Negative Numbers

Sabtu, 10 Januari 2026

Negative Numbers

A negative number is a number smaller than zero. Think about the readings on a thermometer. A reading of –10⁰ means the temperature is 10⁰ below 0⁰ and that the temperature would need to warm up 10⁰ to reach 0⁰. A reading of 10⁰ means the temperature would need to cool down 10⁰ to reach 0⁰.

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.

Examples

–82 + 30 = ____. The difference of 82 and 30 is 52. Because 82 is larger than 30, the sign on 82 will be used on the sum: –82 + 30 = –52.

 

–125 + 75 = ____. The difference of 125 and 75 is 50. Because 125 is larger than 75, the sign on 125 will be used on the sum: –125 + 75 = –50.

 

–10 + 48 = ____. The difference of 48 and 10 is 38. Because 48 is larger than 10, the sign on 48 will be used on the sum: –10 + 48 = 38.

Practice

1.      –10 + 8 =

2.      –65 + 40 =

3.      13 – 20 =

4.      –5 + 9 =

5.      –24 + 54 =

6.      –6 + 19 =

7.      –71 + 11 =

8.      40 – 10 =

9.      12 – 18 =

Solutions

1.      –10 + 8 = –2

2.      –65 + 40 = – 25

3.      13 – 20 = – 7

4.      –5 + 9 = 4

5.      –24 + 54 = 30

6.      –6 + 19 = 13

7.      –71 + 11 = – 60

8.      40 – 10 = 30

9.      12 – 18 = – 6

 

 

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Labels: Mathematician

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