Money maths
Put the whole course to work where it pays: comparing two pack sizes, reading a real discount, splitting a bill with service on top, and spotting an offer that isn't one.
UNIT PRICE
Bring both to the same size
You can't compare 400 g and 750 g directly, so convert both to a price per 100 g. Divide the price by the number of hundred-gram lumps in the pack: 400 g is 4 lumps, 750 g is 7.5. Suddenly the two packs are speaking the same language.
96,000 for 400 g is 96,000 ÷ 4 = 24,000 per 100 g. 165,000 for 750 g is 165,000 ÷ 7.5 = 22,000 per 100 g. The big pack wins.
pack A: 400 g for 96,000
pack B: 750 g for 165,000
A: 96,000 ÷ 4 = 24,000 per 100 g
B: 165,000 ÷ 7.5
= 330,000 ÷ 15
= 22,000 per 100 gB is cheaper, by 2,000 per 100 gDividing by 7.5 looks nasty, so double both sides first: 165,000 ÷ 7.5 is the same as 330,000 ÷ 15. Doubling and halving from lesson 5 works on divisions too.
Check yourself
Pack A is 250 g for 75,000. Pack B is 400 g for 116,000. Which is the better buy?
- B, at 29,000 per 100 g
- A, at 30,000 per 100 g
- A, because it costs less in total
- They work out the same
Show the answer
B, at 29,000 per 100 g
Yes. 75,000 ÷ 2.5 = 30,000 and 116,000 ÷ 4 = 29,000, so B is 1,000 cheaper for every 100 g.
DISCOUNTS
Work out what you pay, not what you save
A 40% discount means you pay 60%, and 60% is one step: 10% six times, or half plus a tenth. Going straight to what you pay removes the subtraction at the end, which is where most sale-price mistakes happen.
40% off 650,000: 10% is 65,000, so 60% is 390,000. That's the price, finished, with no second step.
Check yourself
Work out each sale price and match it
Show the answer
- 20% off 450,000 → 360,000
- 25% off 320,000 → 240,000
- 40% off 650,000 → 390,000
- 15% off 200,000 → 170,000
A bill, a service charge, and six people
- The bill is 840,000 and service is 10%
10% of 840,000 is 84,000. Do the percentage on the bill, never on a figure you've already divided.
- Total to pay: 924,000
840,000 + 84,000. Left to right, as always: 840 + 80 = 920, then + 4.
- Split six ways
6 is 2 × 3. Halve 924,000 to 462,000, then divide by 3: 462 ÷ 3 = 154, so 154,000 each.
- Check it before anyone pays
Six times 154,000 is 924,000. And a rough check: 900,000 ÷ 6 would be 150,000, so 154,000 is exactly the right size.
Check yourself
On a bill of 840,000 with 10% service split between six people, each person owes 154,000.
Show the answer
True
True. The service takes it to 924,000, and 924 ÷ 6 = 154. Note the order: add the service to the whole bill first, then divide. Adding 10% to each person's share afterwards gives the same answer here, but not once someone has ordered differently.
Two questions a price tag answers
What does it cost?
The number on the label. Useful for one thing only: whether you can pay for it today. It says nothing about whether it's good value.
What does it cost per unit?
Price ÷ amount. This is the number that compares two products, two pack sizes, two subscriptions. A yearly plan at 960,000 is 80,000 a month; now you can compare it with the monthly one.
Check yourself
What fraction of the normal price do you actually pay?
- 25% off
- Buy 3, get 1 free
- Half price
- Buy one, get one free
- 10% off
- 10% loyalty discount
Show the answer
You pay 75%: 25% off, Buy 3, get 1 free
You pay 50%: Half price, Buy one, get one free
You pay 90%: 10% off, 10% loyalty discount
Make it a habit
- Per 100 g, per litre, per month. Whatever the unit, put both options on it before you choose.
- For a discount, go straight to what you pay: 30% off is 70% of the price, in one step.
- Add the service charge to the whole bill, then divide. Percentages first, sharing second.
- An offer phrased as free items is a discount in disguise. Count what you take home against what you hand over.
Check yourself
The hard one. A 1,200,000 dinner for eight has 10% service added. Sara pays for herself and a friend. What does she hand over?
- 300,000
- 150,000
- 165,000
- 330,000
Show the answer
330,000
Exactly. 1,200,000 + 120,000 = 1,320,000. Divided by eight that's 165,000 each, and two shares is 330,000.
Lesson recap
- To compare two packs, divide each price by its size and compare per 100 g, per litre or per month.
- For a discount, calculate what you pay, not what you save: 40% off is 60% of the price.
- Add a service charge to the whole bill, then split; break the split into factors, as 6 is 2 then 3.
- 'Buy 3 get 1 free' is a 25% discount, because you pay for 3 of the 4 you take home.