Hello, Super Mathematicians!
Welcome to the amazing world of Addition and Subtraction with two-digit numbers! Don't worry if big numbers seem a little tricky. We're going to break it all down into simple, easy steps. Learning this will help you with so many things in real life, like counting your pocket money, figuring out scores in a game, or sharing sweets with friends. Let's become number explorers together!
Section 1: A Quick Look at Tens and Units
Before we start adding and subtracting, let's remember what two-digit numbers are made of. Every two-digit number has a Tens place and a Units place.
For example, in the number 38:
8 is in the Units place. It just means 8 ones.
3 is in the Tens place. It means 3 tens, which is 30.
So, 38 is the same as 30 + 8. Understanding this will make everything else much easier!
Key Takeaway
Always remember the Tens and Units places. We always work with the Units column first!
Section 2: Addition of Two-Digit Numbers
Addition is all about putting numbers together to find the total, or the sum. Let's learn how to do this in columns.
Part A: Addition Without Carrying
This is the best place to start! It's when the numbers in the units column add up to less than 10.
Let's solve: $$42 + 25$$
Step 1: Line them up!
Write the numbers one on top of the other. Make sure the Units are under the Units and the Tens are under the Tens.
Step 2: Add the Units column.
Look at the column on the right. Add the numbers together. 2 + 5 = 7. Write the 7 under the units column.
Step 3: Add the Tens column.
Now, look at the column on the left. Add the numbers together. 4 + 2 = 6. Write the 6 under the tens column.
Answer: The sum is 67! You did it!
Part B: Addition With Carrying
Sometimes, when you add the units, the answer is 10 or more. We can't fit two digits in one column! So, we need to carry over the ten.
Think of it like this: If you have 13 building blocks, that's the same as one tower of 10 blocks and 3 single blocks. You move the tower of 10 over to the 'Tens' pile!
Let's solve: $$38 + 47$$
Step 1: Line them up.
$$ \begin{array}{c} & 3 & 8 \\ + & 4 & 7 \\ \hline \end{array} $$Step 2: Add the Units column.
8 + 7 = 15. This number has two digits! We write the 5 (from the Units place of 15) in the answer space. We carry the 1 (from the Tens place of 15) over to the top of the Tens column. We write a small '1' there to remind us.
Step 3: Add the Tens column.
Now we add ALL the numbers in the Tens column, including the little '1' we carried over! 1 + 3 + 4 = 8. Write the 8 under the tens column.
Answer: The sum is 85! Amazing work!
Memory Aid
"Units first, then the Tens. If the sum is ten or more, carry one next door!"
Watch Out! Common Mistake
A common mistake is forgetting to add the little '1' you carried over. Always check for a carried number before you add the tens column!
Did You Know?
When you add, the order doesn't matter! 15 + 12 gives you the same answer as 12 + 15. They both equal 27. It's a cool math trick!
Key Takeaway
For addition, always line up the numbers by their place value. Add the units first, and if the sum is 10 or more, write down the unit digit and carry the ten to the next column.
Section 3: Adding Three Numbers
Sometimes you need to add more than two numbers. The rule is simple: just add them from left to right.
Let's solve: $$15 + 10 + 20$$
Step 1: Add the first two numbers.
First, we solve $$15 + 10 = 25$$
Step 2: Add the next number to your result.
Now, we take our answer (25) and add the last number to it. $$25 + 20 = 45$$
Answer: So, $$15 + 10 + 20 = 45$$
Key Takeaway
When you see a sum with three numbers, just solve it in two simple steps, working from left to right.
Section 4: Subtraction of Two-Digit Numbers
Subtraction is about taking a number away from another one to find out what is left. The answer is called the difference.
Part A: Subtraction Without Borrowing
This is when the top digit in each column is bigger than the bottom digit.
Let's solve: $$68 - 34$$
Step 1: Line them up.
The bigger number always goes on top!
Step 2: Subtract the Units column.
