Subtraction Basics

For Elementary Students

What Is Subtraction?

Subtraction means taking away something from a group.

Think about it like this: If you have 8 cookies and eat 3, how many are left? That's subtraction!

8 − 3 = 5 (You have 5 cookies left)

The Subtraction Symbol

The minus sign (−) means "take away" or "subtract."

Example: 9 − 4 = 5

We read this as "nine minus four equals five."

Subtraction Is Like Counting Backwards

Example: 7 − 3 = ?

Start at 7 and count backwards 3 times:

7 → 6 → 5 → 4

Answer: 4

Using a Number Line

A number line helps you see subtraction!

Example: 10 − 4 = ?

         start
           ↓
0 ─ 1 ─ 2 ─ 3 ─ 4 ─ 5 ─ 6 ─ 7 ─ 8 ─ 9 ─ 10
           ↑
         land here
         ← ← ← ←
       jump back 4

Start at 10, jump back 4 steps → land on 6

Answer: 10 − 4 = 6

Taking Away with Pictures

Example: 5 − 2 = ?

Start with 5 stars:

⭐ ⭐ ⭐ ⭐ ⭐

Take away 2 (cross them out):

✗ ✗ ⭐ ⭐ ⭐

Count what's left: 3 stars

Answer: 5 − 2 = 3

Important Rules

Subtracting zero — Nothing is taken away!

• 8 − 0 = 8
• 12 − 0 = 12

Subtracting from itself — Everything is gone!

• 5 − 5 = 0
• 10 − 10 = 0

Order Matters in Subtraction!

Addition: 3 + 5 = 5 + 3 (same answer!)

Subtraction: 9 − 4 ≠ 4 − 9 (different answers!)

• 9 − 4 = 5 ✓
• 4 − 9 = ? (Can't do with positive numbers yet!)

Order matters — you can't flip subtraction around!

For Junior High Students

Understanding Subtraction

Subtraction finds the difference between two numbers or represents taking away a quantity.

Vocabulary:

• Minuend — the starting number (9 in 9 − 4)
• Subtrahend — the number being subtracted (4 in 9 − 4)
• Difference — the result (5 in 9 − 4 = 5)

Subtraction as the Inverse of Addition

Subtraction undoes addition!

If: 7 + 3 = 10

Then: 10 − 3 = 7 and 10 − 7 = 3

Use this to check your work!

Subtracting Larger Numbers (Column Method)

Line up by place value and subtract from right to left.

Example: 86 − 23

  86
− 23
----

Ones place: 6 − 3 = 3

Tens place: 8 − 2 = 6

  86
− 23
----
  63

Answer: 63

Borrowing (Regrouping)

When the top digit is smaller than the bottom digit, borrow from the next column.

Example: 52 − 27

  52
− 27
----

Step 1: Ones place: 2 − 7 → Can't do it!

Step 2: Borrow 1 ten from the tens place

  ⁴⁵₁₂  (5 becomes 4, 2 becomes 12)
− 27
----

Step 3: Now subtract

• Ones: 12 − 7 = 5
• Tens: 4 − 2 = 2

  ⁴⁵₁₂
− 27
----
  25

Answer: 25

Borrowing Across Zeros

Example: 300 − 148

  300
− 148
----

Step 1: Can't subtract ones (0 − 8), need to borrow

Step 2: Borrow through the zeros

  ²⁹⁹₁₀  (3 hundreds → 2 hundreds, 9 tens, 10 ones)
− 148
----

Step 3: Subtract

• Ones: 10 − 8 = 2
• Tens: 9 − 4 = 5
• Hundreds: 2 − 1 = 1

Answer: 152

Checking Your Subtraction

Method 1: Add the difference to the subtrahend

If 52 − 27 = 25, check: 25 + 27 = 52 ✓

Method 2: Estimate first

52 − 27 → About 50 − 30 = 20

Actual answer (25) is close to 20, so it's reasonable! ✓

Mental Math Strategies

Strategy 1: Count up (for numbers close together)

15 − 13 = ? → Count up from 13 to 15: 14, 15 → 2 steps

Strategy 2: Break it apart

17 − 9 = ?

• Break 9 into 7 + 2
• First: 17 − 7 = 10
• Then: 10 − 2 = 8

Strategy 3: Use friendly numbers

64 − 28 = ?

• Add 2 to both: 66 − 30 = 36

Real-Life Uses

Shopping: "I have $20. Item costs $7. Change?"

• $20 − $7 = $13

Temperature: "Was 75°F, dropped 8°. New temp?"

• 75 − 8 = 67°F

Games: "Had 50 points, lost 18. Score now?"

• 50 − 18 = 32 points

Time: "Event is at 3:00. It's 1:45. Time left?"

• Count from 1:45 to 3:00 → 1 hour 15 minutes

Subtraction Properties

Not commutative: a − b ≠ b − a (order matters!)

Not associative: (a − b) − c ≠ a − (b − c)

Example:

• (10 − 3) − 2 = 7 − 2 = 5
• 10 − (3 − 2) = 10 − 1 = 9
• Different answers! Parentheses matter.

Identity: a − 0 = a (subtracting zero doesn't change the number)

Relation to Negative Numbers

When you subtract a larger number from a smaller one, you get a negative number.

Example: 4 − 9 = −5

We will learn more about negative numbers later.

Practice