Super Subtraction: Taking on Big Numbers!
Hello, Math Explorer! Are you ready to learn a super useful skill? This chapter is all about subtraction. That's just a fancy word for "taking away".
We use subtraction every day! When you spend your pocket money, when you eat some sweets from a jar, or when you figure out how many days are left until your birthday, you're subtracting! In these notes, we'll learn how to subtract bigger numbers, even when it gets a little tricky. Let's get started!
1. Subtraction Made Easy: Using Columns!
When we need to subtract bigger numbers, the easiest way is to line them up in columns. This is called column subtraction. It helps us keep everything neat and tidy.
Quick Review: Place Value
Remember place value? It's what makes a number big or small.
- Example: In the number 75, the '5' is in the Units (or Ones) place, and the '7' is in the Tens place.
How to Subtract in Columns (No Tricky Stuff Yet!)
Let's try subtracting 23 from 58. The problem is 58 - 23.
Step 1: Line them up!
Put the bigger number on top. Make sure the Units are under the Units, and the Tens are under the Tens.
Step 2: Start with the Units!
Always, always, always start on the right side, with the Units column. Subtract the bottom number from the top number.
In the Units column, we have 8 - 3. What's that? It's 5!
$$ \begin{array}{r} & T & U \\ & 5 & 8 \\ - & 2 & 3 \\ \hline & & 5 \\ \end{array} $$Step 3: Move to the Tens!
Now, let's do the Tens column. Subtract the bottom number from the top number.
In the Tens column, we have 5 - 2. That's 3!
$$ \begin{array}{r} & T & U \\ & 5 & 8 \\ - & 2 & 3 \\ \hline & 3 & 5 \\ \end{array} $$So, 58 - 23 = 35. See? You did it!
Become a Math Detective: Checking Your Answer!
Here's a cool trick to see if your answer is correct. Addition and subtraction are opposites! To check your subtraction, you can use addition.
Just add the answer you got to the smaller number you subtracted. It should equal the big number you started with!
Our problem was 58 - 23 = 35.
Let's check: 35 (our answer) + 23 (the small number) = ?
It's 58! That matches our starting number, so our answer is correct! Hooray!
Key Takeaway
For simple subtraction, line up the numbers in Tens and Units columns, subtract the Units first, then the Tens. You can always check your answer using addition!
2. Super Subtraction: The Power of Borrowing!
Sometimes, the top digit in a column is smaller than the bottom digit. Uh oh! What do we do? We borrow! Don't worry, it's easier than it sounds.
What is Borrowing?
Think of it like this: The Units column needs more, so it asks its friendly neighbour, the Tens column, for help. The Tens column lends a "ten" to the Units column.
Memory Aid: More on the floor? Go next door and get ten more!
Let's Try It: Subtraction with Borrowing
Let's solve 42 - 17.
Step 1: Line them up.
$$ \begin{array}{r} & T & U \\ & 4 & 2 \\ - & 1 & 7 \\ \hline \end{array} $$Step 2: Check the Units.
We need to do 2 - 7. But we can't! The 2 is too small. More on the floor (7) than on top (2)! Time to go next door!
Step 3: Borrow from the Tens.
Go to the Tens column. We have a 4. We "borrow" one ten from it. So, the 4 becomes a 3. We cross out the 4 and write a little 3 above it.
Step 4: Give the ten to the Units.
The ten we borrowed goes over to the Units column. The 2 becomes 12 (because 10 + 2 = 12).
Step 5: Subtract the Units.
Now we can subtract! What is 12 - 7? It's 5!
Step 6: Subtract the Tens.
Remember, our 4 is now a 3. What is 3 - 1? It's 2!
So, 42 - 17 = 25. You are a borrowing superstar!
Borrowing with Bigger Numbers (3 digits!)
The same idea works for even bigger numbers. Let's try 365 - 128.
1. Units: Can't do 5 - 8. So, borrow from the 6 in the Tens place. The 6 becomes a 5, and the 5 becomes a 15. Now, 15 - 8 = 7.
2. Tens: We now have 5 - 2. We can do that! 5 - 2 = 3.
3. Hundreds: 3 - 1 = 2.
The answer is 237!
Key Takeaway
When the top digit is smaller than the bottom digit, you need to borrow. Go to the column on the left, take one from it, and add ten to your current column.
3. Subtraction Chains: Working Left to Right
What if you see a problem like 50 - 10 - 5? It looks long, but it's simple if you remember one rule: work from left to right.
Step 1: Solve the first part.
First, we solve 50 - 10.
$$50 - 10 = 40$$
Step 2: Use that answer for the next part.
Now our problem is simpler: 40 - 5.
$$40 - 5 = 35$$
So, 50 - 10 - 5 = 35. Easy peasy!
Key Takeaway
For a problem with more than one subtraction sign, just solve it one piece at a time, moving from left to right.
4. Mix It Up: Adding and Subtracting Together!
The "left to right" rule is also super important when you see addition and subtraction in the same problem!
Let's try 88 - 22 + 10.
Step 1: Solve the first part on the left.
The first part is 88 - 22.
$$88 - 22 = 66$$
Step 2: Use the answer for the next part.
Now we have 66 + 10.
$$66 + 10 = 76$$
So, 88 - 22 + 10 = 76.
Did you know?
This "left-to-right" rule is part of the Order of Operations. It's like a set of rules all mathematicians follow to make sure everyone gets the same answer to a problem. You'll learn more about this as you get older!
Key Takeaway
When a math problem has a mix of `+` and `-` signs, just work straight across from left to right.
5. Math in the Real World: Solving Subtraction Stories
The best part about math is using it to solve real problems! Let's try a few.
Tip: Look for clue words in the story that tell you to subtract, like:
- how many are left?
- what is the difference?
- how many more?
Problem 1:
A baker makes 95 bread rolls. He sells 78 of them. How many rolls are left?
This is a subtraction problem: 95 - 78.
$$ \begin{array}{r} & \stackrel{8}{\cancel{9}} & \stackrel{15}{5} \\ - & 7 & 8 \\ \hline & 1 & 7 \\ \end{array} $$Answer: There are 17 rolls left.
Problem 2:
Leo has 50 building blocks. He uses 18 to build a tower, and then 12 to build a car. How many blocks are left?
This is a subtraction chain: 50 - 18 - 12. Remember, left to right!
First part: 50 - 18 = 32
Second part: 32 - 12 = 20
Answer: Leo has 20 blocks left.
You've done an amazing job! You now have the skills to subtract multi-digit numbers, check your answers, and solve real-world problems. Keep practicing, and you'll be a subtraction expert in no time!