Welcome to the World of Big Numbers!

Hello there! Today, we are going on a mathematical adventure to master Four Arithmetic Operations using three-digit numbers. Think of these operations as the "Four Superpowers" of math: Addition (+), Subtraction (-), Multiplication (×), and Division (÷).

Whether you are counting your savings, sharing snacks with friends, or planning a big party, these skills will help you solve real-life problems like a pro. Don't worry if it seems like a lot at first—we will take it one step at a time!

1. Mixed Addition and Subtraction

When we see a math sentence with only addition and subtraction, we follow a very simple rule: Go from left to right.

Imagine you are reading a storybook. You start at the beginning (the left) and move toward the end (the right). Math works the same way!

Step-by-Step Example:

Let's solve: \( 450 - 120 + 300 \)

1. Start on the left: \( 450 - 120 = 330 \)
2. Move to the right: \( 330 + 300 = 630 \)

Quick Review:
• For + and - only: Start from the left.
• Common Mistake: Jumping to addition first even if it's on the right. Always follow the "storyline" from left to right!

Key Takeaway: Treat addition and subtraction like equal partners. Whoever comes first on the left gets done first!

2. The Power of Brackets

Sometimes, we want to change the order of things. This is where Brackets \( ( ) \) come in. Brackets are like a "VIP pass" in a queue—whatever is inside them gets to go first, no matter where they are!

Example with Brackets:

Compare these two:
Without brackets: \( 500 - 200 + 100 = 400 \) (Left to right: \( 300 + 100 \))
With brackets: \( 500 - (200 + 100) \)

In the second one, we must do the VIP part first:
1. Inside brackets: \( 200 + 100 = 300 \)
2. Rest of the problem: \( 500 - 300 = 200 \)

See how the answer changed? Brackets are very powerful!

Memory Aid: Think of brackets as a "Math Hug." You have to take care of the numbers being hugged before you do anything else.

Key Takeaway: Always solve the part inside the Brackets before any other part of the calculation.

3. Mixing Multiplication with Addition or Subtraction

What happens if we have a mix of addition/subtraction AND multiplication? In the world of math, Multiplication is the Boss. It is "stronger" than addition or subtraction and usually goes first.

The Golden Rule:

1. Do the Brackets first (if there are any).
2. Do Multiplication next.
3. Do Addition or Subtraction last (left to right).

Example:

Solve: \( 150 + 50 \times 2 \)
• Multiplication is the boss: \( 50 \times 2 = 100 \)
• Now add: \( 150 + 100 = 250 \)

Did you know?
If you accidentally added first (\( 150 + 50 \)), you would get \( 200 \times 2 = 400 \). That's a huge difference! Always remember the Boss (Multiplication) goes first.

Key Takeaway: Unless there are brackets, Multiplication always beats addition and subtraction in the "who goes first" race.

4. The "Splitting" Trick (Distributive Property)

Sometimes, multiplying big numbers is hard. We can use a trick to split a difficult number into two easier ones.

Analogy: If a heavy box is too hard to carry, you might take the items out and carry them in two smaller trips.

How it works:

To solve \( 4 \times 102 \), we can split \( 102 \) into \( 100 + 2 \).
\( 4 \times (100 + 2) = (4 \times 100) + (4 \times 2) \)
\( 400 + 8 = 408 \)

This also works for subtraction:
\( 3 \times 99 \) is the same as \( 3 \times (100 - 1) \).
\( (3 \times 100) - (3 \times 1) = 300 - 3 = 297 \)

Key Takeaway: You can split a multiplication problem into two smaller ones to make it easier to solve in your head!

5. Solving Real-World Problems

In Primary 3, you will see word problems that use phrases like "more than", "less than", or "altogether."

How to Solve a Word Problem:

1. Read: Find the numbers.
2. Plan: Decide which operations (\( +, -, \times \)) to use.
3. Write: Create a math sentence.
4. Check: Does your answer make sense?

Example: Andy has \( 120 \) stickers. He has \( 30 \) fewer stickers than Betty. How many stickers do they have altogether?

Step 1: Find Betty's stickers.
If Andy has \( 30 \) fewer, Betty must have \( 30 \) more.
Betty: \( 120 + 30 = 150 \)

Step 2: Find the total (altogether).
Andy + Betty: \( 120 + 150 = 270 \)

Quick Review Box:
• Altogether / Sum: Usually means add (\( + \)).
• Fewer / Difference: Usually means subtract (\( - \)).
• Times / Product: Usually means multiply (\( \times \)).

Key Takeaway: Read carefully! Sometimes you need to do two steps to find the final answer.

6. The "Reality Check" (Estimation)

Before you finish, always ask: "Does this answer look right?" We call this Estimation.

If you are adding \( 298 + 405 \), think of it as roughly \( 300 + 400 \). Your answer should be close to \( 700 \). If you get \( 7,000 \), you know you made a mistake!

Key Takeaway: Use "friendly numbers" (like numbers ending in \( 0 \)) to quickly check if your answer is in the right ballpark.

Great job! You’ve completed the notes for the Four Arithmetic Operations. Keep practicing, and these "math superpowers" will become second nature to you!