➖ Subtraction - Grade 3

What is Subtraction?

Subtraction is taking away one number from another to find the difference!

\(\text{Minuend} − \text{Subtrahend} = \text{Difference}\)

In Grade 3, we learn to subtract numbers up to three digits (up to 999)!

🔢 Subtract Numbers Up to Three Digits

Parts of Subtraction

🔵 Minuend: The number we start with (larger number)
🔵 Subtrahend: The number we take away (smaller number)
🔵 Difference: The answer (what's left)

Example: \(567 − 234 = 333\)
Minuend: \(567\) | Subtrahend: \(234\) | Difference: \(333\)

Steps to Subtract 3-Digit Numbers

Line up the numbers by place value (ones under ones, tens under tens, hundreds under hundreds)
Start from the ONES place (rightmost column)
Subtract each column from right to left
Regroup (borrow) if needed (when top digit is smaller)
Write the final answer

Subtraction Without Regrouping

Example: \(589 − 234\)

5 8 9
− 2 3 4
-------
3 5 5

Step 1 - Ones: \(9 − 4 = 5\)
Step 2 - Tens: \(8 − 3 = 5\)
Step 3 - Hundreds: \(5 − 2 = 3\)

Answer: \(589 − 234 = 355\) ✓

Subtraction With Regrouping (Borrowing)

Example: \(524 − 167\)

   5⁴ 2¹ 4¹⁴
   5 2 4
− 1 6 7
-------
   3 5 7

Step 1 - Ones: \(4 < 7\), so borrow!
• Borrow \(1\) ten from tens place → tens becomes \(1\)
• Ones becomes \(14\)
• Now: \(14 − 7 = 7\)

Step 2 - Tens: \(1 < 6\), so borrow again!
• Borrow \(1\) hundred from hundreds place → hundreds becomes \(4\)
• Tens becomes \(11\)
• Now: \(11 − 6 = 5\)

Step 3 - Hundreds: \(4 − 1 = 3\)

Answer: \(524 − 167 = 357\) ✓

Subtraction With Zeros

Example: \(500 − 237\)

When there are zeros, we need to borrow from the next non-zero digit!

Step 1: Can't subtract \(0 − 7\), so borrow
• Tens is also \(0\), so borrow from hundreds
• \(5\) hundreds becomes \(4\) hundreds
• \(0\) tens becomes \(10\) tens, then becomes \(9\) tens (after giving \(1\) to ones)
• \(0\) ones becomes \(10\) ones

Now: \(10 − 7 = 3\) (ones)
\(9 − 3 = 6\) (tens)
\(4 − 2 = 2\) (hundreds)

Answer: \(500 − 237 = 263\) ✓

Key Formula:

\(\text{Difference} = \text{Minuend} − \text{Subtrahend}\)

When top digit \(<\) bottom digit,
Regroup: borrow \(1\) from the next left column

✓ Check Your Answer!

Use addition to check subtraction:
\(\text{Difference} + \text{Subtrahend} = \text{Minuend}\)

Example: If \(524 − 167 = 357\)
Check: \(357 + 167 = 524\) ✓ Correct!

📊 Subtraction Input/Output Tables

What is a Subtraction Input/Output Table?

A subtraction input/output table uses a rule to subtract from input numbers!

\(\text{Output} = \text{Input} − \text{Rule}\)

Example: Finding the Rule

Input	Output
\(567\)	\(367\)
\(845\)	\(645\)
\(923\)	\(723\)

Finding the Rule:
\(567 - 367 = 200\)
\(845 - 645 = 200\)
\(923 - 723 = 200\)

Rule: Subtract \(200\)
Formula: \(\text{Output} = \text{Input} − 200\) ✓

Finding Missing Values

If rule is "subtract \(150\)" and input is \(456\):
Output: \(456 − 150 = 306\)

If rule is "subtract \(125\)" and output is \(375\):
Input: \(375 + 125 = 500\)

⚖️ Balance Subtraction Equations

What is a Balanced Equation?

