Inequalities with addition and subtraction of like and unlike fractions

key notes:

1. Understanding Fractions

• Like Fractions: Fractions that have the same denominator. Example: 3/7​ and 5/7​.
• Unlike Fractions: Fractions that have different denominators. Example: 3/4​ and 2/3​.

2. Inequalities

• Inequalities are expressions used to compare numbers that are not equal.
  • Common inequality symbols:
    • < (less than)
    • > (greater than)
    • ≤ (less than or equal to)
    • ≥ (greater than or equal to)
    • ≠ (not equal to)

3. Comparing Fractions with Inequalities

• To compare fractions, you need to make sure the fractions are expressed in the same form (like fractions) or convert them into equivalent fractions with the same denominator.

4. Addition and Subtraction of Like Fractions

• Like fractions: When adding or subtracting fractions with the same denominator, keep the denominator the same and add or subtract the numerators.

5. Addition and Subtraction of Unlike Fractions

• Unlike fractions: When adding or subtracting unlike fractions, first find a common denominator, convert the fractions, then proceed with the addition or subtraction.
  • Steps:
    1. Find the LCM (Least Common Multiple) of the denominators.
    2. Convert the fractions to equivalent fractions with the common denominator.
    3. Add or subtract the numerators.
    4. Simplify the result if possible.

6. Solving Inequalities with Fractions

• Steps to solve inequalities:
  1. Convert fractions to like fractions (same denominator) or use cross-multiplication for unlike fractions.
  2. Once fractions are comparable, perform addition or subtraction.
  3. Use the inequality symbols (<, >, ≤, ≥) to compare the results.

Learn with an example

let’s practice :