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: Reduce the fraction to its simplest form if necessary.

Example Walkthrough

• Example 1:

  • Fractions: ( \frac{1}{2} \times \frac{2}{5} )
  • Step 1: Multiply the numerators: ( 1 \times 2 = 2 )
  • Step 2: Multiply the denominators: ( 2 \times 5 = 10 )
  • Step 3: Simplify: ( \frac{2}{10} \rightarrow \frac{1}{5} )

• Example 2:

  • Fractions: ( \frac{1}{3} \times \frac{9}{16} )
  • Step 1: Multiply the numerators: ( 1 \times 9 = 9 )
  • Step 2: Multiply the denominators: ( 3 \times 16 = 48 )
  • Step 3: Simplify: ( \frac{9}{48} \rightarrow \frac{3}{16} )
    • Simplification done by dividing both numerator and denominator by 3.

Visual Explanation with Pizza

• Illustration shows how multiplying fractions can be visualized using pizza slices.
  • Example: Half of two-fifths is equivalent to two-tenths, simplifying to one-fifth.

Rhyming Method

• Memorization aid:
  • "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."

Multiplying Fractions and Whole Numbers

• Approach:

  • Convert whole number to a fraction by placing it over 1.
  • Example: 5 becomes ( \frac{5}{1} ).
  • Continue with multiplication as usual.

• Example:

  • Fractions: ( \frac{2}{3} \times 5 )
  • Convert 5: ( \frac{2}{3} \times \frac{5}{1} )
  • Multiply: ( \frac{2 \times 5}{3 \times 1} = \frac{10}{3} )

Alternative Whole Number Approach

• Whole number as a top number:
  • Example: 3 x ( \frac{2}{9} )
  • Multiply tops and bottoms:
    • ( \frac{3 \times 2}{9} = \frac{6}{9} )
  • Simplify: ( \frac{6}{9} \rightarrow \frac{2}{3} )

Multiplying Mixed Fractions

• For more information, explore how to multiply mixed fractions: Link to resource