Positive and Negative Numbers

Those who have been away from using mathematical concepts for a while often have trouble combining positive and negative numbers. Look at the picture below:

negative numbers are illustrated branching away from zero to the left. positive numbers branch away to the right. The whole line, though, represents increasing values from left to right. Yes, that means that -2 is a bigger number than -5. Consider this line a thermometer then you will see that -2 degrees is warmer than -5 degrees. (Not much warmer, but warmer)

Addition of Positive and Negative Numbers

When we add numbers together we wish to know their combined value.

Example:
Mary's section had \$420 left over at the end of the budget year and John's section had \$200 left over. How much did their sections contribute to the department budget at year's end?
\$420 + \$200 = \$620
When both numbers are positive, we simply add their values and get another positive number.

Example:
Mary's section spent \$420 over their budget at the end of the budget year and John's section overspent \$200. How much did their sections affect the department budget at year's end?
(-\$420) + (-\$200) = -\$620
When both numbers are negative, again we simply add their values and we get another negative number.

Example:
Mary's section spent \$420 over their budget at the end of the budget year and John's section had a \$200 surplus. How much did their sections affect the department budget at year's end?
(-\$420) + \$200 = -\$220

Example:
Mary's section had \$420 left over at the end of the budget year and John's section spent \$200 over. How much did their sections affect the department budget at year's end?
\$420 + (-\$200) = \$220
When one number is positive and one number is negative, we must find the difference between the numbers. The result will be positive if the larger value is positive or negative if the larger value is negative.

Subtraction of Positive and Negative Numbers

When we subtract a number from another number, we are looking for the difference between them. If we subtract a smaller number from a larger number, the result is positive whether the numbers are positive, negative, or mixed. If we subtract a larger number from a smaller number, the result is negative whether the numbers are positive, negative or mixed. (Remember, -5 is smaller than -2.)

Example:
Mary's section had \$420 left over at the end of the budget year and John's section had \$200 left over. How much more did Mary's section save than John's?
\$420 - \$200 = \$220

How did John's section compare with Mary's?
\$200 - \$420 = -\$220
When both numbers are positive, we find their difference (subtract one from the other) then apply the appropriate sign.

Example:
Mary's section spent \$420 over their budget at the end of the budget year and John's section spent \$200 over. How much more did Mary's section overspent when compared to John's?
(-\$420) - (-\$200) = -\$220

How did John's section compare with Mary's?
(-\$200) - (-\$420) = \$220
When both numbers are negative, again we find their difference (subtract one from the other) then apply the appropriate sign.

Example:
Mary's section spent \$420 over their budget at the end of the budget year and John's section had \$200 left over. How did Mary's section compare with John's?
(-\$420) - \$200 = -\$620

How did John's section compare with Mary's?
(\$200) - (-\$420) = \$620
When one number is positive and one number is negative, we must add the values (their distance from zero) together . Again, the result will be positive if the value of the larger number is positive or negative is the larger value is negative. Look at the picture below. Do you see why we must add the values?

Now here are some problems for you to evaluate. When you think you have the right answers, check yourself by clicking on the answer box below.

1. 43 + 32
2. 23 - 14
3. 35 - 43
4. -44 + 16
5. -36 - 20
6. -42 + (-44)
7. 39 - (-22)
8. 17 - 12
9.(-36) + 21
10.Jane and Jack were born on, respectively, May 22 and August 14 of the same year. How many days older is Jane than Jack?

11.The record high temperature in Nowhere, USA is 98 degrees and the record low is -23 degrees. What is the temparature variation between the record high and the record low?