Maths Study Notes: Money (Advanced)
Hello, Future Money Experts!
Welcome to your advanced guide to money! Ever wondered how grown-ups figure out the total cost at the shops, or how much change they should get back? It's all about maths! In these notes, you'll learn how to become a real pro with money. We'll discover how to use a magical little dot called a decimal point and use our addition, subtraction, multiplication, and division skills to solve real-life money puzzles. It's a super important skill for shopping, saving, and understanding the world around you. Let's get started!
From Cents to Decimals - A Super Skill!
We already know about dollars ($) and cents (¢). The most important thing to remember is how they are connected.
Quick Review: There are 100 cents in 1 dollar.
Think of a dollar as a whole pizza. The cents are the 100 little slices it's cut into!
The Magical Decimal Point
When we write money, we use a decimal point (a small dot) to separate the whole dollars from the cents. It’s like a little wall between them.
The numbers to the left of the dot are the dollars.
The numbers to the right of the dot are the cents.
Example: Let's look at $12.50
This means we have 12 whole dollars and 50 cents.
Because there are 100 cents in a dollar, we always use two spaces for the cents after the decimal point.
$8 and 25 cents is written as $8.25
$15 and 5 cents is written as $15.05 (We need a 0 to hold the place!)
Just 70 cents is written as $0.70 (We use a 0 for the dollars.)
Key Takeaway
The decimal point is your best friend when working with money. It keeps the dollars and cents in their correct places. Always remember there are two digits for the cents after the point!
Adding and Subtracting Money (Shopping Spree Math!)
This is what you do when you buy a few things and need the total cost, or when you pay and need to work out your change.
The Golden Rule: Line Up the Dots!
When you add or subtract money, the most important rule is to line up the decimal points vertically (one on top of the other). This makes sure you are adding dollars to dollars and cents to cents.
Imagine you are stacking Lego bricks. You have to line up the bumps perfectly for the tower to be straight. It's the same with decimal points!
Step-by-Step: Adding Money
Problem: You buy a storybook for $14.50 and a pen for $3.75. How much do you spend altogether?
1. Write the numbers down, making sure the decimal points are in a perfect line.
$$
\begin{array}{c}
& 14.50 \\
+ & 3.75 \\
\hline
\end{array}
$$
2. Add the columns from right to left, just like you always do. Don't forget to carry over if you need to!
$$
\begin{array}{c}
& 1\ 1\ \\
& 14.50 \\
+ & 3.75 \\
\hline
& 18.25
\end{array}
$$
3. Bring the decimal point straight down into your answer.
So, you spent $18.25 altogether.
Step-by-Step: Subtracting Money
Problem: You pay with a $20.00 note for items that cost $18.25. How much change should you get?
1. Write the numbers down, with the bigger number on top. Line up those decimal points!
$$
\begin{array}{c}
& 20.00 \\
- & 18.25 \\
\hline
\end{array}
$$
2. Subtract from right to left. You'll need to borrow here!
$$
\begin{array}{c}
& \ 9\ 9\ \\
& 1\ \cancel{10}\ \cancel{10}\ 10 \\
& \cancel{2}0.00 \\
- & 18.25 \\
\hline
& 1.75
\end{array}
$$
3. Bring the decimal point straight down into your answer.
You should get $1.75 in change.
Common Mistake Alert!
Forgetting to line up the decimal points can give you a very silly answer. Look at this:
$14.50 + $3.75 written incorrectly gives a wrong answer! Make sure your dots are in a line!
Key Takeaway
For adding and subtracting money, just remember: Line Up the Dots! Then, just add or subtract like you normally would and bring the dot straight down into your answer.
Multiplying Money (Buying in Bunches!)
What if you need to buy three sandwiches for your friends, and they all cost the same? You need to multiply!
The "Count the Jumps" Trick
Multiplying money is a bit different. You don't need to line up the decimal points. Instead, we use a simple trick at the end.
Step-by-Step: Multiplying Money
Problem: You buy 4 movie tickets, and each one costs $21.25. What is the total cost?
