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Negative Number has a value that is less than 0. These numbers are represented by a minus sign in front of the number. They are written on the left side of the number line from the origin. They can be either in fractions, decimals, or whole numbers. Some examples of negative numbers are, -2, -3, -5, -3/7, -8/9, -5.8, -3.4, etc. A negative number refers to the loss or absence of something. Negative numbers can also be called the opposite value of positive numbers.
Read More: What are Real Numbers?
Key Terms: Negative Numbers, Number Line, Fractions, Decimals, Imaginary Numbers, Decimals, Real Numbers
Applications of Negative Numbers
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Here are some applications of negative numbers:
- These numbers are used in weather forecasting to show the temperature of a region on Fahrenheit and Celsius scales.
- In Engineering, Some instruments such as boilers and steam engines use pressure gauges and thermometers calibrated from negative to positive integers.
- In medicine, instruments used for measuring blood pressure, body weight, and drug testing operate on negative and positive scales.
- In Sports, goal differences like football, hockey, and basketball are denoted by negative integers.
- Lifts, speedometers, and Alco-blows also operate on negative and positive values.
- Banks and financial institutions need debits, credits, and money. For that reason, there is a need to have numbers that differentiate between credit and debit transactions. Also, profits and losses are specified by positive and negative integers. They are also used to show the ups and downs of the share market.
Negative Numbers in Number Line
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| Relevant Concepts | ||
|---|---|---|
| Mode of Grouped Data | What are Imaginary Numbers? | Root 2 is Irrational |
Basic Operations on Negative Integers
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Some operations which can be performed on negative numbers:
- Adding a negative and positive integer: When we add a negative and positive number together, subtract the integers and write the sign of greater absolute value. For example, 8+(-2) = 6
- Adding Negative integers: When we add negative numbers, they are added and the sum will have the sign of the original integer. For example, -5+(-1) = -6.
- Multiplication & Division of Negative integers: When a negative number is multiplied by another negative number then the results will be positive. For example, -4*-4 = +16. When we divide a negative number by another negative number it will always result in a positive number. Similarly, Multiplication & division of a positive integer by a negative integer result in a negative number.
- Subtracting Signed integers: Subtracting a positive integer from a negative integer is the same as adding a negative of that integer. For example, -10-15 = -10+(-15) = -25. Subtracting a negative integer by another negative integer is the same as adding the positive of that integer. For example, 13-(-14) = 13+14 = 27.
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Things to Remember
- Zero is a real number. Real numbers can be positive or negative and includes the number 0.
- Negative numbers are the opposite of positive numbers and they are marked on the left side of the number line.
- These numbers usually indicate low value, absence, or decrease in some quantity.
- Integers (whether positive, negative, or zero) are mainly used to describe temperature conditions above/below freezing point, elevator level above/below the ground level, bonus, and penalty in quizzes/games, etc.
Read More: Euclid’s Division Lemma
Sample Questions
Ques. Give some examples of Negative numbers in daily life. (3 Marks)
Ans. Some examples of negative numbers in daily life:
- An altitude above (positive) or below (negative) the sea level.
- Gaining points (positive) or losing points (negative) in a game.
- Having money (positive) or having debt (negative).
- Having a profit (positive) or a loss (negative) in a business or stock market.
- Moving in one direction or in another direction. But we have to take into account which direction we are taking positively.
Ques. What are the various uses of negative numbers in daily life? (3 Marks)
Ans. Negative numbers are used in many day-to-day activities in subtraction or when it is required to compute a loss of any kind. Using negative numbers in most aspects is largely a matter of keeping track of what items must be subtracted instead of added. For example, A girl took $20 from her grandmother, she will use some of it to buy 3 packs of cards, each worth $2.50. So, the left amount will be simply 20 - 3*(2.50) = 20 - 7.50 = $12.50 or as multiplication of a negative number, as in 20 + 3*(-2.50) = 20 + (-7.50) = $12.50.
Ques. What are the basic rules we use when we deal with negative numbers? (3 Marks)
Ans. Some basic rules we use when we deal with negative numbers are:
- When we add a negative number, it is the same as subtracting a positive number. Like 4+(-3) = 4-3.
- Subtracting a negative number is the same as adding a positive number. Like 5-(-2) = 5+2.
- Multiplying or dividing an even number that has a negative sign produces a positive result.
- Multiplying or dividing an odd quantity of negative numbers produces a negative number as a result.
Ques. Find the successor and predecessor of the following numbers: -20, 45, -87, 25, and -57. (3 Marks)
Ans. The predecessor is the number that comes before the given number.
The successor is the number that comes after the given number.
| Given Number | Predecessor | Successor |
|---|---|---|
| -20 | -21 | -19 |
| 45 | 44 | 46 |
| -87 | -88 | -86 |
| 25 | 24 | 26 |
| -57 | -58 | -56 |
Ques. Smith ended round one of a quiz with 300 points. In round two, he scored -400 points and in the third round, he gained 500 points. What was the total score at the end of the third round? (3 Marks)
Ans. Smith’s score in round one: 300 points
His score after second round: 300 + (-400) = -100 points
His score after the third round: -100 + 500 = 400 points
Therefore, Smith scored 400 points at the end of the third round.
Ques. Can zero be considered a negative number? Explain. What are negative numbers called? (3 Marks)
Ans. No, zero is not considered a positive or a negative number because it essentially follows the concept of void. Zero doesn’t depict a lack or excess of some quantity. So, it is generally considered “non-negative” in nature.
Generally, Negative numbers are known as integers which are present on the left side of the number line. Zero and positive numbers are also known as integers.
Ques. What is the formula to calculate negative numbers? (3 Marks)
Ans. The negative numbers are calculated as shown below:
The negative or negation of 35 is -35, 73 is -73 from the number, and so on.
Positive number + Positive number = Positive number
Positive number + Negative number = Subtraction of positive number and negative number
Negative number + Negative number = Addition of two negative numbers
Ques. Can a negative sign be used for a prime number? (3 Marks)
Ans. Yes, along with prime numbers negative signs can be put on integer forms like fractions, decimals, irrational digits etc. Any number which is less than zero will have a negative sign before the number regardless of its units.
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