مقارنة الأعداد النسبية وترتيبها ( رياضيات / ثاني متوسط ف1)

Introduction

This tutorial will guide you through comparing and ordering rational numbers, a fundamental concept in mathematics for second-grade students in Saudi Arabia. Understanding how to compare these numbers is essential for performing operations and solving problems involving fractions and decimals.

Step 1: Understanding Rational Numbers

• Define rational numbers as numbers that can be expressed as the quotient of two integers (a/b), where b is not zero.
• Recognize that rational numbers include:
  • Integers (e.g., -2, 0, 5)
  • Fractions (e.g., 1/2, 3/4)
  • Decimals that terminate or repeat (e.g., 0.75, 0.333...)

Step 2: Finding a Common Denominator

• To compare fractions, it's often necessary to convert them to a common denominator.
• Steps to find a common denominator:
  1. Identify the denominators of the fractions you want to compare.
  2. Determine the least common multiple (LCM) of these denominators.
  3. Convert each fraction to an equivalent fraction with the common denominator.

Example

• Compare 1/3 and 1/4.
  • Denominators: 3 and 4
  • LCM of 3 and 4 is 12.
  • Convert:
    • 1/3 = 4/12
    • 1/4 = 3/12
  • Now you can compare 4/12 and 3/12.

Step 3: Ordering Rational Numbers

• Once the rational numbers are expressed with a common denominator, you can easily compare them.
• Steps to order numbers:
  1. Identify the numerators of the equivalent fractions.
  2. List the numbers in ascending (smallest to largest) or descending (largest to smallest) order based on their numerators.

Example

• Using the previous example:
  • 4/12 > 3/12
  • Thus, 1/3 > 1/4.

Step 4: Comparing Mixed Numbers

• Mixed numbers can also be compared by converting them to improper fractions.
• Steps:
  1. Convert the mixed number to an improper fraction.
  2. Follow the steps for finding a common denominator and ordering as previously described.

Example

• Compare 2 1/2 and 2 2/3:
  • Convert:
    • 2 1/2 = 5/2
    • 2 2/3 = 8/3
  • Find the LCM of 2 and 3 (which is 6), convert:
    • 5/2 = 15/6
    • 8/3 = 16/6
  • Since 16/6 > 15/6, 2 2/3 > 2 1/2.

Conclusion

In this tutorial, you learned how to compare and order rational numbers and mixed numbers. By finding a common denominator and converting fractions, you can effectively determine which numbers are greater or lesser. Practice this method with various rational numbers to enhance your understanding, and remember to convert mixed numbers to improper fractions for easier comparison. Happy studying!