6th Grade - Work With Positive And Negative Numbers

Problem Solving
Work with Positive and Negative Numbers
Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations that use positive and negative integers and combinations of these operations.
Add, subtract, multiply and divide positive and negative numbers using integer rules. Solve problems using appropriate integer rules and operations for real life situations, such as temperature changes and checkbook balances. Use the order of operations to solve problems with multiple operations.

Sample Problems


-2 + 4



-4 - -10



16 x -5



-42 -2



(-16 x -2) + 4 - -1



Reggie checked the temperature before he left for school at it was 5 degrees. He checked it again when he returned from school and it had risen 10 degrees. At 8 p.m. he checked it for the last time and it had dropped 18 degrees since noon. What was the temperature the last time Reggie checked it?


Learning Tips


The rules for adding integers and subtracting integers are different. However, in order to subtract integers you need to apply the rules for adding integers as the last step. It’s important to remember that it takes an extra step to solve subtraction problems.


Memorize the rules to add integers. If you’re adding integers with the same sign you always add the numbers and keep the integer. For example, -4 + -6 = -10. However, if you’re adding integers with different signs you must subtract the numbers and keep the sign of the larger number. For example, 5 + -6 = -1 because 6-5=1. The answer is negative because 6 is negative and it is the larger of the two numbers.


Memorize the first step to subtract integers and then use your addition of integer rules to complete the problem. The first step to solve a problem involving subtracting integers is to change the problem into an addition problem. To do this you always keep the first integer, change the – sign to + and switch the last integer to its opposite. An opposite integer is the same number with the opposite sign. Hence, -2 has the opposite integer of +2, also written as 2. So, following the rules above, the subtraction problem -5 - -6 would change to -5 + 6. Now you simply use the rules for adding integers to solve the problem. Since the signs in the new problem are different, you need to subtract the numbers and keep the sign of the larger number. Your final answer would be 1.


It’s easy to multiply or divide positive and negative integers. First of all, they share the same rules. So, just remember these and you’ll succeed every time. To begin with, you won’t be changing any operations with these, if the problem says multiply you’ll do just that. The same goes for division. So, really the only thing you need to remember is to choose the appropriate sign for your result. If you’re multiplying or dividing two integers with the same sign either (they’re both positive or they’re both negative) the result will always be positive. That’s right, two negative integers make a positive result. The opposite is true for adding integers, so be careful! You may be wondering how you get a negative result when multiplying or dividing integers. This is simple; when the integers of a problem have two different sign (one positive and one negative in any order) the result will always be negative. Thus, -5 x 6 = -30.


Use a number line with positive and negative integers to show visually why an answer will have a positive or negative result. This is the best way to introduce children to the concept of positive and negative integers.


Discuss the importance of positives and negatives in everyday life. For instance, you can discuss the effects of having a negative bank balance or being in -5 degree weather.

Extra Help Problems


-23 + 16



-200 + -40



16 - -5



8 – 19



64 - -6



-150 + 150



134 - -134



-6 x -8



-9 x 9



12 x -160



180 -90



-1420 -10



-120 20



1862 2



1,252 x -1



Jimmy is scuba diving. He descends 15 feet below the surface. After ½ hour he descends another 10 feet. How far did he dive?



Lacey digging a hole. She drills down 25 feet and decides it’s too deep. She fills the hole with 10 feet of dirt. How deep is the hole now?



Will checks the temperature at noon and finds that it is 10 degrees. He checks it again at two and it has dropped 2 degrees. He checks again at five o’clock and it has risen 4 degrees. What is the temperature at 5 o’clock?

(12 degrees)


Vincent puts $200.00 into his bank account. He writes checks for $45.00, 95.00 and 100.00. What is his bank balance?



Tammi is shopping for an outfit to wear to the dance. She would like to buy a dress for $35.00, shoes for $26.25 and a necklace for $15.25. If she has $62.50 in her account will she still have a positive balance if she buys all three items? Explain.
(No, she will have a negative balance of $14.00.)


(-4 + 4) x -2



-4 x -5 + -3



-10 + (-5 x 4)



4 + -5 – 2



(-7 – 3) x (4/-2)



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