Multiplying and Dividing Fractions

using Rectangles

Multiplying and dividing fractions with rectangles helps students visualize the multiplication and division of fractions.  All you need is either regular notebook paper or graphing paper and something to color rectangles with. 

Fraction Rectangles

Draw a rectangle and divide it into the same number of pieces as the denominator.  Below I made the the fractions one-half and three-fourths.

fraction rectangles

Multiplying Fractions

Now we're ready to do some multiplication of fractions using rectangles.  Ready let's go.....

visualize multiplying fractions
  • Draw a rectangle and divide it into the same number of pieces as the denominator of the second fraction.  We divide the rectangle into equal columns. (Remember columns are vertical). 
  • Then create the fraction by coloring the same the number of columns as the numerator of that fraction - three-tenths.
  • Now we split the rectangle in fifths by drawing horizontal lines that divide the rectangle into five equal rows. 
  • Then we color three rows with a different color to show three-fifths of three-tenths.
  • So the answer (product) is the area of the triangle where both of the shadings overlap each other.  In the picture below, the shadings overlap in the small purple rectangle in the upper left corner. 

To Get the Answer

  • The Denominator: Count the number of total small rectangles after you draw the lines for both fractions.  For this example there are 50 total rectangles.
  • The Numerator: Count the number of small rectangles (purple here) where the shadings overlap.  In this example there are 9 rectangles where the shadings overlap.

I'll be putting some more examples up in the next couple of days.  I'll also demonstrate fraction division using rectangles too.  If you would like to share some pics of your rectangles for multiplying and dividing fractions, you can share them here.  Thanks for stopping by!

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