Money and Giving Change
You take a \pounds 5 note to the shop to buy a comic, and the
shopkeeper hands you some coins back. Working out whether that change is right — and counting
up your own coins in the first place — is exactly what this page is about.
Money is made of coins and notes. In Britain we count in
pounds and pence. There are exactly
100 pence in a pound, so \pounds 1 = 100\text{ p} —
just like there are 100 little cubes in a hundred-square.
The coins you can hold are 1p, 2p, 5p, 10p, 20p, 50p, £1 and £2; the paper
(and plastic) notes are £5, £10, £20 and £50. Every price is just a pile of
these put together. An amount like \pounds 3.45 means
3 pounds and 45 pence — the two digits after the point always count the pence.
Most coins are round, but the 50p and 20p have flat-ish sides so a blind person — or a
vending machine — can tell them apart by feel. Clever! Coins come in handy sizes too: small
ones are worth little, big ones are worth more. Long ago people really did pay with chunks
of silver and gold; today the coin just stands for that value. Collect the right
coins and you can make any amount of money.
Making a total from coins
To find out how much money you have, add up the coins. Suppose your purse
holds a 50p, two 20p coins and a 10p:
50\text{ p} + 20\text{ p} + 20\text{ p} + 10\text{ p} = 100\text{ p} = \pounds 1
Four coins, but together they make one whole pound. A good trick is to start with the
biggest coin and count on: "50… 70… 90… 100." When the pence reach 100, swap them for
a £1 — exactly like trading ten ones for a ten in
place value.
Adding amounts of money
Because money uses two decimal places, you add and subtract amounts of money just like any
other
decimals:
line up the decimal points (pounds under pounds, pence under pence), then
work column by column from the right. For example, \pounds 2.30 + \pounds 1.45:
2.30
+ 1.45
------
3.75
So \pounds 2.30 + \pounds 1.45 = \pounds 3.75. The decimal points
stand in a tidy line, one under the other, so the points in the answer line up too.
An apple costs \pounds 0.35 and a slice of cake costs
\pounds 1.20. Buy both and you line up the points:
\pounds 0.35 + \pounds 1.20 = \pounds 1.55. Notice the apple has
no whole pounds, so we still write the 0 in front of the point —
it keeps the pence in the right two columns, just like the 0 in place value holds a column
open.
Giving change by counting up
When you pay with more money than something costs, the shopkeeper gives you back the
difference. That is your change:
\text{change} = \text{amount paid} - \text{price}
You can subtract, but the easiest way is to count up from the price to the
cash you handed over, in friendly hops, and add the hops together. A toy costs
\pounds 6.40 and you pay with a \pounds 10 note:
- From \pounds 6.40, hop 60 p up to a round
\pounds 7.
- Then hop £3 more, up to \pounds 10.
- Add the hops: 60\text{ p} + \pounds 3 = \pounds 3.60 change.
The picture below is a number line: it shows the little hop up to the next
whole pound, then the big pound-sized hops to the money you paid. Press Refresh
for a brand-new shopping trip.
Here is a smaller one you can do in your head. A rubber costs
30\text{ p} and you pay with a 50\text{ p}
coin. Count up from 30: "40… 50" — that is two hops of 10 p, so your change is
20\text{ p}. You never have to take coins away; you just
build back up to what you paid.
The traps that trip people up with money:
- change = what you paid − the price — and the friendly way to find it is
to count UP from the price to the cash you gave, not down.
- Line up the decimal points when you add or subtract money — pounds under
pounds, pence under pence — or the pence end up in the pounds column.
- £1 = 100 p, not 10 p. When the pence reach 100 you trade them for one
whole pound, the same way ten ones become a ten.