Absolute Value
Absolute Value is a skill on Pengi from Lesson 3: Some Basic Graphs in Yoshiwara Intermediate Algebra.
Key Concepts
Property The absolute value of $x$ represents the distance from $x$ to the origin on the number line. Because distance is never negative, the absolute value is always non negative. It is defined piecewise: $$|x| = \begin{cases} x & \text{if } x \geq 0 \\ x & \text{if } x < 0 \end{cases}$$.
Examples To simplify $|3 8|$, first perform the operation inside the bars: $|3 8| = | 5|$. Then take the absolute value, which is $5$. In the expression $|3| |8|$, we evaluate each absolute value first: $3 8$. The result is $ 5$. This shows that $|a b|$ is not always the same as $|a| |b|$. To simplify $5 + 2| 4|$, we first evaluate the absolute value: $| 4| = 4$. The expression becomes $5 + 2(4) = 5 + 8 = 13$.
Explanation Absolute value essentially makes any number positive. It measures a number's distance from zero on a number line, and distance is always a positive concept. Whether a number is positive or negative, its absolute value is its positive counterpart.
Common Questions
What is Absolute Value?
Absolute Value is a skill on Pengi from Lesson 3: Some Basic Graphs in Yoshiwara Intermediate Algebra.
What grade level is Absolute Value for?
Absolute Value is part of the Grade 7 Math curriculum, covered in Yoshiwara Intermediate Algebra. It is designed for students studying Math at the Grade 7 level.
How can I learn Absolute Value?
Pengi offers an AI-guided lesson for Absolute Value that walks you through the key concepts step by step. The lesson is aligned to Yoshiwara Intermediate Algebra so the content matches what you see in class.
How do I practice Absolute Value?
After learning the concept, use the Practice mode to work through targeted exercises on Absolute Value. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Absolute Value?
Absolute Value is covered in Yoshiwara Intermediate Algebra, specifically in Chapter 5: Functions and Their Graphs under Lesson 3: Some Basic Graphs. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Absolute Value free to study on Pengi?
Yes, the core Learn and Practice modes for Absolute Value are available for free on Pengi. No credit card is required to start studying.