Here are nine great worked examples about dividing integers word problems and four more below you can read on your own. Read the solutions carefully, so you will know how to do similar problems.
In each worked example above, every part of the story becomes a positive or a negative integer. Then you divide the integers and use the sign rules to answer the question. The worked examples will help you see how to turn each part of a story into an integer step by step, decide whether the answer is positive or negative, and get ready for the practice problems and the quiz below. Click through the steps one at a time.
Problem #1
A hiker walks down a mountain trail. She goes down 1,200 feet in 4 hours at a steady pace. What is her change in elevation each hour?
Solution
Goes down 1,200 feet can be represented by −1,200
4 hours can be represented by 4
A steady pace means divide
−1,200 ÷ 4 = −300
Her elevation changes by −300 feet each hour. She goes down 300 feet every hour.
Problem #2
A phone battery lost 60% of its charge in 5 hours. It lost the same amount each hour. What was the change in the battery level each hour?
Solution
Lost 60% can be represented by −60
5 hours can be represented by 5
The same amount each hour means divide
−60 ÷ 5 = −12
The battery level changed by −12% each hour. The battery lost 12% every hour.
Problem #3
The temperature in a freezer drops 4 degrees every hour. How many hours will it take for the temperature to drop 28 degrees?
Solution
Drop 28 degrees can be represented by −28
Drops 4 degrees every hour can be represented by −4
How many hours means divide
−28 ÷ −4 = 7
It will take 7 hours.
Problem #4
The population of a small town grew by 2,400 people in 8 years. It grew by the same number of people each year. By how many people did the population grow each year?
Solution
Grew by 2,400 people can be represented by +2,400
8 years can be represented by 8
The same number each year means divide
2,400 ÷ 8 = 300
The population grew by 300 people each year.