Multiplying Fractions

Key Steps to Multiply Fractions

1. Multiply the Numerators

   • Multiply the top numbers of the fractions.

2. Multiply the Denominators

   • Multiply the bottom numbers of the fractions.

3. Simplify the Fraction

   • Simplify the fraction if needed by finding the greatest common divisor of the numerator and denominator.

Example Calculation

• Given fractions: ( \frac{1}{2} ) and ( \frac{2}{5} )

  Step 1: Multiply the numerators:

  • ( 1 \times 2 = 2 )

  Step 2: Multiply the denominators:

  • ( 2 \times 5 = 10 )

  Step 3: Simplify the fraction:

  • ( \frac{2}{10} = \frac{1}{5} )

Visual Example

• Conceptualized using pizza slices to show ( \frac{1}{2} ) of ( \frac{2}{5} ) is ( \frac{2}{10} ), which simplifies to ( \frac{1}{5} ).

Pen and Paper Method

• Step-by-step visual guidance with pen and paper, involving a play button for interactive demonstration.

Another Example

• Given fractions: ( \frac{1}{3} ) and ( \frac{9}{16} )

  Step 1: Multiply the numerators:

  • ( 1 \times 9 = 9 )

  Step 2: Multiply the denominators:

  • ( 3 \times 16 = 48 )

  Step 3: Simplify the fraction:

  • ( \frac{9}{48} = \frac{3}{16} )
  • Simplification by dividing both top and bottom by 3.

Multiplying Fractions and Whole Numbers

• Convert whole numbers into fractions by placing them over 1.
• Example: 5 is ( \frac{5}{1} )
• Multiply as with regular fractions:
  • ( \frac{2}{3} \times 5 = \frac{10}{3} ), already simplified.
• Alternative thinking: Treat whole number as a numerator.

Example

• Given: ( 3 \times \frac{2}{9} )

  Step 1: Multiply tops and bottoms:

  • ( 3 \times 2 = 6 )
  • ( 1 \times 9 = 9 )

  Step 2: Simplify:

  • ( \frac{6}{9} = \frac{2}{3} )

Additional Topics

• Rhyme for memorization:

  • "Multiplying fractions: no big problem, Top times top over bottom times bottom. And don't forget to simplify, Before it's time to say goodbye."

• Mixed Fractions:

  • Reference to further reading on multiplying mixed fractions.

These notes summarize the steps and examples provided for multiplying fractions, including handling whole numbers and simplification techniques.