Subtraction | Fourth Grade

Complete Notes & Formulas

1. Subtract Numbers Up to Five Digits

Definition: Subtracting numbers up to five digits means finding the difference between numbers from 10,000 to 99,999 using column subtraction with regrouping (borrowing).

📝 Steps for Subtracting Large Numbers:

Step 1: Write numbers in columns, aligning place values (larger number on top)
Step 2: Start subtracting from the ONES place (rightmost column)
Step 3: If top digit is smaller, BORROW from the next left column (add 10 to top digit, reduce left digit by 1)
Step 4: Move left through TENS, HUNDREDS, THOUSANDS, TEN THOUSANDS
Step 5: Continue borrowing when needed until all columns are subtracted

✏️ Example with Borrowing/Regrouping:

      ⁴ ⁱ⁶ ⁱ⁴ ⁱ²         (borrowing)
    7 5 , 6 4 2
  - 2 8 , 7 5 8
  ___________
    4 6 , 8 8 4

Step-by-step:

Ones: 2 < 8 → Borrow → 12 - 8 = 4
Tens: 3 (after borrow) < 5 → Borrow → 13 - 5 = 8
Hundreds: 5 (after borrow) < 7 → Borrow → 15 - 7 = 8
Thousands: 4 (after borrow) - 8 → Borrow → 14 - 8 = 6
Ten Thousands: 6 (after borrow) - 2 = 4

🔑 Key Formulas:

Difference = Minuend - Subtrahend

(Minuend = larger number, Subtrahend = number being subtracted)

Minuend = Difference + Subtrahend

2. Subtraction Word Problems

Definition: Real-world problems that require subtracting large numbers to find solutions.

📋 Steps to Solve Word Problems:

Step 1: Read the problem carefully and identify what you need to find
Step 2: Identify the larger number (minuend) and smaller number (subtrahend)
Step 3: Look for keywords: difference, left, remain, how many more, less than, fewer
Step 4: Subtract the numbers using column subtraction
Step 5: Write the answer with proper units (if applicable)

✏️ Example Problem:

Problem: A factory produced 85,423 toys in January and 58,765 toys in February. How many more toys were produced in January?

Solution:

Toys in January: 85,423

Toys in February: - 58,765

Difference = 85,423 - 58,765 = 26,658 toys

💡 Common Subtraction Keywords:

3. Subtraction: Fill in Missing Digits

Definition: Finding unknown digits in subtraction problems by using place value and borrowing logic.

🔍 Strategy to Find Missing Digits:

Step 1: Start from the ONES place (rightmost column)
Step 2: Check if borrowing was needed (if bottom > top in that column)
Step 3: Work backwards: If result + subtrahend = minuend, find missing digit
Step 4: Account for any borrowing from the next column
Step 5: Move to the next column and repeat

✏️ Example:

    6 □ 4 5 8
  - 2 4 □ 6 9
  ___________
    4 2 7 8 9

Solution:

Ones: 8 < 9 → Borrowed → 18 - 9 = 9 ✓
Tens: 4 (after borrow) - 6 → Need to borrow → 14 - 6 = 8 ✓
Hundreds: □ (after borrow) - □ = 7
If 4 - 1 (borrow) = 3, then 3 - 6 needs borrow → 13 - 6 = 7 ✓
So hundreds place missing digits: top = 4, bottom = 6
Thousands: □ (after borrow) - 4 = 2 → □ - 1 = 6 → □ = 7

Answer: Missing digits are 7, 4, and 6

💡 Key Tip:

Use the relationship: Minuend - Subtrahend = Difference OR Difference + Subtrahend = Minuend

4. Subtraction Patterns Over Increasing Place Values

Definition: Recognizing patterns when subtracting numbers with the same digits but different place values.

🔢 Pattern Rule:

If you know a basic subtraction fact, you can solve larger subtractions with the same digits!

Simply add the same number of zeros to your answer!

