Subtraction (Three Digits) - Your Awesome Study Notes!
Hello, Super Mathematician!
Welcome to the amazing world of subtraction! You've already learned how to take away smaller numbers. Now, we're going to level up and learn how to subtract bigger, three-digit numbers. It's like being a detective and finding out what's left behind or what the difference is.
Why is this important? Knowing how to subtract big numbers helps you in real life! You can figure out how much money you have left after buying a toy, how many pages you still have to read in a book, or how many more points you need to win a game. Let's get started!
1. A Quick Review: What is Subtraction?
Remember, subtraction is all about 'taking away' one number from another. We can also use it to find the 'difference' between two numbers.
The symbol for subtraction is the minus sign (–).
Example: If you have 15 cookies and you eat 3, you are 'taking away' 3.
$$15 - 3 = 12$$You have 12 cookies left!
Key Takeaway
Subtraction means taking away, finding what's left, or finding the difference.
2. The Secret Power: Understanding Place Value
Before we subtract big numbers, we need our secret power: Place Value! Every digit in a number has its own special place and value.
For a three-digit number like 472, we have:
- The Hundreds place (H)
- The Tens place (T)
- The Ones place (O)
So, in 472:
- 4 is in the Hundreds place. It means 400.
- 7 is in the Tens place. It means 70.
- 2 is in the Ones place. It means 2.
Did you know?
Thinking about place value is like thinking about money! 4 hundreds, 7 tens, and 2 ones is like having four $100 bills, seven $10 coins, and two $1 coins. Cool, right?
3. Easy Peasy Subtraction: No Borrowing Needed!
Let's start with the easy kind of subtraction. This is when the top digit in each column is bigger than the bottom digit.
Let's solve: 586 - 243
Step-by-Step Guide:
Step 1: Line them up!
Write the numbers one on top of the other. Make sure the Ones, Tens, and Hundreds are in straight columns. This is super important!
H T O 5 8 6 - 2 4 3 ---------
Step 2: Start with the Ones!
Always, always, always start from the right side. Subtract the bottom digit from the top digit in the Ones column.
6 Ones - 3 Ones = 3 Ones
$$6 - 3 = 3$$
H T O
5 8 6
- 2 4 3
---------
3
Step 3: Move to the Tens!
Now, let's subtract the digits in the Tens column.
8 Tens - 4 Tens = 4 Tens
$$8 - 4 = 4$$
H T O
5 8 6
- 2 4 3
---------
4 3
Step 4: Finish with the Hundreds!
Finally, subtract the digits in the Hundreds column.
5 Hundreds - 2 Hundreds = 3 Hundreds
$$5 - 2 = 3$$H T O 5 8 6 - 2 4 3 --------- 3 4 3
So, the answer is 343!
Key Takeaway
For easy subtraction: Line up the numbers, start with the Ones, then subtract the Tens, and finally the Hundreds. Easy peasy lemon squeezy!
4. The Main Event: Subtraction with Borrowing!
Sometimes, the digit on the top is smaller than the digit on the bottom. Oh no! What do we do? Don't worry, this is where the fun begins! We use a trick called borrowing.
Analogy: The "Knock Next Door" Trick
Imagine you have 2 cookies (in the Ones place) but your friend asks for 5. You don't have enough! So, you "knock on the door" of your neighbor, the Tens place. The Tens place has whole boxes of cookies (each box has 10). You can borrow one whole box!
Let's solve: 342 - 125
Step 1: Line them up!
H T O 3 4 2 - 1 2 5 ---------
Step 2: Check the Ones. Can we subtract?
We need to do 2 - 5. We can't! The top number is smaller. Time to knock next door!
Step 3: Borrow from the Tens place!
We go to the Tens place (which has a 4) and borrow 1 Ten.
- The 4 in the Tens place becomes a 3.
- The 1 Ten we borrowed (which is equal to 10 Ones) is given to the Ones place.
- So, the 2 in the Ones place becomes 10 + 2 = 12.
3 12
H T O
3 4 2
- 1 2 5
-----------
Now we can subtract the Ones column! 12 - 5 = 7
$$12 - 5 = 7$$
3 12
H T O
3 4 2
- 1 2 5
-----------
7
Step 4: Subtract the Tens.
Remember, the 4 is now a 3. So we do 3 - 2.
3 12
H T O
3 4 2
- 1 2 5
-----------
1 7
Step 5: Subtract the Hundreds.
This one is easy! 3 - 1.
3 12
H T O
3 4 2
- 1 2 5
-----------
2 1 7
Our final answer is 217! You did it!
What if we need to borrow from the Hundreds?
It's the same idea! If the Tens digit on top is too small, you knock on the Hundreds' door.
Example: 728 - 453
In the Tens column, we can't do 2 - 5. So, we borrow 1 from the Hundreds place.
- The 7 in the Hundreds place becomes a 6.
- The 2 in the Tens place becomes 10 + 2 = 12.
Quick Review Box
- If the top digit is smaller, you must borrow!
- Go to the column on the left.
- Cross out the top digit, make it one smaller.
- Add 10 to the digit you were stuck on.
- Now you can subtract!
Common Mistakes to Avoid!
Mistake: Forgetting to make the number you borrowed from smaller.
Remember: If you borrow a box of cookies from your neighbor, they have one less box! Don't forget to change their number.
Key Takeaway
Borrowing is just moving a group of ten from one column to the next. It makes subtraction possible when a top digit is smaller than a bottom digit.
5. Being a Word Problem Detective
Subtraction isn't just about numbers; it's about solving real-life puzzles! Let's find the clues in word problems that tell us to subtract.
Clue Words for Subtraction:
- How many are left?
- What is the difference?
- How many more?
- How many fewer?
- Take away...
Let's Solve a Problem:
"The school library has 475 books. The students borrowed 138 books this week. How many books are left in the library?"
1. Understand the story: We start with a total number of books, and some are taken away. We need to find what's left. The word "left" is a big clue for subtraction!
2. Find the numbers: The important numbers are 475 and 138.
3. Solve it! Let's set up our subtraction problem.
$$475 - 138$$H T O 4 7 5 - 1 3 8 ---------
- Ones: We can't do 5 - 8. Borrow from the 7. The 7 becomes 6, and the 5 becomes 15. Now, 15 - 8 = 7.
- Tens: The 7 is now a 6. So, 6 - 3 = 3.
- Hundreds: 4 - 1 = 3.
Answer: There are 337 books left in the library.
Key Takeaway
Read word problems carefully and look for clue words. Once you know it's a subtraction story, just line up your numbers and solve!
You've done an amazing job!
Remember, practice makes you better and better. The more you practice subtracting, the easier it will become. Keep being a fantastic number detective!