Mixed Addition and Subtraction

For Elementary Students

What Are Mixed Problems?

Mixed problems have both addition (+) and subtraction (−) in the same problem.

Think about it like this: Real life isn't just adding OR subtracting — sometimes you do both!

Example: You have 5 cookies, get 3 more, then eat 2. How many cookies do you have?

That's: 5 + 3 − 2

The Golden Rule: Work From Left to Right

When you see addition and subtraction together, do them in order from left to right!

Example: 5 + 3 − 2 = ?

Step 1: Do the first operation (left side)

• 5 + 3 = 8

Step 2: Now do the next operation

• 8 − 2 = 6

Answer: 6

Why Left to Right?

Imagine following a path. You can't skip ahead — you follow it step by step!

5  →  +3  →  8  →  −2  →  6
Start    Add 3   Got 8  Subtract 2  End!

Another Example

Problem: 10 − 4 + 2 = ?

Step 1: Start from the left

• 10 − 4 = 6

Step 2: Keep going right

• 6 + 2 = 8

Answer: 8

❌ Wrong way: If you add first (4 + 2 = 6), then 10 − 6 = 4. That's wrong!

✓ Right way: Always go left to right!

Using Your Fingers or Drawing

Problem: 7 + 2 − 3 = ?

Draw it:

Start with 7: ⭐⭐⭐⭐⭐⭐⭐
Add 2: ⭐⭐⭐⭐⭐⭐⭐⭐⭐
Take away 3: ⭐⭐⭐⭐⭐⭐

Answer: 6 stars left

Word Problems with Mixed Operations

Example: "You had 8 marbles. You found 5 more. Then you gave 4 to your friend. How many marbles do you have now?"

Break it down:

• Start: 8 marbles
• Found 5: 8 + 5 = 13
• Gave away 4: 13 − 4 = 9

Answer: 9 marbles

For Junior High Students

Understanding Mixed Operations

When an expression contains only addition and subtraction, they have equal priority in the order of operations.

Rule: Work from left to right.

Example: 15 + 7 − 3 + 2

Solve in order:

1. 15 + 7 = 22
2. 22 − 3 = 19
3. 19 + 2 = 21

Answer: 21

Why Order Matters

Common mistake: Doing all additions first, then subtractions.

Example: 20 − 5 + 8

❌ Wrong: 5 + 8 = 13, then 20 − 13 = 7

✓ Right: 20 − 5 = 15, then 15 + 8 = 23

Always follow left-to-right order!

Longer Expressions

The rule applies no matter how long the expression is.

Example: 50 + 10 − 15 + 5 − 20 + 8

Step-by-step:

1. 50 + 10 = 60
2. 60 − 15 = 45
3. 45 + 5 = 50
4. 50 − 20 = 30
5. 30 + 8 = 38

Answer: 38

Think of It As a Running Total

Keep a "running total" as you go:

Example: 100 − 25 + 15 − 10

Start: 100
After −25: 75
After +15: 90
After −10: 80

Answer: 80

Working with Negative Results

Sometimes your running total becomes negative!

Example: 5 − 8 + 3

Step 1: 5 − 8 = −3 (negative!)

Step 2: −3 + 3 = 0

Answer: 0

Word Problems with Multiple Steps

Example: "Your bank account has $150. You deposit $50, withdraw $75, deposit $25, and withdraw $30. What's your balance?"

Track the balance:

• Start: $150
• Deposit $50: 150 + 50 = 200
• Withdraw $75: 200 − 75 = 125
• Deposit $25: 125 + 25 = 150
• Withdraw $30: 150 − 30 = 120

Answer: $120

Keywords in Word Problems

Addition keywords:

• add, plus, more, gain, increase, total, altogether, combined, received, got

Subtraction keywords:

• subtract, minus, less, fewer, decrease, lost, gave away, spent, remaining, left, difference

Example: "Maya had 20 pencils, gave away 7, bought 12 more, then lost 5. How many now?"

Translate:

• Start: 20
• Gave away: −7 → 20 − 7 = 13
• Bought: +12 → 13 + 12 = 25
• Lost: −5 → 25 − 5 = 20

Answer: 20 pencils

Using Parentheses to Regroup

Without parentheses: 10 − 3 + 2 = ?

• 10 − 3 = 7, then 7 + 2 = 9

With parentheses: 10 − (3 + 2) = ?

• First do parentheses: 3 + 2 = 5
• Then: 10 − 5 = 5

Different answers! Parentheses change the order.

We will learn more about order of operations later.

Checking Your Work

Method 1: Work backwards

• If 5 + 3 − 2 = 6, then 6 + 2 − 3 = 5 ✓

Method 2: Estimate first

• 15 + 8 − 3 → about 15 + 8 = 23, minus 3 is about 20
• Actual: 23 − 3 = 20 ✓ (matches estimate!)

Real-Life Applications

Shopping: "Started with $100, spent $45, earned $30, spent $20. How much left?"

• 100 − 45 + 30 − 20 = 65

Temperature: "Started at 20°C, rose 5°, dropped 8°, rose 3°. Final temp?"

• 20 + 5 − 8 + 3 = 20°C

Sports scores: "Leading by 10, opponent scores 7, you score 3. Lead?"

• 10 − 7 + 3 = 6 points

Practice