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What is the Absolute Value of a Number?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The absolute value of a number tells us its distance from zero on a number line, no matter which direction. It's always a positive value or zero, because distance can never be negative. We use two vertical lines, like |x|, to show the absolute value of x.
Simple Example
Quick Example
Imagine you walk 5 steps forward from your home to a chai shop. The distance is 5 steps. If you walk 5 steps backward from your home to a friend's house, the distance is still 5 steps. So, whether you move +5 steps or -5 steps, the 'absolute distance' you covered is always 5 steps. That's absolute value!
Worked Example
Step-by-Step
Let's find the absolute value of -7.
Step 1: Understand what absolute value means. It's the distance from zero.
---Step 2: Locate -7 on a number line. It's 7 units to the left of zero.
---Step 3: Count the units from 0 to -7. You count 1, 2, 3, 4, 5, 6, 7 units.
---Step 4: Distance is always positive. So, even though it's to the left, the distance is 7.
---Step 5: Write it using the symbol: |-7|.
---Step 6: Therefore, |-7| = 7.
Answer: The absolute value of -7 is 7.
Why It Matters
Common Mistakes
MISTAKE: Thinking absolute value makes a positive number negative. For example, |5| = -5. | CORRECTION: Absolute value always results in a positive number or zero. So, |5| = 5.
MISTAKE: Confusing absolute value with negative numbers. For example, believing |-3| is the same as -3. | CORRECTION: |-3| means 'distance of -3 from zero', which is 3. -3 is just the number itself.
MISTAKE: Forgetting that zero's absolute value is zero. For example, saying |0| is undefined or 1. | CORRECTION: The distance of 0 from 0 is 0. So, |0| = 0.
Practice Questions
Try It Yourself
QUESTION: What is the absolute value of 12? | ANSWER: 12
QUESTION: Find |-25| + |10|. | ANSWER: 25 + 10 = 35
QUESTION: If the temperature in Shimla is -5 degrees Celsius and in Chennai it's 30 degrees Celsius, what is the absolute difference in their temperatures? | ANSWER: |-5 - 30| = |-35| = 35 degrees Celsius. (Or |30 - (-5)| = |35| = 35 degrees Celsius)
MCQ
Quick Quiz
Which of the following statements is true?
|-8| = -8
|0| = 1
|15| = 15
|-4| = 4 and |-4| = -4
The Correct Answer Is:
C
Option C is correct because the absolute value of a positive number is the number itself. Option A is wrong because absolute value is always positive. Option B is wrong because the absolute value of 0 is 0. Option D is wrong because |-4| can only be 4, not -4.
Real World Connection
In the Real World
When your phone's GPS calculates how far you are from a destination, it uses absolute value. It doesn't matter if you are north or south of your destination; the app just tells you the 'distance remaining'. Similarly, in cricket, if a bowler bowls a ball that swings by 10 cm to the left or 10 cm to the right, the 'amount of swing' (its absolute value) is 10 cm in both cases.
Key Vocabulary
Key Terms
ABSOLUTE VALUE: The distance of a number from zero on a number line, always positive or zero. | NUMBER LINE: A visual representation of numbers as points on a line. | DISTANCE: The amount of space between two points, always a positive value. | INTEGER: Whole numbers (positive, negative, or zero) without fractions or decimals.
What's Next
What to Learn Next
Great job understanding absolute value! Now that you know about positive and negative numbers and their distances, you're ready to explore 'Operations with Integers' like adding and subtracting negative numbers. This will help you solve more complex problems involving temperature changes or bank balances!
