Solving Integer Word Problems- Tips and Practice

What Integer Word Problems Actually Are

Integer word problems are math questions written in plain English that require you to translate words into mathematical operations with positive and negative numbers. That's it. No fancy definitions needed.

These problems show up in middle school, high school, and even on standardized tests. They involve adding, subtracting, multiplying, and dividing integers to find answers to real-world scenarios.

The catch? Most students fail them not because they can't do math, but because they can't figure out what the problem is asking. The math part is easy once you decode the wording.

Core Integer Operations You Need to Know

Before touching any word problem, you need these rules locked in your head:

• Adding positive + positive = positive (5 + 3 = 8)
• Adding negative + negative = negative (-5 + -3 = -8)
• Adding positive + negative = subtract the smaller absolute value from the larger, keep the sign of the larger (-5 + 3 = -2)
• Subtracting integers = add the opposite (5 - (-3) = 5 + 3 = 8)
• Multiplying/dividing positives = positive
• Multiplying/dividing negatives = positive (two negatives make a positive)
• Multiplying/dividing mixed signs = negative

Get these wrong, and no amount of reading comprehension will save you. Master these first.

Keywords That Tell You What Operation to Use

This is where most people lose points. These words are your cheat codes:

Addition Keywords

• gain, increase, rise, climb, deposit, earn
• above zero, north of, east of, profit

Subtraction Keywords

• loss, decrease, drop, fall, withdraw, spend
• below zero, south of, west of, debt

Multiplication Keywords

• times, each, every, per, repeated, groups of

Division Keywords

• split, share, divide, equally, average

Watch out for double negatives in phrasing. "Did not decrease" means it increased. "No loss" means a gain. Read carefully.

How to Solve Integer Word Problems: Step by Step

Here's the actual process. No fluff.

Step 1: Read Once for Gist

Don't grab your pencil yet. Read the whole problem to understand the scenario. Is it about temperature? Money? Elevation? Football yards?

Step 2: Identify the Start Value

Find where the situation begins. This is your starting integer.

Step 3: Find Each Change

Look for every increase or decrease. Write each one as a positive (increase) or negative (decrease) number.

Step 4: Write the Expression

Translate everything to math. Replace "went up by" with "+" and "went down by" with "-".

Step 5: Calculate

Follow order of operations if needed. Otherwise, just work left to right for addition/subtraction.

Step 6: Answer the Question

Make sure your final answer actually responds to what was asked. Check units.

Practice Problems with Solutions

Problem 1: The temperature in Minneapolis was -8°F on Monday morning. By afternoon, it rose 15 degrees. That night, it dropped 6 degrees. What was the temperature at night?

Solution:

-8 + 15 = 7, then 7 - 6 = 1°F

Problem 2: Marcus has $45 in his account. He writes a $60 check. What is his account balance now?

Solution:

Writing a check means withdrawing money. He doesn't have enough, so he goes into negative balance.

45 - 60 = -$15

Problem 3: A submarine dives 250 feet below sea level. It ascends 85 feet, then dives another 120 feet. Where is the submarine now?

Solution:

Start at -250. Ascend means add (getting less negative): -250 + 85 = -165. Dive means subtract: -165 - 120 = -285 feet (below sea level)

Problem 4: Sarah loses 3 points on each of 5 homework assignments. What is her total point change?

Solution:

Multiply: 3 × 5 = 15. Since she lost points, it's negative.

-15 points

Common Mistakes That Cost You Points

• Ignoring the sign on the starting number. If something starts at -20 and goes up 5, you don't get +15. You get -15.
• Confusing "difference" with "subtraction. Difference is always positive. But if the problem says "how much lower," you might need to subtract in a specific order.
• Forgetting that subtraction means adding the opposite. 10 - (-5) is not 5. It's 15.
• Rushing the sign rules. When in doubt, write out the number line. Visual learners need this.

Quick Reference Table

How to Get Better at These

Practice. Not just reading. Actual solving.

Start with easier problems involving just addition and subtraction. Move to multiplication/division once those are automatic. Then mix all four operations.

When you get a problem wrong, figure out exactly where you went wrong. Was it the translation? The sign rules? The arithmetic? Fix that specific gap.

Flashcards of keywords help. So does rewriting problems in your own words after solving them.

The Bottom Line

Integer word problems are two-step puzzles: decode the English, then apply the math. Most students fail the first step. Learn to translate phrases into operations, memorize sign rules, and check your work. That's literally all there is to it.