Mathematics
Grade 9
15 min
Absolute value of rational numbers
Absolute value of rational numbers
What you'll learn
- Identify whether an integer is positive, negative, or zero with 100% accuracy.
- Order a set of at least five integers from least to greatest on a number line, and explain the reasoning behind the order.
- Compare two given integers using inequality symbols (, =) and justify their comparison in at least 3 out of 4 cases.
- Solve real-world problems involving comparing and ordering integers, such as temperature changes or elevation differences, achieving a correct solution in at least 2 out of 3 problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define the absolute value of a rational number as its distance from zero on a number line.
Calculate the absolute value of any given rational number, including positive and negative fractions and decimals.
Compare and order a set of rational numbers based on their absolute values.
Solve simple equations of the form |x| = c, where c is a non-negative rational number.
Model and interpret real-world situations involving magnitude, such as temperature changes, financial transactions, or measurement errors, using the absolute value of rational numbers.
If a submarine dives 80.5 meters below sea level, how far is it from the surface? 🤔 The answer is all about magnitude, not direction!
This tutorial will introduce the concept of absolute value, specifically for...
2
Key Concepts & Vocabulary
TermDefinitionExample
Rational NumberAny number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. This includes integers, terminating decimals, and repeating decimals.-3/4, 5, 0.25, -1.333...
Absolute ValueThe distance of a number from zero on the number line. Since distance cannot be negative, the absolute value of a number is always non-negative (positive or zero).The absolute value of -7.5, written as |-7.5|, is 7.5 because it is 7.5 units away from zero.
OppositesTwo numbers that have the same absolute value but different signs. They are the same distance from zero on a number line, but on opposite sides.4/5 and -4/5 are opposites. Both have an absolute value of 4/5.
MagnitudeThe size or 'bigness' of a number, without regard to its sign....
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Core Formulas
Piecewise Definition of Absolute Value
|x| = \begin{cases} x, & \text{if } x \ge 0 \\ -x, & \text{if } x < 0 \end{cases}
This is the formal definition. If a rational number 'x' is positive or zero, its absolute value is itself. If 'x' is negative, its absolute value is its opposite (e.g., the opposite of -5/2 is -(-5/2) = 5/2).
Absolute Value of a Quotient
|\frac{a}{b}| = \frac{|a|}{|b|}, \text{ for } b \neq 0
The absolute value of a fraction is equal to the absolute value of the numerator divided by the absolute value of the denominator. This simplifies calculations with rational numbers.
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Challenging
Let x = -3/4 and y = 1/2. What is the value of -(|x| + |y|)?
A.5/4
B.1/4
C.-1/4
D.-5/4
Challenging
A number 'n' is a negative rational number. Which of the following expressions will result in the largest value?
A.n
B.|n|
C.-n
D.Both B and C
Challenging
The distance on a number line between a rational number 'r' and 0 is 21/8. The number 'r' is located to the left of zero. What is the value of 'r'?
A.21/8
B.-21/8
C.8/21
D.-8/21
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Frequently asked questions
What grade level is "Absolute value of rational numbers"?
Absolute value of rational numbers is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Absolute value of rational numbers?
You'll be able to: Identify whether an integer is positive, negative, or zero with 100% accuracy; Order a set of at least five integers from least to greatest on a number line, and explain the reasoning behind the order; Compare two given integers….
Is "Absolute value of rational numbers" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Absolute value of rational numbers?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.