A balanced equation means both sides of the equal sign (\(=\)) have the same value!

\(\text{Left Side} = \text{Right Side}\)

Steps to Balance Equations

Solve the complete side first
Find what value the other side must equal
Find the missing number
Check your answer

Examples

Example 1: Missing Minuend

Problem: \(? − 234 = 345\)

Step 1: The difference is \(345\)
Step 2: To find the minuend, add difference and subtrahend
Step 3: \(? = 345 + 234 = 579\)
Check: \(579 − 234 = 345\) ✓
Answer: \(? = 579\)

Example 2: Both Sides Have Subtraction

Problem: \(567 − 123 = 789 − ?\)

Step 1: Left side: \(567 − 123 = 444\)
Step 2: Right side must also equal \(444\)
Step 3: \(789 − ? = 444\)
Step 4: \(? = 789 − 444 = 345\)
Check: \(567 − 123 = 444\) and \(789 − 345 = 444\) ✓
Answer: \(? = 345\)

Key Formulas:

If \(a − b = c\), then:
\(a = c + b\) (Minuend = Difference + Subtrahend)
\(b = a − c\) (Subtrahend = Minuend − Difference)

✍️ Complete the Subtraction Sentence

What Does This Mean?

You need to find the missing number to make the subtraction sentence true!

Three Types of Missing Numbers

Type 1: Missing Minuend

Problem: \(? − 345 = 234\)

Solution: Add difference and subtrahend
\(? = 234 + 345 = 579\) ✓

Formula: \(\text{Minuend} = \text{Difference} + \text{Subtrahend}\)

Type 2: Missing Subtrahend

Problem: \(678 − ? = 234\)

Solution: Subtract difference from minuend
\(? = 678 − 234 = 444\) ✓

Formula: \(\text{Subtrahend} = \text{Minuend} − \text{Difference}\)

Type 3: Missing Difference

Problem: \(789 − 345 = ?\)

Solution: Subtract the two numbers
\(? = 789 − 345 = 444\) ✓

Formula: \(\text{Difference} = \text{Minuend} − \text{Subtrahend}\)

Quick Reference:

Missing the first number? ADD
Missing the second number? SUBTRACT
Missing the answer? SUBTRACT

📈 Subtraction Patterns Over Increasing Place Values

What Are Subtraction Patterns?

When you know a simple subtraction fact, you can use it to solve subtractions with larger numbers!

If you know \(8 − 3 = 5\),
Then you also know:
\(80 − 30 = 50\)
\(800 − 300 = 500\)

How It Works

Pattern 1: Basic Fact

\(9 − 4 = 5\)

Pattern 2: Tens

\(90 − 40 = 50\)
(Same digits, but one zero added)

Pattern 3: Hundreds

\(900 − 400 = 500\)
(Same digits, but two zeros added)

More Examples

If \(7 − 2 = 5\), then:
• \(70 − 20 = 50\)
• \(700 − 200 = 500\)

If \(15 − 8 = 7\), then:
• \(150 − 80 = 70\)
• \(1,500 − 800 = 700\)

If \(12 − 5 = 7\), then:
• \(120 − 50 = 70\)
• \(1,200 − 500 = 700\)

Important Rule:

The pattern works when BOTH numbers
have the same number of zeros!

\(\text{Basic Difference} \times 10^n = \text{Larger Difference}\)
(where \(n\) = number of zeros)

🔍 Subtraction: Fill in the Missing Digits

What Does This Mean?

Some digits in the subtraction problem are missing! You need to figure out what they are by using subtraction rules!

