Question

What number is halfway between 1.8 and 3.2 on the number line?

Short answer

2.5

Step-by-step solution

- Understand the Problem

The task is to find the number that is exactly in the middle of 1.8 and 3.2 on the number line. This means finding the average of these two numbers.

- Add the Numbers

First, add the two numbers together. Calculate: \(1.8 + 3.2 = 5.0\)

- Divide by 2

Next, take the sum from Step 2 and divide it by 2 to find the average: \(\frac{5.0}{2} = 2.5\)

- Verify

Confirm that 2.5 is halfway between 1.8 and 3.2 by checking the distances: \(2.5 - 1.8 = 0.7\) \(3.2 - 2.5 = 0.7\). Both distances are equal, so the calculation is correct.

Key concepts

number line

A number line is a visual representation of numbers in order, placed along a straight line. Each point on the line corresponds to a number, and the spacing between these points is consistent.
When working with a number line, it's crucial to understand the position of numbers relative to each other.
For instance, if you want to find a number halfway between two points like 1.8 and 3.2, you visualize both numbers on the line.
This mental image helps you understand that the desired number lies directly in the center between these two points.
Visualizing numbers this way aids in comprehension and problem-solving.

average calculation

To find the midpoint between two numbers, you need to calculate their average.
The average of two numbers gives you a balanced value that lies exactly in the middle of them.
Here's how you do it:

• First, add the two numbers together.
• Then, divide the sum by 2.

For our example, we add 1.8 and 3.2 to get 5.0 and then divide by 2 to get 2.5.
So, 2.5 is the number exactly halfway between 1.8 and 3.2.
Averages are useful because they provide a simple way to identify central points, making comparisons and positioning on a number line easier.

distance verification

Verifying distances helps ensure your calculations are correct.
To confirm that 2.5 is truly halfway between 1.8 and 3.2, we need to check the distances from 2.5 to each number.
We subtract 1.8 from 2.5, which gives us 0.7.
Next, we subtract 2.5 from 3.2, also yielding 0.7.
Since both distances are equal, this confirms that 2.5 is equidistant from 1.8 and 3.2.
This step is essential because it verifies the accuracy of our result.
Distance verification is a practical approach to validate that midpoint calculations and other measurements on a number line are correct.