Money
In this topic you will
- Recognise and use local currency.
- Recognise and use US dollars and cents.
- Use banknotes and coins to make an amount.
Key Words
- currency
- dollar, cents
- euro, euro cents
- pound sterling, pence
- price
- unit of money
- value
- worth
- yen
Show Definitions
- currency: The type of money used in a country, made up of coins and banknotes.
- dollar, cents: A dollar is a unit of money, and a cent is a smaller part of a dollar, where $100$ cents make $1$ dollar.
- euro, euro cents: The euro is a unit of money used in many European countries, and $100$ euro cents make $1$ euro.
- pound sterling, pence: The pound sterling is the money used in the UK, and a penny (pence) is a smaller part of a pound, where $100$ pence make $1$ pound.
- price: The amount of money needed to buy something.
- unit of money: The main named amount used to measure money in a currency, such as a dollar, euro, pound, or yen.
- value: How much something is worth in money.
- worth: Another way to say value, meaning the amount of money something equals or costs.
- yen: The unit of money used in Japan.
Coins and banknotes have their value written on them. Different values can be used together to buy things.
EXERCISES
Exercise $1.8$
$1$.How many cents is each of these coins worth?
👀 Show answer
Penny: $1$
Nickel: $5$
Dime: $10$
Quarter dollar: $25$
Half dollar: $50$
$2$.Erin used a Carroll diagram to sort US$ banknotes and coins.
Which coins or banknotes are missing from each section?
Draw them in the correct places on the Carroll diagram.
👀 Show answer
Missing items are:
• Quarter coin: $25$ c (odd value)
• $5$-dollar banknote (odd value)
• $20$-dollar banknote (not odd value)
$3$.Marcus spent $50$c on some candy.
He did not have a half dollar coin.
Which other coins could he pay with?
👀 Show answer
Examples of ways to make $50$c without a half dollar coin:
• $2$ quarters ($2 \times 25 = 50$)
• $5$ dimes ($5 \times 10 = 50$)
• $10$ nickels ($10 \times 5 = 50$)
• $50$ pennies ($50 \times 1 = 50$)
• $1$ quarter + $2$ dimes + $1$ nickel ($25 + 20 + 5 = 50$)
• $1$ quarter + $1$ dime + $3$ nickels ($25 + 10 + 15 = 50$)
Think like a Mathematician
Task: Zara says there must be at least $10$ different ways to make $20$c. Do you agree? How many different ways can you find?
Check each way you find by adding the coin values carefully.
Method:
- List the coin values you can use (for example: $1$c, $5$c, $10$c, $20$c).
- Start with the largest coin and work down, writing combinations that total $20$c.
- Record each combination in a neat way (for example: $10+5+5$ or $5+5+5+5$).
- Make sure you do not count the same combination twice in a different order.
Follow-up Questions:
👀 show answer
- $1$: Yes. There are more than $10$ different ways to make $20$c using common coin values (like $1$c, $5$c, $10$c, $20$c), so “at least $10$” is true.
- $2$: Here are $10$ different combinations (order does not matter):
$20$$10+10$$10+5+5$$10+5+1+1+1+1+1$$10+1+1+1+1+1+1+1+1+1+1$$5+5+5+5$$5+5+5+1+1+1+1+1$$5+5+1+1+1+1+1+1+1+1+1+1$$5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1$$1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1$
- $3$: Use a fixed order (largest coin to smallest) and only add equal-or-smaller coins as you continue. This way, $10+5+5$ is counted once, and you do not also count $5+10+5$ as a “new” way.
EXERCISES
$4$.Zara spent US$25$ on a T-shirt.
Which banknotes could she pay with?
👀 Show answer
Examples of ways to pay US$25$ using banknotes:
• US$20$ + US$5$
• US$10$ + US$10$ + US$5$
• US$5$ + US$5$ + US$5$ + US$5$ + US$5$
(Any combination of available banknotes that adds to US$25$ is correct.)
Think like a Mathematician
Task: You have $2$ different banknotes. Each banknote is less than US$100$. How much could you have?
