Absolute Value of Rational Numbers Worksheets Grade 7

📚 Topic Summary

The absolute value of a rational number is its distance from zero on the number line. Since distance is always non-negative, the absolute value of a number is always positive or zero. For any rational number $x$, the absolute value is denoted by $|x|$. If $x$ is positive or zero, then $|x| = x$. If $x$ is negative, then $|x| = -x$. Understanding absolute value is crucial for solving equations and inequalities involving rational numbers.

Absolute value is essential because it helps us understand the magnitude of a number without considering its sign. This concept is used in various mathematical contexts, including finding distances, defining intervals, and solving equations where only the magnitude of a number matters.

🧮 Part A: Vocabulary

Match the term with its definition:

1. Term: Absolute Value
2. Term: Rational Number
3. Term: Integer
4. Term: Number Line
5. Term: Magnitude

1. Definition: A line on which numbers are marked at intervals, used to illustrate numerical relationships.
2. Definition: The size or extent of something.
3. Definition: Any number that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers.
4. Definition: The distance of a number from zero on the number line.
5. Definition: A whole number (not a fraction) that can be positive, negative, or zero.

✍️ Part B: Fill in the Blanks

Complete the following paragraph using the words: positive, zero, distance, negative, absolute value.

The ______ of a number is its ______ from ______ on the number line. The absolute value is always ______ or ______. If a number is ______, its absolute value is its opposite.

🤔 Part C: Critical Thinking

Explain, in your own words, why the absolute value of any number is never negative. Provide an example to support your explanation.