Super Skills: Mixed Addition and Subtraction!

Hello Math Explorer! Are you ready to level up your math skills? In this chapter, we're going to learn how to solve problems that have both addition AND subtraction with big numbers. It's like solving a fun puzzle!

Learning this is super useful for everyday life, like figuring out how much money you have after buying sweets and getting your allowance, or counting how many video game levels you've completed and have left to go. Let's begin!


Part 1: A Quick Power-Up! (Review)

Before we mix things up, let's quickly remember how to add and subtract using the column method. This is a great tool for working with bigger numbers.

Adding with Carrying

Sometimes when you add the numbers in a column, the answer is 10 or more. We need to 'carry over' the ten to the next column on the left.

Example: Let's solve 148 + 75

$$ \begin{array}{@{}c@{\,}c@{}c} & \overset{1}{1} & \overset{1}{4} & 8 \\ + & & 7 & 5 \\ \hline & 2 & 2 & 3 \\ \end{array} $$

Step 1 (Units): 8 + 5 = 13. Write down the 3 and carry the 1 over to the tens column.
Step 2 (Tens): 1 + 4 + 7 = 12. Write down the 2 and carry the 1 over to the hundreds column.
Step 3 (Hundreds): 1 + 1 = 2. Write down the 2.
So, 148 + 75 = 223.

Subtracting with Borrowing

What if the top number in a column is smaller than the bottom number? We need to 'borrow' from our neighbour to the left!

Example: Let's solve 345 - 67

$$ \begin{array}{@{}c@{\,}c@{}c} & \overset{2}{\cancel{3}} & \overset{13}{\cancel{4}} & \overset{15}{\cancel{5}} \\ - & & 6 & 7 \\ \hline & 2 & 7 & 8 \\ \end{array} $$

Step 1 (Units): We can't do 5 - 7. So, we borrow 1 ten from the 4. The 4 becomes a 3, and the 5 becomes 15. Now we can do 15 - 7 = 8.
Step 2 (Tens): We can't do 3 - 6. So, we borrow 1 hundred from the 3. The 3 becomes a 2, and the 3 tens become 13 tens. Now we can do 13 - 6 = 7.
Step 3 (Hundreds): We have 2 left. 2 - 0 = 2.
So, 345 - 67 = 278.


Part 2: The Golden Rule: Left to Right

When you see a math problem with a mix of '+' and '-' signs but no brackets, there's one simple rule to follow.

The Golden Rule: Always work from left to right.

Think of it like reading a story in a book. You start at the beginning of the sentence (the left) and read towards the end (the right). We do the same in math!

Let's try it!

Example: Solve $$150 - 40 + 25$$

Step 1: Start with the first part on the left.

$$150 - 40 = 110$$

Step 2: Now, use the answer from Step 1 and finish the problem.

$$110 + 25 = 135$$

So, the final answer is 135!

Common Mistake Alert!

For $$150 - 40 + 25$$, some people might be tempted to do the addition first (40 + 25 = 65) and then subtract (150 - 65 = 85). This gives the wrong answer! Always, always go from left to right if there are no brackets.

Key Takeaway

For mixed addition and subtraction, if you don't see any brackets, just solve the problem in the order it appears, from left to right.


Part 3: The Superpower of Brackets! ()

Sometimes, you will see parts of a math problem inside these symbols: ( ). These are called brackets (or parentheses).

Brackets have a special power. They tell you: "Do this part first!"

Think of brackets as a VIP pass at a concert. The people with the VIP pass get to go in first, no matter where they are in the line! In a math problem, you MUST solve what's inside the brackets first.

Let's see the difference brackets make!

Example 1 (No Brackets): $$200 - 80 + 30$$

We use the left-to-right rule:

$$200 - 80 = 120$$

$$120 + 30 = 150$$

The answer is 150.


Example 2 (With Brackets): $$200 - (80 + 30)$$

The brackets have the superpower! We solve them first:

$$80 + 30 = 110$$

Now, we put this answer back into the problem:

$$200 - 110 = 90$$

The answer is 90.

Wow! See how the brackets changed the answer completely? They are very important!

Did you know?

The word "parenthesis" comes from Greek words meaning "to put beside". You are putting a special instruction beside the main problem!

Key Takeaway

When you see brackets ( ) in a problem, always solve the part inside the brackets first. Then, solve the rest of the problem.


Part 4: Putting It All Together - Solving Word Problems

Let's use our new superpowers to solve some real-world problems. The trick is to turn the words into a number sentence first.

Problem 1: The Library Trip

A library has 350 books on a shelf. On Monday, 25 people borrow books. On Tuesday, the librarian adds 40 new books to the shelf. How many books are on the shelf now?

Step 1: Turn the story into a math problem.

It starts with 350 books, then 25 are taken away (subtraction), then 40 are added (addition).

The problem is: $$350 - 25 + 40$$

Step 2: Solve it! There are no brackets, so we go left to right.

$$350 - 25 = 325$$

$$325 + 40 = 365$$

Answer: There are 365 books on the shelf.


Problem 2: The School Canteen

The canteen has 120 apples. A group of 30 students and 15 teachers each take one apple for lunch. How many apples are left?

Step 1: Turn the story into a math problem.

We need to find out the total number of people who took an apple first. This is a perfect time to use brackets!

The problem is: $$120 - (30 + 15)$$

Step 2: Solve it! The brackets get to go first.

$$30 + 15 = 45$$

Now, solve the rest:

$$120 - 45 = 75$$

Answer: There are 75 apples left.


Part 5: Smart Guesses - Estimation!

Before you do a big calculation, it's a great idea to make a "smart guess" or an estimate. This helps you know if your final answer is sensible.

To estimate, we round the numbers to the nearest 10 or 100 to make them easier to work with.

Example: Estimate the answer for $$497 - 104 + 248$$

Step 1: Round the numbers.
497 is very close to 500.
104 is very close to 100.
248 is very close to 250.

Step 2: Solve with the easy numbers.
Our estimated problem is $$500 - 100 + 250$$.
Left to right: $$500 - 100 = 400$$.
Then: $$400 + 250 = 650$$.
Our smart guess is about 650.

Step 3: Find the real answer.
$$497 - 104 = 393$$ $$393 + 248 = 641$$

Our estimate of 650 was very close to the real answer of 641! This tells us we probably did our calculation correctly. Good job!


Chapter Summary: You're a Math Whiz!

Congratulations! You've learned the secret rules for mixed addition and subtraction. Let's remember the main points:

The Two Super Rules:

1. If a problem has NO brackets, solve it by reading it like a book, from left to right.

2. If a problem HAS brackets ( ), solve the part inside the brackets FIRST!

Handy Tips:

- Always read word problems carefully to turn them into the correct number sentence.
- Use estimation to make a smart guess before you start. It helps you check if your final answer makes sense.
- Don't worry if this seems tricky at first. Practice makes perfect, and you'll be a pro in no time!