Have you found all the possible answers?
Share your ways to pay US$100$ by checking your solutions carefully.
Method:
- List the banknote values you are allowed to use (for example: US$1$, US$5$, US$10$, US$20$, US$50$).
- Choose $2$ different banknotes (for example, US$20$ and US$50$).
- Add their values to find the total amount of money you could have.
- Systematically try all different pairs so you do not miss any possibilities (start with the smallest note and pair it with all larger notes).
- For each pair, check: are both notes less than US$100$, and are they different?
Follow-up Questions:
👀 show answer
- $1$: Using common US banknote values below US$100$ (US$1$, US$5$, US$10$, US$20$, US$50$), the different totals you can make with $2$ different notes are:
US$1$ + US$5$ = US$6$US$1$ + US$10$ = US$11$US$1$ + US$20$ = US$21$US$1$ + US$50$ = US$51$US$5$ + US$10$ = US$15$US$5$ + US$20$ = US$25$US$5$ + US$50$ = US$55$US$10$ + US$20$ = US$30$US$10$ + US$50$ = US$60$US$20$ + US$50$ = US$70$
- $2$: You can be sure you found them all by using a systematic method: fix the smaller note and pair it with every larger note exactly once. This prevents repeats (like counting US$10$ + US$5$ separately from US$5$ + US$10$) and guarantees no pair is missed.
- $3$: One way to pay exactly US$100$ using only banknotes is: US$50$ + US$50$ = US$100$. Another example is: US$20$ + US$20$ + US$20$ + US$20$ + US$20$ = US$100$.
EXERCISES
$5$.Arun spent US$8$ and $60$c in the supermarket.
Which banknotes and coins could he pay with?
👀 Show answer
One way is to pay US$8$ with banknotes, and $60$c with coins:
• Banknotes: US$5$ + US$1$ + US$1$ + US$1$ = US$8$
• Coins: $50$c + $10$c = $60$c
Here are some other examples (many answers are possible):
• Banknotes: US$10$ (then you would need $1$ dollar change back), and coins: $50$c + $10$c
• Banknotes: US$5$ + US$1$ + US$1$ + US$1$, and coins: $25$c + $25$c + $10$c
• Banknotes: US$1$ + US$1$ + US$1$ + US$1$ + US$1$ + US$1$ + US$1$ + US$1$, and coins: $20$c + $20$c + $10$c + $10$c
Any combination of US banknotes and coins that totals US$8$ and $60$c is correct.
EXERCISES
$6$.Find the total amount of money in each row and each column.
Two answers have been done for you.
👀 Show answer
Row totals
Row $1$: US$12$ and $50$c
Row $2$: US$5$ and $35$c
Row $3$: US$70$ and $5$c
Column totals
Column $1$: US$22$ and $25$c
Column $2$: US$5$ and $55$c
Column $3$: US$60$ and $10$c
Think like a Mathematician
Let’s investigate
Work on your own.
Think of a US coin or banknote.
Ask yourself questions, for example, “Is it a coin?” “Is it worth more than a dime?”
You can only answer yes or no.
Method:
- Choose one US coin or banknote and keep it secret (write it down so you don’t change it).
- Write three yes/no questions you could use to identify it (for example: “Is it a coin?”, “Is it worth more than a dime?”).
- Answer your own questions honestly with only “yes” or “no”.
- After the 3 questions, decide which coin or banknote it must be.
Follow-up Question:
👀 show answer
1: Sometimes yes, sometimes no — it depends on how “smart” your questions are.
To make it work in only 3 questions, pick questions that split the possibilities as much as possible each time (like a decision tree). A strong set is:
- Coin or banknote?
- If coin: worth more than a dime? (or “more than 25 cents?”)
- Use the last question to separate what’s left (for example: “Is it a quarter?” or “Does it have Washington on it?”).
Math idea hiding inside: each yes/no question gives 1 bit of information, so 3 questions can distinguish up to $2^3 = 8$ possibilities if your questions split the choices efficiently.