Operations with Fractions | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Adding & Subtracting Fractions

Dealing with mixed numbers

• Always convert mixed numbers to improper fractions before adding or subtracting.

Adding & subtracting

• Adding and subtracting are approached similarly:
  • Find the smallest whole number that each denominator divides, known as the lowest common denominator.
  • Convert each fraction to an equivalent fraction with the lowest common denominator by scaling the numerator and denominator proportionally.
  • Add or subtract the numerators and write the result over the single lowest common denominator without changing the denominators.
  • Check for any simplifications by canceling out common factors, especially if converting improper fractions to mixed numbers is required.

Multiplying Fractions

Dealing with mixed numbers 

• Convert mixed numbers into improper fractions before multiplication.

 Multiplying fractions 

• Cancel any numbers on the numerators with numbers on the denominators (from either fraction).
• Multiply the numerators.
• Multiply the denominators.
• Cancel any common factors again if possible.
• Convert improper fractions back into mixed numbers (if necessary or requested).

Dividing Fractions

Dealing with mixed numbers

• Always convert mixed numbers into top-heavy fractions before dividing.

Dividing fractions

• Instead of dividing fractions, "flip 'n' times" (flip the second fraction and change ÷ into ×).
• 
• Then multiply the fractions (multiply the numerators and denominators).
• Cancel the final answer if possible.