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Negative Numbers Help

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By — McGraw-Hill Professional
Updated on Sep 27, 2011

Introduction to Negative Numbers

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 10° 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.

Adding Negative Numbers

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.

Find practice problems and solutions at Negative Numbers Practice Problems - Set 1.

Subtracting Negative Numbers

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.

Examples

410 – 500 = –90     10 – 72 = –62

Be careful what you call these signs; a negative sign in front of a number indicates that the number is smaller than zero. A minus sign between two numbers indicates subtraction. In 3 – 5 = –2, the sign in front of 5 is a minus sign and the sign in front of 2 is a negative sign. A minus sign requires two quantities and a negative sign requires one quantity.

Find practice problems and solutions at Negative Numbers Practice Problems - Set 2.

Subtracting Negatives and Negative Quantities

A Negative Minus a Negative

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.

Examples

Division with Decimals Examples

Find practice problems and solutions at Negative Numbers Practice Problems - Set 3.

Double Negatives

A negative sign in front of a quantity can be interpreted to mean “opposite.” For instance –3 can be called “the opposite of 3.” Viewed in this way, we can see that –(–4) means “the opposite of –4.” But the opposite of –4 is 4: –(–4) = 4.

Examples

Double Negatives Examples

More practice problems for this concept can be found at: Algebra: Negative Numbers Practice Test.

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