Integers are all positive and negative whole numbers, including zero. You use them every day, often without thinking about it.
- Temperature above or below zero
- Bank balances with deposits (+) and withdrawals (-)
- Elevation above or below sea level
- Time measured in B.C. (-) and A.D. (+)
Word problems give us these real-life scenarios. The key is to translate the words into a mathematical expression with positive and negative integers.
- Words like "rise," "gain," "deposit," or "above" usually mean a positive number.
- Words like "fall," "drop," "lose," "withdraw," or "below" usually mean a negative number.
Worked Example
A Roman emperor was born in 42 B.C. and died in 15 A.D. How many years did he live?
Solution First, we translate the years into integers.
- B.C. (Before Christ) years can be treated as negative numbers. So, 42 B.C. is -42.
- A.D. (Anno Domini) years can be treated as positive numbers. So, 15 A.D. is +15.
To find his total lifespan, we must find the difference between his death year and his birth year.
Difference = (End Year) - (Start Year)
Subtracting a negative number is the same as adding its positive:
Answer: The emperor lived for 57 years.
Practice Questions and Solutions
A customer in a grocery store moves from the chilled vegetable section at 4 degrees celsius to the frozen fish section at -18 degrees celsius. What is the change in temperature?
To find the change, we subtract the starting temperature from the final temperature.
Final Temperature = -18
Start Temperature = 4
Answer: The temperature dropped by 22 degrees celsius.
A drill in a well moves from a depth of 120m below ground up to a storage tank 30m above ground. What is the total vertical distance the oil is displaced?
First, we assign integer values to the positions.
Below ground is negative: -120m
Above ground is positive: +30m
To find the total distance, we find the difference between the final position and the start position.
Answer: The total vertical distance is 150m.
You have £70 in your bank account. You buy a game for £45 and then pay a phone bill for £30. What is the new balance in your account?
We start with £70 and subtract the two payments.
Start = +70
Purchases = -45 and -30
First, subtract the game:
Now subtract the phone bill:
Answer: The new balance is -£5 (or £5 overdrawn).
The temperature at sea level (0m) is 12 degrees celsius. For every 1000m a plane climbs, the temperature drops by 6 degrees celsius. What is the temperature at a height of 4000m?
First, find out how many times the temperature will drop.
The temperature will drop 4 times. Now, find the total temperature drop.
Finally, apply this change to the starting temperature.
Answer: The temperature at 4000m is -12 degrees celsius.
A tank contains 1000 litres of water. A pipe adds 25 litres per minute, but a drain removes 40 litres per minute. What is the volume of water in the tank after 30 minutes?
First, find the net change in water every minute.
Next, find the total change over 30 minutes.
Finally, apply this total change to the starting volume.
Answer: There will be 550 litres in the tank.
Did you like this article? Rate it!
Loading...
Integer word problems with answers
Goooooooood exercises
Awesome👏👍😊
hey tamilu
The questions were good even though I was confused with the 5th one
Questions are Awesome..
I like it!