Unit 6 — Multi-Digit Addition and Subtraction

Welcome back!

Now that you understand place value, you are ready to work confidently with larger numbers.

Addition and subtraction are important skills used every day in shopping, science, engineering, finance, and many other areas of life.

Today you will strengthen your ability to solve problems accurately using multi-digit numbers.

Reviewing Addition

Addition combines two or more quantities.

Example:

   24,586
+  13,947
---------

Begin with the ones column.

Add each column from right to left.

Regroup (carry) whenever the sum in a column is 10 or greater.

Careful alignment of place values helps prevent mistakes.

Reviewing Subtraction

Subtraction finds the difference between two quantities.

Example:

   52,304
− 18,769
---------

Subtract each column from right to left.

If the top digit is smaller than the bottom digit, regroup (borrow) from the next place value.

Always check that digits remain correctly aligned.

Estimating Before Solving

Good mathematicians estimate before calculating.

Example:

24,586 + 13,947

Estimate:

25,000 + 14,000 ≈ 39,000

After solving exactly, compare your answer with the estimate.

If the answers are very different, check your work.

Solving Word Problems

Many real-world problems require addition or subtraction.

Example:

A library owned 18,745 books.

It purchased 2,865 more books.

How many books does the library own now?

Step 1:

Identify the important information.

Step 2:

Choose the correct operation.

Step 3:

Solve carefully.

Step 4:

Check whether your answer makes sense.

Checking Your Work

Always verify your answer.

You can check addition by using subtraction.

You can check subtraction by using addition.

Example:

If:

52,304 − 18,769 = 33,535

Then verify:

33,535 + 18,769 = 52,304

Checking helps catch simple mistakes.

Avoiding Common Errors

Watch for these common mistakes:

• misaligned place values
• forgetting to regroup
• borrowing from the wrong digit
• copying numbers incorrectly
• skipping a column

Working carefully is usually more important than working quickly.

Activity

Solve five addition problems and five subtraction problems using numbers greater than 10,000.

For each problem:

• estimate first
• solve exactly
• check your answer using the opposite operation

Explain how estimation helped you.

Practice

Answer these questions.

Why is place value important when adding and subtracting?

When do you regroup during addition?

When do you borrow during subtraction?

Why should you estimate before solving?

How can you check an addition problem?

How can you check a subtraction problem?

Review

Today you learned:

• multi-digit numbers must be aligned by place value
• regrouping makes addition possible when sums exceed nine
• borrowing allows subtraction when needed
• estimation helps judge whether answers are reasonable
• checking your work improves accuracy
• careful organization reduces mistakes

Strong addition and subtraction skills provide the foundation for more advanced mathematics.

Looking Ahead

Next we will learn multi-digit multiplication, discovering efficient methods for solving larger multiplication problems and applying them to real-world situations.