MBRA: Multiplying fractions

Example: 8⁄9 × 5⁄7:

  1. We start by drawing a picture of the multiplication. This is very similar to the picture(s) we would have drawn for Natural Number multiplication:
    5⁄7
    8⁄9

  2. Next, we break the area up into denominator parts.

    Our picture then looks like this ... 7 pieces wide (from the 7 in 5⁄7) and 9 pieces high (from the 9 in 8⁄9):

    5⁄7
    8⁄9

  3. We need to find the numerator parts, so we'll color them differently.

    Our picture then looks like this ... 7 pieces wide (from the 7 in 5⁄7) with 5 colored red (from the 5 in 5⁄7):

     5⁄7  =>
    Which, because 5⁄7 = 45⁄63 is the same as:

    and 9 pieces high (from the 9 in 8⁄9) with 8 colored blue (from the 8 in 8⁄9):

    8⁄9 => which is the same as =>

    We put them together, coloring the pieces covered by both fractions in magenta:

    5⁄7
    8⁄9

  4. How many pieces are part of both fractions (magenta)?5 × 8 =40
    How many pieces do we have total?7 × 9 =63
    What is the result of 8⁄9 × 5⁄7?40⁄63