Subtraction of Whole Numbers with Regrouping

P6 Mathematics - Term I, Topic 3

Lesson 2 of 5

Learning Objectives:

• Subtract whole numbers with regrouping up to 7 digits
• Use correct subtraction vocabulary
• Solve word problems involving subtraction

Warm-Up: Quick Mental Subtraction Facts

Quick Subtraction

1. 90 - 40 = ?
2. 800 - 300 = ?
3. 7,000 - 2,000 = ?
4. 50,000 - 20,000 = ?

Checking the Warm-Up Answers Together

1. 90 - 40 = 50
2. 800 - 300 = 500
3. 7,000 - 2,000 = 5,000
4. 50,000 - 20,000 = 30,000

Where We Use Subtraction Daily

Real-Life Examples

• Shopping: Finding change
• Comparison: How many more/less?
• Distance: How much farther?
• Population: People who left
• Stock: Items sold or remaining
• Money: Calculating balance

Learning the Vocabulary of Subtraction

Different Ways to Say "Subtract"

• Difference → What is the difference between 100 and 40? = 60
• Take away → Take away 25 from 80 = 55
• Minus → 500 minus 200 = 300
• Less than → 30 less than 100 = 70

They all mean SUBTRACTION!

Subtracting with No Regrouping Needed

Example 1

  876,543
- 234,321
---------

Let's solve this...

Solving Example 1 Step by Step

  876,543
- 234,321
---------
  642,222

• Ones: 3 - 1 = 2
• Tens: 4 - 2 = 2
• Hundreds: 5 - 3 = 2
• Thousands: 6 - 4 = 2
• Ten-thousands: 7 - 3 = 4
• Hundred-thousands: 8 - 2 = 6

Recognizing When You Need to Regroup

The Big Question

When the top digit is SMALLER than the bottom digit!

Examples:

• 2 - 7 → Need to regroup!
• 5 - 8 → Need to regroup!
• 0 - 4 → Need to regroup!

Solution: Borrow 1 from the next place value!

The Steps for Borrowing a Digit

The Process

Can't do 2 - 7?

1. Borrow 1 from the next column (tens)
2. The 2 becomes 12
3. Now: 12 - 7 = 5
4. The next column reduces by 1

Remember: What you borrow, you must pay back!

A Bigger Example with Regrouping

  543,210
- 287,654
---------

This needs lots of regrouping!

Borrowing in the Ones and Tens

  ⁴¹³⁻¹²⁻¹¹⁰
  543,210
- 287,654
---------
      56

Ones: Can't do 0 - 4

• Borrow from tens: 10 - 4 = 6

Tens: Now 0, can't do 0 - 5

• Borrow from hundreds: 10 - 5 = 5

Continuing into Hundreds and Thousands

  ⁴¹³⁻¹²⁻¹¹⁰
  543,210
- 287,654
---------
     556

Hundreds: Now 1, can't do 1 - 6

• Borrow from thousands: 11 - 6 = 5

Thousands: Now 2, can't do 2 - 7

• Borrow from ten thousands: 12 - 7 = 5

Finishing Off the Regrouping Example

  ⁴¹³⁻¹²⁻¹¹⁰
  543,210
- 287,654
---------
  255,556

Ten thousands: Now 3, can't do 3 - 8

• Borrow from hundred thousands: 13 - 8 = 5

Hundred thousands: Now 4

• 4 - 2 = 2

Answer: 255,556

Subtracting Across a String of Zeros

Example 3

  8,000,000
- 3,456,789
-----------

All zeros! How do we borrow?

The Trick for Borrowing Across Zeros

  ⁷⁹⁹⁹⁹⁹⁹⁻¹⁰
  8,000,000
- 3,456,789
-----------
  4,543,211

Strategy: Borrow across all the zeros!

• 8 becomes 7
• Each 0 becomes 9 (except the last, which becomes 10)

The Golden Rules of Subtraction

1. Line up numbers by place value
2. Start from the ones place (right side)
3. Borrow when top digit is smaller
4. Reduce the borrowed-from digit by 1
5. Check by adding your answer to the bottom number

A Word Problem About Population

Population Change

Problem: A district had 5,678,900 people in 2020. By 2023, 2,345,678 people moved to cities. How many remained?