1. Write the problem down and pretend the decimal point isn't there for a minute. Just multiply 2125 by 4.
$$
\begin{array}{c}
& 2125 \\
\times & 4 \\
\hline
& 8500
\end{array}
$$
2. Now, let's find where the decimal point goes. Look back at the money amount ($21.25). How many digits are after the decimal point? There are two (the 2 and the 5).
3. In your answer (8500), start from the very right and jump two places to the left. Place your decimal point there.
$$ 85.00 $$
4. Add the dollar sign. The total cost is $85.00.
Did You Know?
The dollar sign ($) is thought to have come from the symbol for an old Spanish currency. It's one of the most recognised symbols in the world!
Key Takeaway
To multiply money: 1. Multiply like normal. 2. Count the decimal places in the money number. 3. Jump that many places in your answer and place the dot!
Dividing Money (Sharing the Cost!)
Division helps us find the price of one item in a multi-pack or figure out how to split a bill between friends.
The "Raise the Roof" Rule
When you divide a money amount by a whole number, the decimal point is easy to handle. It just goes straight up!
Step-by-Step: Dividing Money by a Whole Number
Problem: A box of 5 identical toys costs $32.25. How much does each toy cost?
1. Set up your division problem as usual.
$$ 5 \overline{)32.25} $$
2. Before you start dividing, "Raise the Roof!". Take the decimal point in 32.25 and put it directly above in the answer line.
$$ 5 \overline{)32.25} \begin{array}{l} \ . \\ \end{array} $$
3. Now, just divide as you normally would, making sure your numbers line up correctly.
$$
\begin{array}{r}
6.45 \\
5 \overline{)32.25} \\
\end{array}
$$
The answer is already perfectly formatted! Each toy costs $6.45.
Step-by-Step: A Trickier Division (The Magic Slide)
Problem: You have $27. How many packets of stickers can you buy if each packet costs $4.50?
Don't worry, we have a trick for this! We can't easily divide by a number with a decimal point ($4.50). So, we need to change it.
1. Set up the problem: $$ 4.50 \overline{)27} $$
2. We need to make the outside number (4.50) a whole number. We can do this with the "Magic Slide". Slide the decimal point two places to the right. It becomes 450.
3. Fairness Rule! Whatever you do to the outside number, you MUST do to the inside number. The number 27 has a hidden decimal point at the end (27.00). Slide its decimal point two places to the right too! It becomes 2700.
4. Your new problem is much easier: $$ 450 \overline{)2700} $$
5. Now you can solve it! The answer is 6.
You can buy 6 packets of stickers.
Key Takeaway
When dividing money, if the divisor is a whole number, just Raise the Roof with the decimal point. If the divisor is a decimal, use the Magic Slide on both numbers to make it a whole number first!
Putting It All Together - Solving Word Problems!
Now you have all the skills! Let's use them to solve some money mysteries. The first step is to read the question carefully and figure out what it's asking.
Clue Words to Help You
Look for these words to decide if you need to add, subtract, multiply, or divide.
Addition Clues: total, altogether, in all, combined, sum.
Subtraction Clues: how much more/less, change, left over, difference, remain.
Multiplication Clues: each, every, total for 5 items, product.
Division Clues: shared equally, split between, cost for one, average.
Practice Mysteries
Mystery 1: Aisha saves $15.50 from her pocket money. Her grandmother gives her another $20.00 for her birthday. She then buys a book that costs $8.95. How much money does she have left?
Thinking: First, I need to find her total money (add $15.50 and $20.00). Then, I need to find out what's left after buying the book (subtract $8.95 from the total).
Mystery 2: A football team of 11 players goes out for pizza after a game. The total bill is $123.75. If they split the bill equally, how much does each player pay?
Thinking: The words "split the bill equally" are a big clue! I need to divide the total cost by the number of players.
You've done an amazing job! Working with money is a skill you will use your entire life. Keep practising, and soon you'll be a true Money Master!