Welcome to the World of Subtraction!
Hello, Math Explorer! Get ready for an exciting adventure into subtraction. Subtraction is just a fancy word for "taking away". It helps us figure out what's left when we use, give away, or lose something.
For example, if you have 15 cookies and you eat 5, subtraction helps you know you have 10 left!
In this chapter, we will learn how to subtract numbers that have two digits. This is a super useful skill for things like counting your pocket money, sharing toys with friends, and so much more. Let's get started!
1. Quick Review: Our Friends, Tens and Ones
Before we start taking away, let's remember how two-digit numbers are built. They are made of Tens and Ones. This is called place value.
Think of it like this:
- Ones are like single building blocks.
- Tens are like a stack of 10 blocks already stuck together!
So, in the number 38:
- The 8 is in the Ones place. It means 8 single blocks.
- The 3 is in the Tens place. It means 3 stacks of ten blocks (which is 30).
Quick Review Box
Number: 52
Tens Digit: 5 (means 50)
Ones Digit: 2 (means 2)
Remembering Tens and Ones will make subtraction a piece of cake!
2. Easy Peasy Subtraction: No Borrowing Needed!
Let's start with the simplest kind of two-digit subtraction. This is what we use when the digits on top are bigger than the digits on the bottom in each column. Don't worry, we'll show you what that means!
The Column Method: Let's Get Organised!
The best way to subtract is using the column form. It helps keep our Tens and Ones in the right place.
Let's solve: 56 - 22
Step 1: Line them up!
Write the bigger number on top. Put the Tens in the Tens column and the Ones in the Ones column. It should look like this:
Step 2: Subtract the Ones column first.
A cool trick to remember: "Always start on the right, that's the way to do it right!"
We look at the Ones (O) column and do $$6 - 2$$.
$$6 - 2 = 4$$
We write the 4 in the answer space, under the Ones column.
$$ \begin{array}{c} & T & O \\ & 5 & 6 \\ - & 2 & 2 \\ \hline & & 4 \\ \end{array} $$Step 3: Subtract the Tens column.
Now we move to the Tens (T) column and do $$5 - 2$$.
$$5 - 2 = 3$$
We write the 3 in the answer space, under the Tens column.
$$ \begin{array}{c} & T & O \\ & 5 & 6 \\ - & 2 & 2 \\ \hline & 3 & 4 \\ \end{array} $$So, 56 - 22 = 34. You did it!
Let's Check Our Work!
Did you know that addition is the opposite of subtraction? We can use addition to check if our subtraction answer is correct!
To check, we add our answer to the smaller number we subtracted. It should equal the big number we started with.
Example: For 56 - 22 = 34, we can check by adding 34 + 22.
$$ \begin{array}{c} & 3 & 4 \\ + & 2 & 2 \\ \hline & 5 & 6 \\ \end{array} $$The answer is 56, which was our starting number. Hooray! Our answer is correct.
Key Takeaway
- Write numbers in columns (Tens and Ones).
- Subtract the Ones first, then the Tens.
- Check your answer by using addition.
3. Super Subtraction: Time to Borrow!
Now for a new challenge! Sometimes, the top digit in the Ones column is smaller than the bottom digit. What do we do? We borrow!
Don't worry if this seems tricky at first. It's like learning a cool new power-up in a game!
When Do We Need to Borrow?
Look at this problem: 42 - 17.
$$ \begin{array}{c} & T & O \\ & 4 & 2 \\ - & 1 & 7 \\ \hline \end{array} $$In the Ones column, we need to do $$2 - 7$$. But we can't take 7 away from 2! This is a sign that we need to borrow.
Memory Aid: "More on the floor? Go next door and get ten more!"
How Borrowing Works: A Real-World Example
Imagine you have 4 ten-dollar notes and 2 one-dollar coins ($42). You need to buy a toy for $17.
To pay the 7 one-dollars, you need more coins! So, you go to the cashier and "borrow" by changing one of your ten-dollar notes into 10 one-dollar coins.
Now you have:
- 3 ten-dollar notes
- 2 + 10 = 12 one-dollar coins
Step-by-Step Guide to Borrowing
Let's solve: 42 - 17
Step 1: Look at the Ones column.
Is the top digit (2) smaller than the bottom digit (7)? Yes! Time to borrow.
Step 2: Go "next door" to the Tens column.
The Tens column has a 4. We are going to borrow 1 Ten from it. So, we cross out the 4 and write a 3 above it.
Step 3: Give the borrowed Ten to the Ones column.
Remember, 1 Ten = 10 Ones. We add these 10 Ones to the 2 that's already there.
$$10 + 2 = 12$$
So, we cross out the 2 and write 12 above it.
Step 4: Now subtract the Ones.
Our new Ones column problem is $$12 - 7$$.
$$12 - 7 = 5$$
Write the 5 in the answer space under the Ones column.
$$ \begin{array}{c} & T & O \\ & \stackrel{3}{\cancel{4}} & \stackrel{12}{\cancel{2}} \\ - & 1 & 7 \\ \hline & & 5 \\ \end{array} $$Step 5: Subtract the Tens.
Our new Tens column problem is $$3 - 1$$.
$$3 - 1 = 2$$
Write the 2 in the answer space under the Tens column.
$$ \begin{array}{c} & T & O \\ & \stackrel{3}{\cancel{4}} & \stackrel{12}{\cancel{2}} \\ - & 1 & 7 \\ \hline & 2 & 5 \\ \end{array} $$So, 42 - 17 = 25. Amazing work!
Common Mistakes to Avoid
- Forgetting to change the Tens digit: When you borrow from the Tens column, always remember to make it one smaller!
- Adding 1 instead of 10: When you borrow, you are borrowing 1 Ten, which is worth 10 Ones. Make sure you add 10 to the Ones digit, not just 1.
Did you know?
The minus sign ( – ) we use for subtraction was first seen in a German math book written in 1489. That's over 500 years ago!
Key Takeaway
- If the top Ones digit is smaller than the bottom one, you need to borrow.
- Borrow 1 from the Tens column (making it one less).
- Add 10 to the Ones column.
- Then, subtract as usual!
4. Subtraction Challenge: Subtracting More Than Two Numbers
Sometimes you will see a problem with more than one subtraction sign. It looks like a chain!
Example: 68 - 20 - 5
The rule is simple: Work from left to right, one step at a time.
Step 1: Solve the first part of the chain.
First, we do $$68 - 20$$.
$$68 - 20 = 48$$
Step 2: Use the answer from Step 1 to solve the next part.
Now, our problem becomes $$48 - 5$$.
$$48 - 5 = 43$$
So, 68 - 20 - 5 = 43. Great job!
You solve it just like reading a book - from left to right!