Subtraction Strategies

For Elementary Students

Different Ways to Subtract

There are many ways to subtract! You don't always have to count backwards or "take away."

Think about it like this: Subtraction is about finding the difference between two numbers — how far apart they are!

Strategy 1: Counting Up (Adding Up)

Instead of taking away, you can count up from the smaller number to the larger number.

Example: 12 - 8 = ?

Think: "Start at 8. How many do I need to add to get to 12?"

Count: 8 → 9 → 10 → 11 → 12

That's 4 steps.

Answer: 12 - 8 = 4

Why this works: The difference between 8 and 12 is 4!

When Counting Up is Easiest

Use counting up when the numbers are close together.

Example: 15 - 13 = ?

Count up: 13 → 14 → 15 (2 steps)

Answer: 2

Much easier than counting backwards from 15!

Strategy 2: Think Addition (Fact Families)

Since addition and subtraction are related, you can think addition instead!

Example: 11 - 7 = ?

Think: "What plus 7 equals 11?"

You know that 7 + 4 = 11.

Answer: 11 - 7 = 4

Strategy 3: Use a Number Line

Jump backwards on a number line to subtract.

Example: 10 - 3 = ?

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

Start at 10, jump back 3: land on 7

Answer: 10 - 3 = 7

Strategy 4: Breaking Apart Numbers

Break the number into easier pieces.

Example: 15 - 7 = ?

Break 7 into 5 + 2:

• First subtract 5: 15 - 5 = 10
• Then subtract 2: 10 - 2 = 8

Answer: 15 - 7 = 8

Why it works: Taking away 5 and then 2 is the same as taking away 7!

For Junior High Students

Strategy 5: Compensation (Adding/Subtracting Both)

Make the numbers friendlier by adjusting both the same way.

Example: 64 - 38 = ?

Step 1: Add 2 to both numbers (to make 38 → 40, which is easier) 66 - 40 = 26

Answer: 26

Why it works: If you add the same amount to both numbers, the difference stays the same!

Proof:

• Original: 64 - 38 = 26
• Adjusted: 66 - 40 = 26
• Same answer! ✓

Strategy 6: Constant Difference

You can add or subtract the same amount from both numbers.

Example: 100 - 47 = ?

Strategy: Subtract 7 from both

• 100 - 7 = 93
• 47 - 7 = 40
• New problem: 93 - 40 = 53

Answer: 53

Check: 100 - 47 = 53 ✓

Strategy 7: Use Benchmark Numbers

Use friendly numbers like 10, 50, 100 as stepping stones.

Example: 82 - 35 = ?

Think in steps:

• 82 - 30 = 52 (easy!)
• 52 - 5 = 47 (finish the 35)

Answer: 47

Strategy 8: Counting Up in Chunks

For larger differences, count up in groups instead of one at a time.

Example: 500 - 276 = ?

Count up from 276 to 500:

• 276 to 280 = 4 (first step to round number)
• 280 to 300 = 20 (to next hundred)
• 300 to 500 = 200 (hundreds)
• Total: 4 + 20 + 200 = 224

Answer: 500 - 276 = 224

Choosing the Best Strategy

Different strategies work better for different problems:

Subtraction with Larger Numbers

All these strategies work with bigger numbers too!

Example: 1,000 - 378 = ?

Count up strategy:

• 378 to 400 = 22
• 400 to 1,000 = 600
• Total: 22 + 600 = 622

Example: 650 - 295 = ?

Compensation:

• Add 5 to both: 655 - 300 = 355

Answer: 355

Mental Math Practice

The more you practice these strategies, the faster you'll get at mental subtraction!

Quick check: Does your answer make sense?

• If 100 - 60 = ? and your answer is 140, something's wrong!
• The answer should be less than 100 (the number you started with)

Real-Life Uses

Shopping: "I have $20. The toy costs $13. How much change?" → Count up from 13 to 20

Time: "It's 4:15. My show starts at 5:00. How long?" → Count up from 4:15 to 5:00

Games: "I need 50 points. I have 32. How many more?" → 50 - 32, count up

Practice