Problem 1 - Prealgebra and Introductory Algebra

Question

Fill in the blank with left or right. a. On a number line, the number \(-8\) is to the \(_______\) \(-3\) b. On a number line, the number 0 is to the \(________\) \(-4\)

Step-by-Step Solution

Answer

a. Left, b. Right

Step 1: Understand the relative position of numbers

On a number line, numbers are placed according to their value. Smaller numbers are on the left, larger numbers are on the right. So a number will be left to the other if it is smaller, and right if it is greater.

Step 2: Apply understanding to part a

For part a, \( -8 \) and \( -3 \) are given. Comparing both numbers, -8 is smaller than -3. So, \( -8 \) is to the left of \( -3 \) on a number line.

Step 3: Apply understanding to part b

For part b, the numbers are 0 and -4. Comparing these numbers, 0 is larger than -4. So, 0 is to the right of -4 on a number line.

Key Concepts

Relative Position of Numbers

On a number line, numbers have a specific order based on their values. This means every part of the line represents a number with a specific size. The smaller a number, the more it will be positioned to the left on the number line. Larger numbers move towards the right.

Think of it like reading a book. Just as words follow a specific order, numbers do too. This arrangement helps us quickly understand where one number stands compared to another. For example:

• The number -10 will always be to the left of -5.
• Meanwhile, the number 5 is always to the right of 0.

This order helps us easily identify which number is greater or lesser by simply looking at their positions.

Comparing Numbers

Comparing numbers is like playing a game of size and order. It helps us figure out which number is larger or smaller. On a number line, comparing isn't tough once you understand the relative positions.

Here's how it works:

• If a number is to the right of another, it's bigger.
• If a number is to the left of another, it's smaller.

Let's say we compare -8 and -3 from our exercise. When you observe their position on the number line, you'll notice that -8 is more to the left than -3. Therefore, -8 is smaller. This simple observation is all you need to compare numbers effectively!

Negative Numbers

Negative numbers might seem a bit tricky at first, but they're simply numbers with a minus sign in front. They are used to represent values below zero, commonly seen in places like temperatures or bank balances.

On a number line, negative numbers are always found to the left of zero. The more negative they are, the further left they are placed. Consider these points:

• -1 is closer to zero than -5, making -1 larger than -5.
• -100 is far to the left, meaning it's much smaller than, say, -20.

Understanding their placement helps in comparing and using them effectively, especially when dealing with real-life situations.