Addition and Subtraction Within 100

Welcome to the World of Numbers up to 100!

Hello, Math Explorer! In this chapter, we are going to become masters of Addition and Subtraction using numbers all the way up to 100. Whether you are counting marbles, sharing snacks, or saving up pocket money, knowing how to add and subtract quickly is like having a superpower!

Don't worry if these numbers look a bit big at first. We are going to break them down into small, easy steps. By the end of these notes, you will be a pro at "putting together" and "taking away"!

Step 1: The Secret Key - Place Value

Before we start adding and subtracting, let's remember our best friends: Tens and Ones. Every number up to 100 is made of these two parts.

Imagine Tens are like big boxes of 10 crayons, and Ones are just single crayons lying on the desk.

Example: The number 42 is just 4 Tens and 2 Ones. \( 40 + 2 = 42 \).

Quick Review: To add or subtract big numbers, we always look at the Ones first, then the Tens!

Step 2: Adding Without Regrouping

This is the easiest way to add! We just add the neighbors together. Let's try \( 23 + 15 \).

How to do it:
1. Look at the Ones: \( 3 + 5 = 8 \).
2. Look at the Tens: \( 2 + 1 = 3 \).
3. Put them together: 3 Tens and 8 Ones make 38!

Analogy: Think of it like a team. The "Ones Team" plays their game, and the "Tens Team" plays theirs. They don't mix yet!

Key Takeaway: Always start on the right side (the Ones) and move to the left (the Tens).

Step 3: The "Make a Ten" Trick (Addition with Regrouping)

Sometimes, the Ones get too crowded. If the Ones add up to 10 or more, they have to move some of their friends over to the Tens house. This is called Regrouping or "carrying over."

Let's try \( 27 + 5 \):
1. Add the Ones: \( 7 + 5 = 12 \).
2. Wait! 12 is too big for the "Ones" spot. 12 is actually 1 Ten and 2 Ones.
3. Keep the 2 in the Ones place.
4. Give the 1 Ten to the Tens house.
5. Now add the Tens: \( 2 + 1 (the extra one) = 3 \).
6. Your answer is 32!

Did you know? In the old days, people called this "carrying the one" because you literally carry the extra ten over to its new home!

Step 4: Subtraction Without Borrowing

Subtraction is just taking things away. Let's try \( 48 - 26 \).
1. Subtract the Ones: \( 8 - 6 = 2 \).
2. Subtract the Tens: \( 4 - 2 = 2 \).
3. Put them together: 22!

Common Mistake: Make sure you always put the bigger number on top or first. You can't eat 5 apples if you only have 2!

Step 5: "Borrowing" from a Neighbor (Subtraction with Regrouping)

What happens if you need to subtract a big number from a small number in the Ones place? Like \( 42 - 7 \)? You can't do \( 2 - 7 \). You need help!

How to borrow:
1. Look at the Ones: \( 2 - 7 \). Oops, not enough!
2. Go to your neighbor, the Tens. Ask, "Can I borrow a Ten?"
3. The 4 Tens become 3 Tens.
4. You give that Ten (which is 10 ones) to your 2. Now you have \( 10 + 2 = 12 \).
5. Now subtract the Ones: \( 12 - 7 = 5 \).
6. Now look at the Tens: You have 3 left. \( 3 - 0 = 3 \).
7. Your answer is 35!

Memory Aid: If there's "More on the floor, go next door and get ten more!"

Step 6: Mental Math Super-Tricks

You can do some math in your head very quickly using these tricks:

The "Plus 9" Trick

To add 9 to any number, just add 10 and then take 1 away.
Example: \( 35 + 9 \). Think \( 35 + 10 = 45 \). Then \( 45 - 1 = 44 \). So fast!

The "Friendly Numbers" Strategy

Try to get to a "friendly" number (a multiple of 10 like 10, 20, 30).
To solve \( 28 + 5 \), think: "I need 2 more to get to 30."
Take 2 from the 5, make 30, and you have 3 left over. \( 30 + 3 = 33 \).

Step 7: Solving Word Problems

Math isn't just numbers; it's stories! When reading a problem, look for these "Clue Words":

Addition Clue Words: Total, Sum, In all, Altogether, Plus, Combined.
Subtraction Clue Words: Difference, Left, Fewer, How many more, Take away.

Example Story: Sam has 45 stickers. He gives 12 to Maya. How many are left?
The word left tells us to subtract! \( 45 - 12 = 33 \).

Final Quick Review Box

- Always start with the ONES.
- Regrouping (Addition): If the ones make 10 or more, move the ten to the next column.
- Borrowing (Subtraction): If the top number is smaller, borrow 10 from the neighbor.
- Check your work: You can check subtraction by adding the answer back! If \( 10 - 3 = 7 \), then \( 7 + 3 \) should equal 10.

Great job! Mathematics takes practice, so don't worry if you need to read this a few times. You are doing a wonderful job building your math muscles! Keep exploring!