Modeling Multiplying Fractions

2/3 of 7/10 means 2/3 x 7/10.  The of can be replaced with a multiplication sign.  We begin by drawing a square.

Split the box according to the denominator of the SECOND factor.

Mark off the amount that makes the second factor true.  In this case we marked out 3/10 of the whole because we only have 7/10 of the whole left.

Then split the WHOLE box by the denominator of the FIRST factor.

I labeled the top 1/3 to show that each vertical bar represents 1/3 and the left side 1/10 to show that each horizontal bar represents 1/10.




















I then shaded 2 out of every 3 boxes left over in green.  (sorry the picture is blurry).

The total green boxes represents my numerator.  The TOTAL boxes of the whole becomes my denominator, not just the part leftover.

This shows mathematically why that works.