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

Mental Warm-Up!

Quick Subtraction

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

Mental Warm-Up: Answers

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

When Do We Subtract?

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

Subtraction Vocabulary

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!

Subtraction Without Regrouping

Example 1

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

Let's solve this...

Example 1: Solution

  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

Easy!

When Do We 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!

How to Regroup (Borrow)

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!

Example 2: Subtraction WITH Regrouping

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

This needs lots of regrouping!

Example 2: Step-by-Step (Ones & 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

Example 2: Continued (Hundreds & 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

Example 2: Final Steps

  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

Special Case: Subtracting from Zeros!

Example 3

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

All zeros! How do we borrow?

Subtracting from Zeros: Solution

  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

Word Problem!

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?

Word Problem: Solution

We need to SUBTRACT!

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

Answer: 3,333,222 people remained

Practice Problem 1

Try This!

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

Work through it step by step!

Practice Problem 1: Answer

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

Did you remember to regroup?

Practice Problem 2

Larger Numbers

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

Practice Problem 2: Answer

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

Great work!

Practice Problem 3

Subtracting from Millions

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

Watch out for those zeros!

Practice Problem 3: Answer

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

Word Problem Practice 1

School Graduation

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

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

Word Problem 1: Answer

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

2,675 learners remain in the school

Word Problem Practice 2

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
-----------
      ?

Word Problem 2: Answer

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

Uganda exported 5,308,643 kg more

Quick Assessment ✓

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: 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 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

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 ✓

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 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

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!

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 can now subtract large numbers with regrouping!

Next lesson: Multiplication of Large Numbers

Keep practicing your skills!