Strategies to Find Missing Digits

Start with the ones column (rightmost)
Use what you know about subtraction
Look for borrowing clues
Work column by column
Check if your answer makes sense

Example Problems

Example 1: Missing Digit in Difference

6 8 9
− 2 3 4
-------
4 ? 5

Step 1 - Ones: \(9 − 4 = 5\) ✓
Step 2 - Tens: \(8 − 3 = ?\)
\(8 − 3 = 5\), so \(? = 5\)
Step 3 - Hundreds: \(6 − 2 = 4\) ✓

Answer: The missing digit is \(5\) ✓

Example 2: Missing Digit in Minuend

? 6 8
− 2 3 2
-------
5 3 6

Step 1 - Ones: \(8 − 2 = 6\) ✓
Step 2 - Tens: \(6 − 3 = 3\) ✓
Step 3 - Hundreds: \(? − 2 = 5\)
What minus \(2\) equals \(5\)? Answer: \(7\)
So \(? = 7\)

Answer: The missing digit is \(7\) ✓
Complete number: \(768\)

Example 3: With Regrouping

5 ? 3
− 1 6 5
-------
3 5 8

Step 1 - Ones: \(3 < 5\), so we borrowed!
\(13 − 5 = 8\) ✓ (This confirms borrowing happened)

Step 2 - Tens: After giving \(1\) to ones, \(? − 1\)
\((? − 1) − 6 = 5\)
\(? − 1 − 6 = 5\)
\(? − 7 = 5\)
\(? = 12\), but since we borrowed, the original digit was \(12 + 1 = 13\)... wait, that's not right.

Let me recalculate: If the tens digit after borrowing minus \(6\) equals \(5\), then:
\((? − 1) − 6 = 5\)
\(? − 1 = 11\)
\(? = 12\), but \(12\) is two digits!

Actually: The digit \(?\) became \((? − 1)\) after giving to ones.
\((? − 1) − 6 = 5\)
\(? − 1 = 11\)
\(? = 12\), so we need to borrow from hundreds too!
Original \(?\) was \(2\), became \(12\) after borrowing from hundreds, then \(11\) after giving to ones.
\(11 − 6 = 5\) ✓

Answer: The missing digit is \(2\) ✓
Complete number: \(523\)

📖 Subtraction Word Problems

Key Words for Subtraction

✓ Difference - How much more/less?
✓ Take away - Remove
✓ Left - Remaining
✓ Remaining - What's left
✓ Less - Fewer
✓ Minus - Subtract
✓ How many more - Compare
✓ Decrease - Goes down
✓ Fewer - Less than

Steps to Solve Word Problems

Read the problem carefully (maybe twice!)
Circle or underline the numbers
Look for subtraction key words
Identify which number is bigger (minuend)
Write the subtraction sentence
Solve the problem
Check your answer - Does it make sense?
Write the answer with labels (books, students, etc.)

Example Problems

Problem 1: Take Away

A library has 678 books. They gave away 234 books to another library. How many books are left?

Step 1: Numbers: \(678\) and \(234\)
Step 2: Key words: "gave away" and "left" → Subtraction!
Step 3: Subtraction sentence: \(678 − 234 = ?\)
Step 4: Solve: \(678 − 234 = 444\)
Answer: There are \(444\) books left in the library. ✓

Problem 2: Comparison

School A has 845 students. School B has 567 students. How many more students does School A have than School B?

Step 1: Numbers: \(845\) and \(567\)
Step 2: Key words: "how many more" → Subtraction!
Step 3: Subtraction sentence: \(845 − 567 = ?\)
Step 4: Solve: \(845 − 567 = 278\)
Answer: School A has \(278\) more students than School B. ✓

Problem 3: Finding the Missing Part

Maria had some stickers. She gave 156 stickers to her friend. Now she has 289 stickers left. How many stickers did Maria have at first?

Step 1: This is a missing minuend problem!
Step 2: We know: \(? − 156 = 289\)
Step 3: To find the starting amount, add!
Step 4: Solve: \(289 + 156 = 445\)
Answer: Maria had \(445\) stickers at first. ✓