The "absolute value" may seem complicated to us, but it is simply the distance between a given number and the figure .Β
Absolute Value Practice Problems - Free Worksheets & Solutions
Master absolute value with step-by-step practice problems. Learn distance from zero, solve equations, and work with positive and negative numbers effectively.
πMaster Absolute Value Through Interactive Practice
- Calculate absolute values of positive and negative numbers using distance concept
- Solve absolute value equations by dividing into two cases systematically
- Compare absolute values using inequality symbols (<, >, =) accurately
- Evaluate complex expressions involving absolute value and arithmetic operations
- Apply absolute value rules to real-world distance and measurement problems
- Identify when absolute values equal the original number versus its opposite
Understanding Absolute value
Complete explanation with examples
What is absolute value?
An absolute value is denoted by ββ and expresses the distance from zero points.
The absolute value of a positive number - will always be the number itself.
For example:
The absolute value of a negative number: will always be the same number, but positive.
For example:
Note that the absolute value of a number will always be a positive number given that distance is always positive.
The absolute value of a number is the distance between the number itself and 0 along a number line.
For example:
- The distance between the number and is units. Therefore, the absolute value of is .
- The distance between the number and is also units. Therefore, the absolute value of will also be .Β
As we can see, from the point of view of absolute value, it doesn't matter if the number is positive or negative.
To denote the absolute value, the number is written between two vertical lines.
Practice Absolute value
Test your knowledge with 14 quizzes
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Examples with solutions for Absolute value
Step-by-step solutions included
Exercise #1
Determine the absolute value of the following number:
Step-by-Step Solution
The "absolute value" can be viewed as the distance of a number from 0.
Therefore, the absolute value will not change the sign from negative to positive, it will always be positive.
Answer:
Video Solution
Exercise #2
Determine the absolute value of the following number:
Step-by-Step Solution
The absolute value of a number is the distance of the number from zero on a number line, without considering its direction. For the number , the absolute value is because it is 25 units away from zero without considering the negative sign.
Answer:
Exercise #3
Solve for the absolute value of the following integer:
Step-by-Step Solution
The absolute value of a number is always non-negative because it represents the distance from zero. Therefore, the absolute value of is .
Answer:
Exercise #4
What is the value of ?
Step-by-Step Solution
The absolute value of a number is the distance of the number from 0 on a number line, regardless of direction. Therefore, the absolute value of is the same as moving 3.5 units away from 0, which results in . Hence, .
Answer:
Exercise #5
Step-by-Step Solution
To solve this problem, we will determine the absolute value of the number 3:
- Step 1: Recognize that the number given is 3, which is a positive number.
- Step 2: According to the rules of absolute values, the absolute value of a positive number is the number itself.
- Step 3: Therefore, .
In conclusion, the absolute value of 3 is .
Answer:
Video Solution
Frequently Asked Questions
What is absolute value in simple terms?
+Absolute value is the distance between a number and zero on a number line. It's always positive because distance is always positive. For example, |5| = 5 and |-5| = 5 because both numbers are 5 units away from zero.
How do you solve absolute value equations step by step?
+To solve absolute value equations like |x + 7| = 12, create two cases: Case 1: x + 7 = 12 (solve to get x = 5), and Case 2: x + 7 = -12 (solve to get x = -19). Both solutions should be checked in the original equation.
Why is the absolute value of a negative number positive?
+Absolute value represents distance, and distance is always positive. When you have |-3|, you're asking 'how far is -3 from zero?' The answer is 3 units, so |-3| = 3.
What are the rules for absolute value calculations?
+Key rules include: 1) |positive number| = the same positive number, 2) |negative number| = the opposite positive number, 3) |0| = 0, 4) Solve expressions inside absolute value bars first, then apply the absolute value.
How do you compare numbers with absolute values?
+First calculate each absolute value, then compare the results. For example, |-9| vs +6 becomes 9 vs 6, so |-9| > +6. Remember that absolute values are always non-negative.
What's the difference between |-5 + 6| and |-5| + 6?
+Order of operations matters! |-5 + 6| = |1| = 1 (solve inside first), while |-5| + 6 = 5 + 6 = 11 (absolute value first, then add). Always follow the grouping shown by the absolute value bars.
When do absolute value equations have no solution?
+Absolute value equations have no solution when they equal a negative number, like |x + 3| = -5. Since absolute values are always non-negative, this equation is impossible to solve.
How is absolute value used in real life?
+Absolute value appears in measuring distances, calculating errors or differences, determining temperature variations, and finding profit/loss amounts. Anytime you need the magnitude without considering direction, you use absolute value.