Mathematics notes, unit 3
Money
Textbook Mathematics Year 6 SK (DLP, Semakan 2017), pages 103–136
What this chapter covers
- You can explain cost price, selling price, profit and loss, and calculate any one of them from the other two (3.1.1, 3.1.2)
- You can calculate discount, rebate and voucher values, and the price after a discount or rebate (3.1.1, 3.1.2)
- You can read and complete an invoice, a bill and a receipt, and calculate service tax (3.1.1, 3.1.2)
- You can calculate interest on savings and dividend on an investment for one year (3.1.1, 3.1.2)
- You can tell an asset from a liability, and explain insurance and takaful (3.2.1, 3.2.2)
- {'You can solve money problems with several steps': 'understand, plan, solve and check (3.3.1)'}
3.1Cost price, selling price, profit and loss
A retailer buys goods and then sells them to customers. Two prices matter, and the difference between them decides whether the retailer gains or loses money.
Cost price: the price the retailer paid for the goods (the buying price).
Selling price: the price the buyer has to pay.
Profit: the money gained when the selling price is more than the cost price.
Loss: the money lost when the selling price is less than the cost price.
Selling price: the price the buyer has to pay.
Profit: the money gained when the selling price is more than the cost price.
Loss: the money lost when the selling price is less than the cost price.
| To find | Use |
|---|---|
| Profit | Selling price − Cost price |
| Loss | Cost price − Selling price |
| Selling price (with profit) | Cost price + Profit |
| Cost price (with profit) | Selling price − Profit |
| Selling price (with loss) | Cost price − Loss |
| Cost price (with loss) | Selling price + Loss |
Worked example: profit and loss
Step 1. A piano costs RM9 000 and is sold for RM10 800. Selling price is more than cost price, so there is a profit.Step 2. Profit = RM10 800 − RM9 000 = RM1 800.
Step 3. A watch costs RM1 286.80 and is sold for RM1 100.50 in a clearance sale. Selling price is less, so there is a loss.
Step 4. Loss = RM1 286.80 − RM1 100.50 = RM186.30.
Always subtract the smaller price from the larger one, and then say whether it is a profit or a loss. Two goods with different prices can have the same profit: RM9 000 sold for RM10 800 and RM12 000 sold for RM13 800 both give RM1 800.
Be honest. A fair seller sets the selling price to cover the cost and the service, and does not cheat the buyer.
A shirt costs a shop RM28.50. It is sold for RM35.00. Is it a profit or a loss? How much?
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Selling price is more than cost price, so a profit: RM35.00 − RM28.50 = RM6.50.
3.2Discount, rebate and voucher
Discount: the amount taken off the original price. Also called special price or offer price.
Rebate: a deduction from the total you must pay, or part of the money refunded after you pay. Examples are a toll fare rebate or a cash rebate on a receipt.
Voucher: a small piece of paper that gives the owner a discount, or can be exchanged for goods.
Rebate: a deduction from the total you must pay, or part of the money refunded after you pay. Examples are a toll fare rebate or a cash rebate on a receipt.
Voucher: a small piece of paper that gives the owner a discount, or can be exchanged for goods.
Worked example: 20% discount on a school bag
Step 1. Original price: RM80.Step 2. Discount value = 20% × RM80 = 20/100 × RM80 = RM16.
Step 3. Price after discount = RM80 − RM16 = RM64.
Worked example: 10% toll rebate on RM51.50
Method 1. 10% of RM51.50 = RM5.15. Then RM51.50 − RM5.15 = RM46.35.Method 2. 100% − 10% = 90%. 90% × RM51.50 = 9/10 × RM51.50 = RM46.35.
Method 2 is quicker: pay (100% − rebate%) of the price. A 25% discount means you pay 75%, a 20% discount means you pay 80%.
A voucher has a value and often a condition, for example "RM10 voucher if you spend RM50 and above in one receipt, valid for 14 days". Read the condition before you use it.
A discount value is not the price you pay. Find the discount first, then subtract it from the original price. Do not forget this last step.
A fan costs RM150 and has a 30% discount. What is the price after discount?
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30% × RM150 = RM45. Price = RM150 − RM45 = RM105. (Or 70% × RM150 = RM105.)
3.3Invoice, bill, receipt and service tax
| Document | What it is | Who gives it |
|---|---|---|
| Invoice | A list of goods or services with prices, sent to the buyer to ask for payment. It shows the invoice number and the sales discount. | The supplier, before payment |
| Bill | A detailed statement of the price of goods or services received, such as a restaurant, telephone or electricity bill. | The seller or service provider, before payment |
| Receipt | An official statement that payment has been received. It shows the cash given and the balance. | The seller, after payment |
Service tax is tax paid on the services of certain businesses, such as restaurants and hotels. In the textbook it is 6% of the total price.
