Multiplying fractions--the area model
This applet explains why, when you multiply fractions, you multiply the numerators and multiply the denominators.
The main idea is that the area of a rectangle is the product of its base and height. The two fractions that you are multiplying are the base and height (lengths), and the product of the fractions is the area of the rectangle.
How to use the applet:
Enter the numerators and denominators for two fractions in the boxes. These two fractions will be multiplied.
The yellow square is the unit of area (one square unit).
The area of the green rectangle is the product of the fractions.
For more control over size and views, zoom in or out. Use the buttons by using the triangle at the lower right of the Move Graphics View button.
Questions
The light yellow shaded square represents 1 square unit, the "whole".
The green rectangle hatched with green lines represents the product of the two fractions.
Lengths are measured along the horizontal and vertical axes.
- Look at the base of the yellow square, along the horizontal axis. How many pieces do the dotted lines divide this length into?
- How many of these smaller lengths make the base of the green rectangle?
- Look at the height of the yellow square, along the vertical axis. How many pieces do the dotted lines divide this length into?
- How many of these smaller lengths make the height of the green rectangle?
- How many small rectangles are in the yellow square? This is the number of parts in the whole.
- How many small rectangles are in the green rectangle? This is the number of parts in the green rectangle
- Write an equation multiplying the fractions and check that it agrees with your answers to #1-#6 and agrees with the equations in the applet.