• Understand how to use a number line to place numbers and figure out which numbers are bigger or smaller using signs like [latex]<[/latex] and [latex]>[/latex]

Using Number Lines to Compare Numbers

Number lines are powerful tools that help us visualize numbers and their relationships. They’re especially useful for understanding which numbers are bigger or smaller, and for using comparison symbols like [latex]<[/latex] (less than) and [latex]>[/latex] (greater than).

Number Line

A number line is a straight line where each point represents a number. Here are some key features:

1. The line extends infinitely in both directions.
2. Numbers increase as you move right and decrease as you move left.
3. The space between each whole number is divided into equal parts.

Number Line

A number line is a visual representation of numbers on a straight line, typically drawn horizontally.

 

Each point on the line corresponds to a number, with equal spacing between consecutive numbers, which allows for accurate measurement and comparison of the size of numbers.

 

The line includes a central point, typically marked as zero, with positive numbers extending infinitely to the right and negative numbers extending infinitely to the left.

 

How to: Place Numbers on a Number Line

To place a number on a number line:

1. Identify the nearest whole numbers.
2. Count the spaces between those whole numbers.
3. Place your number in the correct position between them.

Plot the numbers on a number line: [latex]4, -3, -1.2 \text{ and } \frac{1}{2}[/latex]

Show Answer

• To plot [latex]4[/latex], start at [latex]0[/latex] and count four units to the right.
• To plot [latex]-3[/latex], start at [latex]0[/latex] and count three units to the left.
• To plot [latex]-1.2[/latex], start at [latex]0[/latex] and count one units to the left. From [latex]-1[/latex], move slightly further left. Since [latex]-1.2[/latex] is [latex]0.2[/latex] units less than [latex]-1[/latex], you move[latex]0.2[/latex] units towards [latex]-2[/latex]. The precise spot is [latex]20\%[/latex] of the way from [latex]-1[/latex] to [latex]-2[/latex].
• The number [latex]\frac{1}{2}[/latex] lies halfway between [latex]0[/latex] and [latex]1[/latex]. Identify the halfway mark and place the point there.

Comparing Numbers Using a Number Line

We can use the number line to compare and order positive and negative numbers. Going from left to right, numbers increase in value. Going from right to left, numbers decrease in value.

We can use inequality symbols to show the ordering of positive and negative numbers.

• [latex]a < b[/latex]: [latex]a[/latex] is less than [latex]b[/latex]
  • Use [latex]<[/latex] when the first number is to the left of the second number on the number line.
• [latex]a > b[/latex]: [latex]a[/latex] is greater than [latex]b[/latex]
  • Use [latex]>[/latex] when the first number is to the right of the second number on the number line.

The same principles apply to negative numbers, but remember:

• Negative numbers are to the left of zero.
• The more negative a number, the smaller it is.

Order each of the following pairs of numbers using [latex]<[/latex] or [latex]>[/latex].

• [latex]14 \text{ and }6[/latex]
• [latex]-1 \text{ and }9[/latex]
• [latex]-1 \text{ and }-4[/latex]
• [latex]2 \text{ and }-20[/latex]

Show Answer

1. Compare [latex]14[/latex] and [latex]6[/latex]
[latex]14[/latex] is to the right of [latex]6[/latex] on the number line.	[latex]14>6[/latex]

2. Compare [latex]-1[/latex] and [latex]9[/latex]
[latex]-1[/latex] is to the left of [latex]9[/latex] on the number line.	[latex]-1<9[/latex]

3. Compare [latex]-1[/latex] and [latex]-4[/latex]
[latex]-1[/latex] is to the right of [latex]-4[/latex] on the number line.	[latex]-1>-4[/latex]

4. Compare [latex]2[/latex] and [latex]-20[/latex]
[latex]2[/latex] is to the right of [latex]-20[/latex] on the number line.	[latex]2>-20[/latex]