fuel cost = litres per 100 km x hundreds of km x price per litre.
• Real-world fuel use is usually higher than the official figure.

7. Reading Numbers in the News

News stories, adverts and social posts are full of averages, polls and huge numbers. A few questions help you see what a number really means. (Relative versus absolute risk and misleading charts are covered in Critical Thinking: Statistics and Charts in the News; this lesson adds averages, polls and scale.)

• Mean, median and mode answer different questions; outliers pull the mean.
• Polls have margins of error, and smaller groups have bigger ones.
• Ask who produced a number, from what sample, and compared with what.
• Turn big totals into rates or per-person figures.

8. Estimating and Sense-Checking

Most mistakes with numbers are not hard maths. They are a slipped decimal point or a mistyped digit. A quick estimate before you calculate lets you spot an answer that cannot be right, and gives you confidence when you have no calculator at all.

• Round to 1 significant figure, then calculate.
• Estimate before you calculate, so you can spot slips.
• Check size, direction and units.
• For big questions, break them into small guessable steps.

Talk about it, then try it

The real-life practice tasks from each lesson. Pick one or two a week and agree when you will check in.

1. Percentages Without a Calculator
   • This week, when you see any discount or price, work out 10 percent, 5 percent and 1 percent of it in your head before checking on your phone.
   • Find one news story or advert that mentions a change in a rate. Write down the change in percentage points and as a percent of the original.
   • Take a price you know from a year ago (a snack, a transport fare, a subscription) and work out the percentage change.
2. Shopping Maths: Deals, Unit Prices and Shrinkflation
   • On your next supermarket trip, compare the unit price of two sizes of the same product and of a store brand against a big brand.
   • Find one multi-buy deal and work out whether it is cheaper per item than buying a single.
   • Check the weight of a snack you buy regularly and note it on your phone. Check again in a few months.
3. VAT and Tax on a Receipt
   • Pick up a receipt from your next purchase in the UAE. Check that the VAT shown is close to the total divided by 21.
   • Choose a price from a UK website and work out how much of it is VAT (divide by 6).
   • Write the two key formulas on a note in your phone: price before VAT = total / 1.05; VAT = total / 21.
4. Splitting Bills and Tipping Fairly
   • Next time you eat out with friends or family, offer to work out the split and the tip, and check that the shares add up to the bill.
   • Look at your last restaurant receipt and check whether a service charge was included.
   • Practise mental tipping: for three bills you see this week, work out 10 and 15 percent in your head.
5. Currency Conversion and Hidden Fees
   • Find today's mid-market rate for a currency you might use (pounds, euros or dollars) and compare it with the rate a local exchange shop advertises. Work out the mark-up percentage.
   • Write a one-line 'rough converter' for one currency in your phone notes, and practise converting three prices with it.
   • Ask a parent or check online what foreign transaction fee applies to a card your family uses.
6. Time, Speed, Distance and Running Costs
   • Plan a real journey you will make this week: work out the distance, an average speed, the journey time in hours and minutes, and the time you need to leave.
   • With an adult, check a family car's fuel use (L/100 km) from the trip computer or by the fill-up method, and work out the cost per km at this month's fuel price.
   • Work out the fair share of fuel for a shared trip with friends.
7. Reading Numbers in the News
   • Find one news story that uses an 'average'. Decide whether it is a mean or a median, and whether outliers could distort it.
   • Find a poll in the news and look for the sample size and margin of error. Is the reported lead bigger than the margin?
   • Take one large number from the news and turn it into a per-person or per-1,000 figure.
8. Estimating and Sense-Checking
   • At the next shop you visit, estimate your total before you reach the till and compare it with the real total.
   • Pick one Fermi question (for example, how many bottles of water your household uses in a year) and estimate it step by step with a family member.
   • Each time you use a calculator this week, make a 1 significant figure estimate first.

Quiz

Name: ______________________ Date: ____________ Circle one answer for each question.

Answer key

1. D: Third Space Learning's building method: 10 percent is 24 and 5 percent (half of 10 percent) is 12, so 15 percent is 24 + 12 = 36.
2. A: Tutorful: the sale price is 70 percent of the original, so divide by 0.70: 63 / 0.70 = 90 pounds. Adding 30 percent of 63 back on (81.90) is a common mistake.
3. A: Using multipliers (Tutorful): 200 x 0.8 = 160, then 160 x 0.9 = 144. Discounts multiply, so the total saving is 28 percent, not 30.
4. D: 12.50 / 5 = 2.50 and 17.25 / 7.5 = 2.30 per 100 g. New Zealand Consumer Protection advises comparing unit prices because bigger is not always, but sometimes is, cheaper.
5. C: u.ae: VAT was introduced on 1 January 2018 and the rate of VAT is 5 percent.
6. C: VAT is 5 out of every 105, so divide by 21: 210 / 21 = 10. Taking 5 percent of 210 (10.50) is the common mistake.
7. B: The platter split four ways is AED 15 each, so 140 + 15 = 155. The shares (100, 155, 110, 115) add up to the AED 480 bill.
8. C: Gulf News (2023): tipping is customary in most cases but not compulsory; 10 to 15 percent is customary depending on service, and rounding up can be enough.
9. C: The National: the peg of 1 US dollar = 3.6725 dirhams took official effect in November 1997.
10. A: Bankrate: dynamic currency conversion carries a mark-up, averaging around 5 percent in Europe, so always pay in the local currency.
11. B: MME: time = distance / speed = 140 / 100 = 1.4 hours. 0.4 x 60 = 24 minutes, so 1 hour 24 minutes.
12. B: CarsGuide's method: 8 litres per 100 km x 1.4 hundred km = 11.2 litres.
13. B: The median is the middle value (La Trobe), which is AED 10,000. The mean is 290,000 / 10 = 29,000, pulled up by one outlier.
14. A: La Trobe: extreme scores strongly affect the mean but not the median, so the median is preferred when there are outliers.
15. B: Mr Mathematics: keep the first non-zero digit and round using the next digit; 578 rounds to 600.
16. A: Rounding each to the nearest dirham gives 13 + 9 + 24 + 4 + 18 + 7 = 75; the exact total is AED 74.24.

General information only, written from the sources listed in each online lesson. Laws, numbers and services change, so check official sources. Life-Ready Society, https://lifereadysociety.com/everyday-maths/