8 - 4 = 4. Write the 4 in the answer space below.
Step 3: Subtract the Tens column.
6 - 3 = 3. Write the 3 in the answer space below.
Answer: The difference is 34. Well done!
Part B: Subtraction With Borrowing
This is what we do when the top unit is smaller than the bottom unit. We need to borrow from the Tens place next door.
Imagine this: The Units house has only 2 sweets but needs to give away 9. That's impossible! So, it asks the Tens house next door for help. The Tens house gives it one of its 'packs of ten'. Now the Units house has its original 2 plus the 10 it borrowed, which is 12 sweets!
Let's solve: $$72 - 49$$
Step 1: Line them up.
$$ \begin{array}{c} & 7 & 2 \\ - & 4 & 9 \\ \hline \end{array} $$Step 2: Look at the Units column.
We need to do 2 - 9. We can't do that! So, we need to borrow from the 7 in the Tens column.
We cross out the 7 and write a 6 above it. We 'borrowed' one ten.
We take that '1 ten' (which is 10 units) and give it to the 2 in the units column. So, 10 + 2 = 12. We cross out the 2 and write 12 above it.
Step 3: Subtract the new Units column.
Now we can subtract! 12 - 9 = 3. Write the 3 in the answer space.
Step 4: Subtract the new Tens column.
Remember, the 7 is now a 6! So we do 6 - 4 = 2. Write the 2 in the answer space.
Answer: The difference is 23. You're a subtraction superstar!
Watch Out! Common Mistake
Never just swap the numbers to make it easier (like doing 9 - 2 instead of 2 - 9). You must borrow from the tens column if the top unit is smaller!
Subtracting two numbers from a number
Just like with addition, we solve this from left to right.
Let's solve: $$80 - 20 - 15$$
Step 1: Subtract the first two numbers.
First, we solve $$80 - 20 = 60$$
Step 2: Subtract the next number from your result.
Now, we take our answer (60) and subtract the last number. $$60 - 15 = 45$$ (You might need to use borrowing for this step!)
Answer: So, $$80 - 20 - 15 = 45$$
Key Takeaway
For subtraction, always put the bigger number on top. Subtract the units first. If the top unit is smaller than the bottom one, borrow a ten from the tens column.
Section 5: How to Check Your Work!
Great mathematicians always check their answers. There's a very simple way to check your subtraction. You can use addition!
Addition and Subtraction are opposites, like a secret code and its key.
If you solved: $$72 - 49 = 23$$
To check it, you add the answer (23) to the number you subtracted (49).
$$ \begin{array}{c} & 2 & 3 \\ + & 4 & 9 \\ \hline \end{array} $$Do the sum (you'll need to carry!): 3 + 9 = 12 (write 2, carry 1). Then 1 + 2 + 4 = 7. The answer is 72.
Does it match the number we started with? Yes! So our subtraction was correct!
Key Takeaway
To check subtraction, add your answer to the bottom number. You should get the top number!
Section 6: Solving Word Problems
Let's use our new skills to solve some real-world puzzles!
Tips for Word Problems:
Read the problem carefully. What is it asking?
Find the key numbers.
Look for clue words!
Clue words for Addition: in total, altogether, sum, add, more.
Clue words for Subtraction: how many are left, take away, difference, fewer than, how many more.
Write down the sum and solve it.
Example 1 (Addition)
Leo has 35 red cars. He gets 17 blue cars for his birthday. How many cars does he have altogether?
The clue word is "altogether," so we add!
$$35 + 17 = 52$$Answer: Leo has 52 cars altogether.
Example 2 (Subtraction)
There are 50 birds in a tree. 28 of them fly away. How many birds are left?
The clue word is "left," so we subtract!
$$50 - 28 = 22$$Answer: There are 22 birds left in the tree.
Key Takeaway
Be a word problem detective! Look for the numbers and clue words to decide if you need to add or subtract. You've got this!