✏️ Pattern Examples:

Pattern 1: Basic fact 9 - 4 = 5

9 - 4 = 5 (ones)
90 - 40 = 50 (tens)
900 - 400 = 500 (hundreds)
9,000 - 4,000 = 5,000 (thousands)
90,000 - 40,000 = 50,000 (ten thousands)

Pattern 2: Basic fact 8 - 3 = 5

8 - 3 = 5
80 - 30 = 50
800 - 300 = 500
8,000 - 3,000 = 5,000
80,000 - 30,000 = 50,000

📐 Formula for Pattern:

If a - b = c, then (a × 10ⁿ) - (b × 10ⁿ) = c × 10ⁿ

(where n = number of zeros added)

5. Choose Numbers with a Particular Difference

Definition: Selecting specific numbers from a given set that have a target difference when subtracted.

🎯 Strategy to Find Numbers:

Step 1: Identify the target difference you need
Step 2: Look at all available numbers in the set
Step 3: Pick a number from the set (try the larger ones first)
Step 4: Subtract the target difference from that number
Step 5: Check if the result is in the set

✏️ Example Problem:

Available numbers: 15,234 | 28,567 | 42,891 | 31,345 | 54,236

Target Difference: 22,891

Solution:

Try largest: 54,236 - 22,891 = 31,345

Check: Is 31,345 in the set? YES! ✓

Answer: 54,236 and 31,345

💡 Key Tips:

Use the formula: Larger Number - Smaller Number = Difference
Or: Smaller Number + Difference = Larger Number
Try different combinations systematically
Start with extreme values (largest or smallest numbers)

6. Estimate Differences

Definition: Finding an approximate answer by rounding numbers before subtracting them.

📝 Steps to Estimate Differences:

Step 1: Decide what place value to round to (nearest 10, 100, 1000, etc.)
Step 2: Round both numbers to that place value
Step 3: Subtract the rounded numbers
Step 4: Write "≈" (approximately equals) symbol

✏️ Examples of Estimating Differences:

Example 1: Estimate to nearest 10

Subtract: 87 - 43

Round: 90 - 40

Estimated Difference: 50

(Actual difference = 44)

Example 2: Estimate to nearest 100

Subtract: 876 - 423

Round: 900 - 400

Estimated Difference: 500

(Actual difference = 453)

Example 3: Estimate to nearest 1,000

Subtract: 78,654 - 32,891

Round: 79,000 - 33,000

Estimated Difference: 46,000

(Actual difference = 45,763)

📐 Estimation Formula:

Estimated Difference ≈ Rounded Minuend - Rounded Subtrahend

🎯 When to Use Estimation:

When you need a quick approximate answer
To check if your exact answer is reasonable
When exact values are not needed
To compare large numbers quickly

7. Estimate Differences: Word Problems

Definition: Real-life problems where you estimate differences by rounding to find approximate answers.

📋 Steps for Word Problems:

Step 1: Read the problem and identify numbers to subtract
Step 2: Look for keywords: about, approximately, estimate, around, roughly
Step 3: Decide which place value to round to
Step 4: Round both numbers
Step 5: Subtract rounded numbers and write answer with units

✏️ Example Word Problems:

Problem 1: A stadium has 67,854 seats. During a match, 39,276 people attended. About how many seats were empty?

Solution:

Round to nearest thousand:

67,854 ≈ 68,000

39,276 ≈ 39,000

68,000 - 39,000 = 29,000

Answer: About 29,000 empty seats

Problem 2: A company earned ₹85,432 in sales last month and ₹56,789 this month. Estimate the decrease in sales.

Solution:

Round to nearest thousand:

85,432 ≈ 85,000

56,789 ≈ 57,000

85,000 - 57,000 = 28,000

Answer: About ₹28,000 decrease

💡 Estimation Keywords:

Subtraction Quick Reference Chart

Concept	Key Formula/Rule
Basic Subtraction	Difference = Minuend - Subtrahend
Inverse Operation	Minuend = Difference + Subtrahend
Borrowing/Regrouping	When top digit < bottom digit, borrow 10 from left
Pattern Rule	If 9-4=5, then 90-40=50, 900-400=500
Choosing Pairs	Larger Number - Smaller Number = Difference
Estimation	Round both numbers, then subtract
Word Problem Keywords	Difference, Left, Remain, How Many More, Less Than