Worked example: the receipt above
Step 1. Total of the items: RM6.00 + RM8.00 + RM7.50 = RM21.50.Step 2. Service tax = 6% × RM21.50 = 6/100 × RM21.50 = RM1.29.
Step 3. Total payment = RM21.50 + RM1.29 = RM22.79.
Step 4. Balance = RM50.00 − RM22.79 = RM27.21.
On an invoice, a sales discount is subtracted from the total. On a bill or receipt, service tax is added. Check the line before you decide which one to do.
Check every item on a bill, and pay your bills by the date given.
A hotel room is RM280 a night. Find the payment for 2 nights including 6% service tax.
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2 × RM280 = RM560. Tax = 6% × RM560 = RM33.60. Payment = RM560 + RM33.60 = RM593.60.
3.4Interest and dividend
Interest: money a bank pays you for keeping your savings with it for a period of time.
Dividend: a share of the profit paid to you for the money you invest in a business or shares.
Dividend: a share of the profit paid to you for the money you invest in a business or shares.
Both are found with a rate "per annum" (every year):
Interest and dividend for one year
Interest = Interest rate × Savings. RM10 000 at 2% per annum: 2% × RM10 000 = RM200. Balance after 1 year = RM10 000 + RM200 = RM10 200.Dividend = Dividend rate × Investment. RM3 000 at 4% per annum: 4% × RM3 000 = RM120. Total after 1 year = RM3 120.
Do not forget "per annum" means per year. And the interest or dividend is only the extra money. Add it to the savings to find the total balance. 104% × RM3 000 gives the total in one step.
Saving regularly is a good habit. A dividend can rise when the company gains more profit.
Find the interest on RM8 000 saved for 1 year at 1.5% per annum.
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1.5% × RM8 000 = 1.5/100 × 8 000 = RM120.
3.5Asset, liability, insurance and takaful
Asset: what you own that has value, such as cash, savings, a house and gold jewellery.
Liability: money you owe, a financial commitment such as a home loan, car loan or education loan.
Liability: money you owe, a financial commitment such as a home loan, car loan or education loan.
Some assets, like a house, can keep or gain value. Others lose value, such as a car or a phone. We call this depreciation: a decrease in value. A person is managing money well when the assets are larger than the liabilities.
| Insurance | Takaful | |
|---|---|---|
| Concept | Buy and sell | Contribution (donation) |
| Who bears the risk | The insurance company | The participants, in a group |
| Money paid | Premium, owned by the company | Contribution, owned by the takaful fund; the operator manages it |
| Law | Government laws; not syariah compliant | Syariah laws and government laws; syariah compliant |
Insurance and takaful protect us, our family and our property if something happens, for example medical expenses, an accident, travel loss or a house destroyed by fire. "Takaful" comes from the Arabic word kafala: to guarantee, protect or look after.
Name two things that insurance or takaful can cover.
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Any two: medical expenses, car repair and injury after an accident, loss during travel, house destruction, life, education.
3.6Solving money problems
Use the same four steps every time: understand the problem (underline the important information), plan a strategy (a table, a bar model or a number sentence), solve, and check your answer by working backwards.
Worked example: a purchase with a rebate
A bed costs RM1 978 and a sofa set RM1 150. There is a RM50 rebate for every RM1 000 spent. Is RM3 000 enough?Step 1. Total = RM1 978 + RM1 150 = RM3 128.
Step 2. RM3 128 has three lots of RM1 000, so the rebate is 3 × RM50 = RM150.
Step 3. To pay = RM3 128 − RM150 = RM2 978. RM3 000 is enough.
Worked example: trial and error
French beans: cost RM5, profit RM1 a kg. Chilli: cost RM8, profit RM2 a kg. Selling prices: RM6 and RM10. Which masses give selling prices that total RM120?Trial 1. 10 kg of beans (RM60) and 6 kg of chilli (RM60): total RM120.
Trial 2. 5 kg of beans (RM30) and 9 kg of chilli (RM90): total RM120.
Both work, so more than one answer is possible.
| Money words | Operation |
|---|---|
| total payment, altogether, with service tax | add |
| balance, after discount, after rebate, profit, loss | subtract |
| percent of, interest, dividend, discount value | multiply by rate / 100 |
When a question gives a rate on one part of the money only, apply the rate to that part. If RM10 000 is split into RM6 000 for savings and RM4 000 for a unit trust, the 8% dividend is on the RM4 000 only: RM320.
A shop buys 4 phones at RM829 each and loses RM1 020 on all four. What is the selling price of one phone?
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Loss for one phone = RM1 020 ÷ 4 = RM255. Selling price = RM829 − RM255 = RM574.