Welcome to the World of 3-Digit Numbers!

In this chapter, we are going to learn how to handle Mixed Addition and Subtraction using numbers up to 1,000. Think of this as being the manager of your own toy shop! Sometimes you get new toys in (addition), and sometimes you sell them to happy customers (subtraction). Being able to do both at the same time is a "math superpower" that helps you solve real-life problems easily.

Don't worry if this seems a bit big at first. We will break it down into small, easy steps, and you'll be a pro in no time!


Quick Review: The Basics

Before we start mixing operations, let's remember our Place Value. In a 3-digit number like \(245\):

  • The 2 is in the Hundreds place (stands for \(200\)).
  • The 4 is in the Tens place (stands for \(40\)).
  • The 5 is in the Units place (stands for \(5\)).

Quick Review Box:
1. Addition with Carry: When a column adds up to more than 9, we move the extra to the next door neighbor on the left.
2. Subtraction with Borrowing: If the top number is too small, we "borrow" from the neighbor on the left.


The Golden Rule: Moving from Left to Right

When you see a math sentence that has both plus (+) and minus (-) signs, you might wonder: "Which one do I do first?"

The secret is simple: Always work from Left to Right!

Imagine a train moving on a track. The train hits the first calculation on the left, finishes it, and then moves to the next one on the right. We never skip around!

Example: \(500 - 200 + 100\)
Step 1: Do the left side first: \(500 - 200 = 300\).
Step 2: Take that answer and do the next part: \(300 + 100 = 400\).
The final answer is 400.

Key Takeaway: Treat a math sentence like reading a book—start at the left and move to the right!


Step-by-Step: Solving Mixed Problems

Let’s try a harder one together: \(145 + 238 - 120\).

Step 1: The First Pair

Look at the first two numbers on the left: \(145 + 238\).
Use Column Form to find the sum:
\( \ \ 145 \)
\( \underline{+ 238} \)
\( \ \ 383 \)
(Remember to carry the 1 from the Units to the Tens!)

Step 2: The Final Step

Now, take your new number (\(383\)) and subtract the last number (\(120\)).
\( \ \ 383 \)
\( \underline{- 120} \)
\( \ \ 263 \)

So, \(145 + 238 - 120 = 263\).

Did you know? This two-step process is called Horizontal Form when we write it out in one line, but we use Column Form on the side to do the heavy lifting!


Real-World Example: The Birthday Party

Imagine you have 350 stickers. Your friend gives you 125 more for your birthday. Then, you give 50 stickers to your little brother. How many do you have now?

The math sentence is: \(350 + 125 - 50\)

  1. First: \(350 + 125 = 475\) (Now you have a big pile of stickers!)
  2. Next: \(475 - 50 = 425\) (You gave some away, so you have a bit less).

You have 425 stickers left!


Estimation: The "Does it make sense?" Check

Sometimes we make a small mistake. Estimation helps us catch it! To estimate, we round the numbers to the nearest 10 or 100 to get a "quick guess."

If you are calculating \(201 + 298 - 102\):
Think: \(200 + 300 - 100\).
\(200 + 300 = 500\).
\(500 - 100 = 400\).
If your final answer is near 400, you are likely correct! If you got 800, you know you should check your work again.


Common Mistakes to Avoid

  • The "Jumping Bean" Mistake: Doing the subtraction first just because it looks easier. Always stay on the "Left-to-Right" track!
  • The "Invisible Carry": Forgetting to write down the number you carried or borrowed. Always write those little numbers at the top!
  • The "Sign Swap": Accidentally adding when the sign says subtract. Always double-check the sign before you start the column!

Summary Checklist

Check your understanding:

1. Did I work from Left to Right?
2. Did I use Column Form to solve the big numbers accurately?
3. Did I remember to Carry or Borrow if needed?
4. Does my answer pass the Estimation test?

Keep practicing! Mathematics is like a sport—the more you train, the stronger you get!