How to Add and Subtract Integers: Word Problems

To solve an integer word problem, identify the starting value, describe each change with a signed number, and write an expression before calculating. First check what the question asks: a final value, a signed change, or a distance between two values. These can use the same numbers but give different answers.

How to choose addition or subtraction

1. Choose a reference point. Zero might mean sea level, no money owed, or no points. A value below the reference is negative; a value above it is positive.
2. State what you need to find. For a final value, combine the starting value and each signed change. For a signed change, calculate final value minus starting value. For a distance or gap, report the nonnegative separation.
3. Write the expression, then calculate. Replace subtraction with addition of the opposite: a − b = a + (−b). For addition, same signs mean add the magnitudes and keep the sign; different signs mean subtract the smaller magnitude from the larger and keep the larger magnitude’s sign.
4. Answer in context. Include units and explain a negative result. Check whether your answer agrees with the direction of the change.

Avoid relying on keywords alone. “The temperature fell” describes a negative change, but “How far did it fall?” asks for a positive amount. Similarly, a negative starting balance does not turn a deposit into a withdrawal.

Worked integer word problems

1. Temperature: find the final value

At sunrise, the temperature is −6°C. It rises 9°C. What is the new temperature?

Translate: start at −6 and add the rise: −6 + 9.
Calculate: 9 − 6 = 3, with a positive sign.
Answer: the temperature is 3°C. On a number line, moving nine units right from −6 lands at 3.

2. Money: combine a deposit and withdrawal

A bank balance is −$18. A $45 deposit is followed by a $32 withdrawal. What is the final balance? Ignore fees.

Translate: −18 + 45 − 32.
Calculate: −18 + 45 = 27, then 27 − 32 = −5.
Answer: the balance is −$5, so the account is overdrawn by $5. The deposit raises the balance; the withdrawal lowers it.

3. Elevation: find a signed change

A diver moves from −12 meters to −5 meters relative to the water’s surface. What is the change in position?

Translate: final minus starting position: −5 − (−12).
Calculate: −5 + 12 = 7.
Answer: the change is +7 meters: the diver rose 7 meters and is still 5 meters below the surface. Both positions are negative, but the change is positive.

4. Temperature: distinguish change from difference

The temperature falls from 4°C to −7°C. What is the signed change, and how many degrees did it fall?

Signed change: −7 − 4 = −11°C.
Amount of the fall: 11°C.
Check: 4 + (−11) = −7. The negative sign describes the direction; the positive amount describes the size of the fall.

Try three integer word problems

Write an expression and an answer with units before opening the solutions.

1. A game score starts at −8 points. You gain 15 points, then lose 6. What is the final score?
2. An elevator moves from floor −3 to floor 5. Each consecutive floor is one level apart. How many levels does it move, and in which direction?
3. The temperature changes from −2°C to −9°C. Find the signed change and the amount of the drop.

What to practice next

If the arithmetic is the difficult part, review integer addition and subtraction rules before trying another word problem. For printable skill practice, use the free Pre-Algebra worksheet collection; choose the integer topic you need rather than treating the entire collection as word-problem practice.

Use the free Pre-Algebra learning hub for related review. If you want a book for a broader study routine, preview Pre-Algebra for Beginners before choosing it. Check the sample’s level and format against your needs.

Pre-Algebra for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

Further reading: OpenStax Prealgebra 2e: Subtract Integers, including subtraction in applications. The worked problems and practice above are original examples.