What operation do we use?

Solving the Population Word Problem

We need to SUBTRACT!

  5,678,900
- 2,345,678
-----------
  3,333,222

Answer: 3,333,222 people remained

Practice Problem: Try It Yourself

Try This!

  654,321
- 234,567
---------
    ?

Work through it step by step!

Practice Problem 1: The Answer

  ⁵¹⁴⁻¹³⁻¹²⁻¹¹¹
  654,321
- 234,567
---------
  419,754

Did you remember to regroup?

More Practice with Larger Numbers Here

Larger Numbers

  9,876,543
- 1,234,567
-----------
      ?

Practice Problem 2: The Answer

  ⁸¹⁷⁻¹⁶⁻¹⁵⁻¹⁴⁻¹³
  9,876,543
- 1,234,567
-----------
  8,641,976

Great work!

Practice: Subtracting from the Millions

Subtracting from Millions

  7,000,000
- 2,456,789
-----------
      ?

Watch out for those zeros!

Practice Problem 3: The Answer

  ⁶⁹⁹⁹⁹⁹⁹⁻¹⁰
  7,000,000
- 2,456,789
-----------
  4,543,211

Word Problem About School Graduation Day

School Graduation

Problem: A school had 4,567 learners. 1,892 graduated. How many remain?

  4,567
- 1,892
-------
   ?

The School Graduation Problem, Answered

  ³¹⁵⁻¹⁶⁻¹⁷
  4,567
- 1,892
-------
  2,675 learners

2,675 learners remain in the school

Word Problem: Comparing Coffee Exports

Coffee Export Comparison

Problem: Uganda exported 8,765,432 kg of coffee. Kenya exported 3,456,789 kg. What is the difference?

  8,765,432
- 3,456,789
-----------
      ?

Coffee Export Comparison: The Answer

  ⁷¹⁶⁻¹⁵⁻¹⁴³²
  8,765,432
- 3,456,789
-----------
  5,308,643 kg

Uganda exported 5,308,643 kg more

Quick Assessment: Check Your Understanding

1. Subtract: 543,210 - 234,567 = ?

2. When subtracting, which place do we start from?

3. When do we need to regroup (borrow)?

Quick Assessment: The Correct Answers

1. 543,210 - 234,567 = 308,643

2. Start from the ones place (right side)

3. When the top digit is smaller than the bottom digit

Common Subtraction Mistakes to Avoid

Don't do this:

• Subtracting smaller from larger (wrong order)
• Forgetting to reduce after borrowing
• Not borrowing across zeros correctly
• Not lining up by place value

How to Fix Each Common Mistake

Do this instead:

• Keep the order correct (top - bottom)
• Mark your regrouping clearly
• Borrow across all zeros when needed
• Carefully align digits

Checking Your Answer with Addition

Use Addition!

If 8,765,432 - 3,456,789 = 5,308,643

Then 5,308,643 + 3,456,789 = 8,765,432 ✓

Your answer + bottom number = top number

Summary: What We Learned Today

Today we learned to:

• Subtract numbers up to 7 digits with regrouping
• Use different subtraction vocabulary
• Borrow from the next place value
• Handle zeros in subtraction
• Solve real-life word problems
• Check answers using addition

Homework: More Practice Problems Ahead

1. 876,543 - 234,567 = ?
2. 6,543,210 - 2,987,654 = ?
3. 9,000,000 - 4,567,890 = ?
4. Word problem: A farmer had 567,890 kg of maize. He sold 234,567 kg. How much remains?

Check each answer by adding!

Remember the Steps for Next Time

1. Line up by place value
2. Start from the ones
3. Borrow when top < bottom
4. Reduce the borrowed-from digit
5. Check by adding

Practice makes perfect!

Well Done, You've Mastered Subtraction

You can now subtract large numbers with regrouping!

Next lesson: Multiplication of Large Numbers

Keep practicing your skills!