Rational numbers can be a bit tricky to understand and work with, but with practice, you’ll become more comfortable and confident. In this worksheet, we’ll go through some examples and exercises to help you master ordering rational numbers.
What are Rational Numbers?
Rational numbers are numbers that can be expressed as the ratio of two integers, i.e., a fraction. They can be positive, negative, or zero. Examples of rational numbers include:
- Integers: 5, -3, 0
- Fractions: 1⁄2, 3⁄4, 2⁄3
- Decimals: 0.5, -0.25, 0.75
How to Order Rational Numbers
To order rational numbers, we need to compare their values. Here are the steps:
- Convert to equivalent decimals: Convert each rational number to a decimal by dividing the numerator by the denominator.
- Compare the decimals: Compare the decimal values. If one decimal is greater than another, then the corresponding rational number is greater.
Let’s practice with some examples:
Examples
- Order the rational numbers: 1⁄2, 3⁄4, 2⁄3
Solution:
- Convert to equivalent decimals: 1⁄2 = 0.5, 3⁄4 = 0.75, 2⁄3 = 0.67
- Compare the decimals: 0.5 < 0.67 < 0.75
- Therefore, the correct order is: 1⁄2, 2⁄3, 3⁄4
- Order the rational numbers: -2⁄3, -1⁄2, 0
Solution:
- Convert to equivalent decimals: -2⁄3 = -0.67, -1⁄2 = -0.5, 0 = 0
- Compare the decimals: -0.67 < -0.5 < 0
- Therefore, the correct order is: -2⁄3, -1⁄2, 0
Exercises
Now it’s your turn to practice! Order the rational numbers in each of the following exercises:
Exercise 1
Order the rational numbers: 3⁄4, 2⁄3, 1⁄2
- Convert to equivalent decimals: _______________________
- Compare the decimals: _______________________
- Correct order: _______________________
Exercise 2
Order the rational numbers: -1⁄3, -2⁄5, -1⁄4
- Convert to equivalent decimals: _______________________
- Compare the decimals: _______________________
- Correct order: _______________________
Exercise 3
Order the rational numbers: 2⁄5, 3⁄4, 1⁄3
- Convert to equivalent decimals: _______________________
- Compare the decimals: _______________________
- Correct order: _______________________
Answer Key
Exercise 1
- Convert to equivalent decimals: 3⁄4 = 0.75, 2⁄3 = 0.67, 1⁄2 = 0.5
- Compare the decimals: 0.5 < 0.67 < 0.75
- Correct order: 1⁄2, 2⁄3, 3⁄4
Exercise 2
- Convert to equivalent decimals: -1⁄3 = -0.33, -2⁄5 = -0.4, -1⁄4 = -0.25
- Compare the decimals: -0.4 < -0.33 < -0.25
- Correct order: -2⁄5, -1⁄3, -1⁄4
Exercise 3
- Convert to equivalent decimals: 2⁄5 = 0.4, 3⁄4 = 0.75, 1⁄3 = 0.33
- Compare the decimals: 0.33 < 0.4 < 0.75
- Correct order: 1⁄3, 2⁄5, 3⁄4
We hope this worksheet has helped you understand and practice ordering rational numbers. Remember to always convert to equivalent decimals and compare the decimals to determine the correct order.
🤔 Note: Make sure to check your answers with the answer key provided above.
What is a rational number?
+A rational number is a number that can be expressed as the ratio of two integers, i.e., a fraction.
How do I order rational numbers?
+To order rational numbers, convert each rational number to a decimal by dividing the numerator by the denominator, and then compare the decimals.
Can I use a calculator to help with ordering rational numbers?
+Yes, you can use a calculator to help with converting rational numbers to decimals, but make sure to double-check your work to ensure accuracy.
Mastering rational numbers takes time and practice, but with this worksheet and the tips provided, you’ll be well on your way to becoming a pro at ordering rational numbers!
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