A negative number is a number smaller than zero. Think about the readings on a thermometer. A reading of –10° means the temperature is –10° below 0° and that the temperature would need to warm up 108 to reach 0°. A reading of 10° means the temperature would need to cool down 10° to reach 0°.
Let us use a test example to discover
some facts about arithmetic with negative numbers. Suppose you are taking a test where one
point is awarded for
each correct answer and one point is deducted for each incorrect answer. If you miss the first three problems,
how many would you need to answer correctly to bring your score to 10? You would need to answer
three correctly to bring your answer up to zero, then you would need to answer
10 more correctly to bring your score to
10; you would need to answer 13 correctly to bring a score of –3 to 10: 10 = –3 + 3 +
10 = –3 + 13. Now suppose you miss the first eight
problems and get the next two answers correct. You now only need to answer six more correctly to
reach zero: –8 +
2 = –6.
When adding a negative number to a
positive number (or a positive number to a negative number), take the
difference of the numbers. The sign on the sum will be the same as the sign of the ‘‘larger’’
number. If no sign appears
in front of a number, the number is positive.
Practice
1. – 10 + 8 =
2. 13 + (– 20) =
3. 40 + (– 10) =
Solutions
1. –10 + 8 = –2
2. 13 + (– 20) = –7
3. 40 + (– 10) = 30
Returning
to the test example, suppose you have gotten the first five correct but missed
the next two. Of course, your score would be 5 – 2 = 3. Suppose now that you
missed more than five, your score would then become a negative number. If you
missed the next seven problems, you will have lost credit for all five you got
correct plus another two: 5 – 7 = –2. When subtracting a larger positive number
from a smaller positive number, take the difference of the two numbers. The
difference will be negative.
Practice
1.
28 – 30 =
2.
4 – 75 =
3.
5 – 90 =
Solutions
1.
28 – 30 = –2
2.
4 – 75 = –71
3.
5 – 90 = –85
Finally,
suppose you have gotten the first five problems incorrect. If you miss the next
three problems, you move even further away from zero; you would now need to get
five correct to bring the first five problems up to zero plus another three
correct to bring the next three problems up to zero. In other words, you would
need to get 8 more correct to bring your score up to zero: –5 – 3 = –8. To
subtract a positive number from a negative number, add the two numbers. The sum
will be negative.
Practice
1.
–16 – 4 =
2.
–35 – 5 =
3.
–99 – 1 =
Solutions
1.
–16 – 4 = –20
2.
–35 – 5 = –40
3. –99 – 1 = –100
Sumber
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