Compare and order rational numbers

key notes :

Understand Rational Numbers

  • Rational numbers are numbers that can be expressed as a fraction a/b ​, where a and b are integers, and b≠0.
  • They include integers, fractions, and decimals that either terminate or repeat.

Convert to a Common Form

  • Fractions: Ensure all fractions have a common denominator to compare them easily. Find the least common multiple (LCM) of the denominators, convert each fraction, and then compare the numerators.
  • Decimals: Convert decimals to fractions if necessary, or compare them directly by looking at their digits. For example, 0.75 is greater than 0.5 because 0.75 has more value.

Compare Fractions

  • Find a Common Denominator: Convert fractions to have the same denominator.
  • Compare Numerators: Once fractions have the same denominator, compare the numerators. The fraction with the larger numerator is greater.

Example:

2⁄5 and 3⁄7

  • LCM of 5 and 7 is 35.
  • 2⁄5 = 14⁄35
  • 3⁄7 = 15⁄35
  • 14⁄35 < 15⁄35 so 2⁄5 <3⁄7.

Compare Decimals

  • Align Decimal Points: Compare digits from left to right.
  • Add Zeros if Necessary: Extend decimals with fewer digits by adding zeros to make them the same length.

Example:

  • Compare 0.85 and 0.8.
  • 0.85 is greater than 0.80 (adding a zero for comparison).

Order Rational Numbers

  • List Rational Numbers: Once you have converted or compared them, list them in ascending or descending order based on their values.

Example:

  • Rational numbers: 3⁄4, –1⁄2, 5⁄6.
  • Convert to decimals: 0.75, -0.5, 0.833
  • Order: −0.5, 0.75, 0.833.

Use a Number Line (Optional)

  • Plot the rational numbers on a number line to visually compare and order them.

Practice Example

Order the following rational numbers: 1⁄2, 0.4 , 3⁄4

  • Convert all to decimals: 1⁄2 = 0.5; 3⁄4 = 0.75.
  • Compare decimals: 0.4, 0.5, 0.75.
  • Order: 0.4 < 0.5 < 0.75.

Learn with an example

🎯 Which sign makes the statement true?

11/50 ? 1/50

  • >
  • <
  • =

11/50 is greater than 1/50 , so:

11/50 > 1/50 .

🎯 Which sign makes the statement true?

39/40 ? -1/2

  • >
  • <
  • =

39/40 is positive and -1/2 is negative. A positive number is always greater than a negative number. So:

39/40 > -1/2 .

🎯 Which sign makes the statement true?

1/2 ? 3/6

  • >
  • <
  • =

Simplify.

1/2 ? 3/6

1/2 ? 1/2

The fractions are the same. So:

1/2 = 3/6

Let’s Practice!