Question

Write a problem that can be solved by finding \(|9-17|\). What is the value of \(|9-17| ?\)

Short answer

The value of \(|9-17|\) is 8.

Step-by-step solution

Understanding Absolute Values

The absolute value of a number refers to its distance from zero on the number line, regardless of the direction. It is always a non-negative number.

Rewriting the Expression

To solve the problem, we start by rewriting the expression with the numbers given: \(|9-17|\).

Solving the Subtraction Inside the Absolute Value

Calculate the result of the expression inside the absolute value: \(9 - 17 = -8\).

Applying the Absolute Value

Take the absolute value of the result obtained in the previous step. The absolute value of \(-8\) is \(8\) since absolute values disregard the sign and only consider the magnitude.

Key concepts

Number Line

Imagine the number line as a long straight line where numbers are placed at equal intervals. It's like a ruler for numbers. Zero is usually at the center. Positive numbers stretch out to the right, like 1, 2, 3, and so on. Negative numbers go to the left, such as -1, -2, -3, and so forth.
This line helps us understand where each number sits in relation to zero. For instance, if you were to stand on number 9, you're nine steps to the right of zero.

• Positive numbers increase as you move right.
• Negative numbers decrease as you move left.
• Zero is the neutral point between positives and negatives.

Understanding the number line is key to grasping many math concepts, especially with operations like subtraction and in deciphering distance on this line.

Negative Numbers

Negative numbers can be tricky, but they're not so bad once you get to know them. They are simply numbers less than zero. Think of negative numbers as owing money. For instance, if you have -$8, it's like saying you owe someone 8 dollars.
On the number line, negative numbers extend to the left of zero. This is why when we subtract larger numbers from smaller ones, like in the expression \(9 - 17\), we end up with a negative result (-8).

• Negative sign changes the direction of the value on the number line.
• They represent quantities less than zero.
• Useful for understanding depths below sea level, debts, and temperatures below freezing.

Mastery of negative numbers is essential for understanding various mathematical operations and real-world applications.

Distance from Zero

In math, the distance from zero is known as absolute value. It's important because it tells us how far a number is from zero on the number line, without worrying about direction. For any number, its absolute value is always positive.
Let's consider the expression \(|9 - 17|\). When subtracting 17 from 9, we get -8. However, to find the absolute value, we only care about how far -8 is from zero, which is 8 steps. This distance is noted without a negative sign, as we're focusing on the magnitude.

• Absolute value ignores whether the number is negative or positive.
• Always a non-negative result.
• Think of it as simply measuring the length from zero to the number's position.

Recognizing the absolute value allows you to understand the concept of magnitude in various contexts, making math problems simpler to handle.