Integer Word Problems

Learn to translate real-world situations into integer operations and solve them step by step.

Intermediate25 minLesson
Printable worksheet

Definition

Integer word problems describe real-world situations using positive and negative whole numbers. To solve them, you need to:
  1. 1.Identify the quantities - What numbers are involved?
  2. 2.Determine the operation - Is it addition, subtraction, or comparison?
  3. 3.Translate to math - Write an expression with integers
  4. 4.Solve and interpret - Calculate and explain what the answer means
Key phrases to watch for:
  • *"below zero"* or *"under sea level"* → negative numbers
  • *"increased by"* or *"gained"* → addition
  • *"decreased by"* or *"lost"* → subtraction
  • *"how much more/less"* or *"difference"* → subtraction

Try it now

The temperature was −3°C-3°C in the morning. It rose by 88 degrees. What is the temperature now?

Worked Examples

At 6 AM, the temperature was −8°C-8°C. By noon, it had risen by 1515 degrees. What was the temperature at noon?

1

Identify the starting value

The temperature at 6 AM was −8°C-8°C → Start: −8-8

2

Identify the change

"Risen by" means we add. The change is +15+15 → Change: +15+15

3

Write the expression

−8+15-8 + 15 → Expression set up

4

Calculate

Starting at −8-8, moving 1515 units right: −8+15=7-8 + 15 = 7

5

Interpret the answer

Positive 77 means above zero → 7°C7°C

Common Mistakes

Confusing 'how much deeper' with subtraction order

Why it's wrong: Students often subtract in the wrong order when comparing values.

Correct: To find how much deeper A is than B, calculate the distance: ∣(−120)−(−85)∣=35|(-120) - (-85)| = 35 meters. Or think: from −85-85 to −120-120 is 3535 meters down.

Ignoring negative signs in the answer

Why it's wrong: Students calculate correctly but forget to consider what a negative result means.

Correct: Always interpret: negative balance = debt, negative temperature = below zero, negative floor = basement level.

Adding when the problem says 'lost' or 'decreased'

Why it's wrong: Key words like 'lost,' 'dropped,' and 'fell' indicate subtraction, not addition.

Correct: Lost 10 points means subtract 10: if you had 55 points, now you have 5−10=−55 - 10 = -5 points.

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Practice Problems

15 problems
Problem 1 of 15
Easy

The temperature was −3°C-3°C in the morning. It rose by 88 degrees. What is the temperature now?

Why It Matters

Integer word problems appear everywhere in daily life:
  • Weather: A temperature of −5°C-5°C rises by 1212 degrees
  • Finance: Your account has −50-50 dollars (debt), then you deposit 7575
  • Geography: A submarine at −200-200 meters descends 5050 more meters
  • Sports: A football team gains 88 yards then loses 1515 yards
Being able to translate words into math helps you solve real problems quickly and accurately!

Real World Applications

Weather Forecasting

Meteorologists calculate temperature changes using integers every day.

Example:

If tonight's low is −12°C-12°C and tomorrow's high is 8°C8°C, the temperature range is 8−(−12)=208 - (-12) = 20 degrees.

1Try It Yourself

The temperature at midnight was −7°C-7°C. It dropped 44 degrees by 3 AM, then rose 99 degrees by 9 AM.

What was the temperature at 9 AM?

Step 1: Write the mathematical expression

Calculate: −7+(−4)+9-7 + (-4) + 9

Football Yardage

Football teams track yards gained and lost throughout a game.

Example:

A team gains 1212 yards, loses 55, then gains 88. Net yardage: 12+(−5)+8=1512 + (-5) + 8 = 15 yards.

2Try It Yourself

A football team starts at the 30-yard line. They gain 15 yards, lose 8 yards, then lose 12 more yards.

What yard line are they on now?

Step 1: Write the mathematical expression

Calculate: 30+15+(−8)+(−12)30 + 15 + (-8) + (-12)

Scuba Diving Depth

Divers track their depth below sea level using negative numbers.

Example:

A diver at −15-15 meters descends 1010 more meters to reach −25-25 meters.

3Try It Yourself

A diver is at −30-30 meters. She ascends 1212 meters, rests, then descends 88 meters.

What is her final depth?

Step 1: Write the mathematical expression

Calculate: −30+12+(−8)-30 + 12 + (-8)

Key Takeaways

  • 1Read carefully to identify starting values, changes, and what the question asks
  • 2Translate key words: 'rise/gain/deposit' → add, 'fall/lose/withdraw' → subtract
  • 3Use negative numbers for values below zero (debt, basement floors, underwater depths)
  • 4After calculating, interpret what the answer means in the real-world context

Frequently Asked Questions

Think about the context: if someone owes money, is below sea level, or is at a temperature below freezing, the answer is negative. Your calculation will show this naturally if you set it up correctly.
Think about the context: if someone owes money, is below sea level, or is at a temperature below freezing, the answer is negative. Your calculation will show this naturally if you set it up correctly.
'Decreased by 5' means subtract 5 from a value: x−5x - 5. 'Is 5 less than' compares two values: if A is 5 less than B, then A=B−5A = B - 5.

Glossary

Integer
A whole number that can be positive, negative, or zero
Elevation
Height above or below sea level (sea level = 0)
Deposit
Money added to an account (increases balance)
Withdrawal
Money taken from an account (decreases balance)
Net change
The overall result after all increases and decreases

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