1/15
00:00

O.1 Multiply two proper fractions

Loading questions...

Proper fractions

A proper fraction is a fraction where the numerator (top number) is less than the denominator (bottom number). Proper fractions represent a part of a whole that is less than one.

Examples:
  • 34 – three-fourths
  • 25 – two-fifths
  • 78 – seven-eighths
Note

Always check that the numerator is smaller than the denominator. If it is equal or greater, it is not a proper fraction.

Multiplying two proper fractions

To multiply two proper fractions, multiply the numerators together and multiply the denominators together. The result may need to be simplified.

Example:
  • Multiply 23 × 34
  • Step 1: Multiply the numerators: 2 × 3 = 6
  • Step 2: Multiply the denominators: 3 × 4 = 12
  • Step 3: Combine into a fraction: 612
  • Step 4: Simplify: 12
Note

Always simplify your fraction if possible. Divide both numerator and denominator by their greatest common factor (GCF).

Tips for multiplying proper fractions

When multiplying fractions, remember these key strategies:

Helpful Tips:
  • Check if the fractions are proper fractions before multiplying.
  • Multiply straight across: numerator × numerator, denominator × denominator.
  • Simplify the result by dividing both numerator and denominator by their GCF.
  • Practice visualizing fractions as parts of a whole to understand multiplication better.
Note

Multiplying fractions does not make the product larger than 1 if both fractions are proper. The answer will always be smaller than each original fraction.