Finding five rational numbers between any two numbers, such as 1 and 2, is quite simple. A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero. Here’s a step-by-step guide to help you find five rational numbers between 1 and 2:
- Understanding the Range: First, we acknowledge that the numbers we need to find are between 1 and 2. This means that our numbers must be greater than 1 and less than 2.
- Choosing the Denominator: One of the easiest ways to find rational numbers is by converting the numbers into fractions. We can use a common denominator, such as 10, which makes it easier to find numbers within that range.
- Creating Fractions: To create rational numbers between 1 and 2, we can divide the interval into equal parts. For example:
- 1.1 = 11/10
- 1.2 = 12/10
- 1.3 = 13/10
- 1.4 = 14/10
- 1.5 = 15/10
- Listing the Numbers: So the five rational numbers we found between 1 and 2 are:
- 11/10
- 12/10
- 13/10
- 14/10
- 15/10
- Alternative Methods: Besides using 10 as the denominator, you can also choose other denominators, such as 2 or 5, to find different rational numbers. For instance, using a denominator of 4 gives us:
- 5/4
- 6/4
- 7/4
- 8/4
- 9/4
In summary, to find rational numbers between 1 and 2, you can create fractions that fall within that range. The possibilities are virtually endless, so feel free to experiment with different fractions!