Mathematics notes, unit 3

Money

Textbook Mathematics Year 4 (DLP), pages 105–134

What this chapter covers

You can add and subtract values of money up to RM100 000, including sen, and check your answer with an estimate (3.1.1, 3.1.2)
You can multiply and divide values of money by one-digit, two-digit numbers, 10 and 100 (3.1.3, 3.1.4)
You can solve addition and subtraction together, and multiplication and division together, working from left to right (3.2.1, 3.2.2)
You can record savings and expenses in a budget and say why a budget helps you save (3.3.1, 3.3.2, 3.3.3)
You can tell needs from wants, choose a priority and plan how to reach it (3.4.1, 3.4.2, 3.4.3)
You can name the currencies of some countries and use an exchange rate (3.5.1, 3.5.2)
You can name payment instruments and choose a suitable one (3.6.1, 3.6.2)
You can solve money problems in several steps (3.7.1)

3.1Adding and subtracting money

In Year 4 we work with money up to RM100 000, and with sen as well. Add and subtract money just like whole numbers, but line up the decimal points.

Value of money is written with the RM symbol and two sen places, for example RM23 156.75. RM1 = 100 sen.

Worked example: add RM23 156.75 and RM4 857

Step 1. Write RM4 857 as RM4 857.00 so both numbers have two sen places.
Step 2. Line up the decimal points. Add from the sen, then ringgit, tens, hundreds and thousands, and regroup when needed.
Step 3. RM23 156.75 + RM4 857.00 = RM28 013.75.

Estimate first. Round each amount to the nearest thousand ringgit, then add. For RM6 932.86 + RM48 900 + RM10 973.42, the estimate is RM7 000 + RM49 000 + RM11 000 = RM67 000. The exact answer is RM66 806.28, which is near RM67 000, so the answer is reasonable.

Worked example: subtract with sen

RM85 000 − RM35 500 − RM30 287.95 =
Step 1. RM85 000 − RM35 500 = RM49 500.
Step 2. Write RM49 500 as RM49 500.00 and subtract RM30 287.95.
Step 3. RM49 500.00 − RM30 287.95 = RM19 212.05.

When you regroup, RM1 becomes 100 sen, not 10 sen. Always write the RM symbol in the answer.

Check subtraction by adding. If RM68 476 − RM23 936.30 = RM44 539.70, then RM44 539.70 + RM23 936.30 must give RM68 476.

Calculate RM12 450 + RM8 365.50, then RM50 000 − RM12 345.60.

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RM20 815.50 and RM37 654.40.

3.2Adding and subtracting in one sum

When a number sentence has both + and −, work one step at a time from left to right.

Worked example: RM4 000 − RM1 250.50 + RM800

Step 1. RM4 000 − RM1 250.50 = RM2 749.50.
Step 2. RM2 749.50 + RM800 = RM3 549.50.

An account balance goes down when money is taken out and up when money is put in. Present the facts in a table with the columns cash in, cash out and balance.

Particular	Cash in	Cash out	Balance
Savings			RM85 600.40
Tuition fees		RM27 000	RM58 600.40
Cheque	RM33 565		RM92 165.40

3.3Multiplying money

Multiply money like whole numbers, then put the decimal point back so there are two sen places.

Worked example: 38 × RM2 400

Step 1. Split 38 into 30 + 8.
Step 2. 30 × RM2 400 = RM72 000 and 8 × RM2 400 = RM19 200.
Step 3. RM72 000 + RM19 200 = RM91 200.

Shortcut: multiplying by 10 moves the decimal point one place to the right, and multiplying by 100 moves it two places. 10 × RM5 095.30 = RM50 953. For 19 × RM864.70, think 20 × RM864.70 − RM864.70 = RM17 294 − RM864.70 = RM16 429.30.

What is the cost of 23 drones at RM2 900 each?

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23 × RM2 900 = RM66 700.

3.4Dividing money

Worked example: RM6 000 ÷ 40

RM6 000 ÷ 40 = RM600 ÷ 4 = RM150. (Cancel one zero from both numbers first.)

Dividing by 10 moves the decimal point one place to the left (by 100, two places): RM10 907.50 ÷ 10 = RM1 090.75. When the ringgit do not divide exactly, put a decimal point and carry on with the sen: RM29 063 ÷ 5 = RM5 812.60.

To check a division, estimate: RM70 213 ÷ 52 is about RM70 000 ÷ 50 = RM1 400, and the exact answer RM1 350.25 is near it.

3.5Multiplying and dividing in one sum

Again, work from left to right. Do not multiply the two numbers on the right first.

Worked example: 12 × RM3 500 ÷ 7

12 × RM3 500 = RM42 000. Then RM42 000 ÷ 7 = RM6 000.

A bar of five equal boxes representing RM1 500, with the first two shaded as paid and three left as balance — A bar model: RM1 500 in 5 equal payments. Each payment is RM1 500 ÷ 5 = RM300. Two payments = RM600; the balance is RM900.

RM20 000 ÷ 5 × 8 is not RM20 000 ÷ 40. Divide first: RM4 000, then multiply by 8 to get RM32 000.

3.6Managing money wisely

A budget is a plan that records the money received, the savings and the expenses. Savings = money received − expenses.

Record your income and spending every day, then add them up for the week and month.
A record helps you see where money goes, spend less on things you only want, and reach your target sooner.
Keeping records also helps you avoid debt, control spending, put needs first and save for the future.
Ways to save: bring food from home, switch off lights, set aside money first, keep it in a savings account.
Ways to earn extra money: wash cars, sell kuih, sell used items.

Day	Money received	Expense	Savings
Monday	RM4.00	RM1.20	RM2.80
Tuesday	RM4.00	RM1.50	RM2.50
Total	RM8.00	RM2.70	RM5.30

Needs are things you must have, such as rice and school shoes. Wants are things you would like, such as branded shoes. Choose a priority, work out the amount still needed and how long it takes: amount needed ÷ amount saved each month = number of months.

3.7Foreign currency and payment instruments

Every country has its own currency: the USA uses the dollar, Great Britain the pound sterling, Japan the yen, South Korea the won, China the renminbi, Bangladesh the taka and France the euro. Several countries share the name "dollar".

An exchange rate tells us how much foreign money RM1 can buy. In the textbook table, RM1 = 25.823 yen and RM1 = 0.238 US dollar. So RM10 = 10 × 25.823 = 258.23 yen. Rates change from day to day.

Payment instrument	How it works
Cash	Direct payment using notes and coins
Debit card	Pays straight from your savings account
Credit card	Spend first and pay the bank later
Internet banking	Pays through an online account
E-wallet / prepaid card	Uses a balance you topped up
Cheque	A written order to the bank to pay a stated amount
Postal order	Cash sent to a named person, issued by the post office

3.8Solving money problems

Follow four steps: understand the problem (underline the keywords), plan the strategy (draw a bar model or write a number sentence), solve, then check.

Worked example

A house renovation costs RM75 000. Encik Ming Ho pays in 5 equal instalments from April to August. How much is left to pay after June?
Plan. April, May and June are 3 of the 5 instalments.
Paid = RM75 000 ÷ 5 × 3 = RM45 000.
Balance = RM75 000 − RM45 000 = RM30 000.

Keywords: "total" and "altogether" mean add, "how much less" means subtract, "each" often means divide, "each of the same item" or "groups of" means multiply.

A company pays RM1 500 in 5 equal payments. How much has it paid after 2 payments, and what is the balance?

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Each payment RM300. Paid RM600; balance RM900.