Strategies and Models
Fractions of Fractions: Use the grid model
1. Draw a rectangle
2. Make 5 columns for the first fraction. Shade in two of the columns since you have 2/5 (blue)
3. Make 3 rows for the second fraction. Shade in two of the rows since you have 2/3 (red)
4. You will see that the rectangle is now divided into smaller parts; in this case, we have 15 small parts. This is your new denominator.
5. How many parts are shaded in with both colours (purple)? This is your new denominator.
Mixed fraction times mixed fraction: use the area model
1. Draw a rectangle and divide it into the four areas (1 large, 2 medium, 1 small)
2. Multiply the whole numbers (1x2). This goes in the large area.
3. Multiply one whole by the OTHER fraction (1 x 2/3). This goes into one of the medium areas.
4. Multiply the other whole number by the OTHER fraction (2 x 1/2). This goes into the other medium area.
5. Multiply the two fractions (1/2 x 2/3). This goes into the smallest area.
6. Add up the four products from steps 2-5. Remember to use common denominators.
7. Reduce to lowest terms if necessary.
- fraction of a fraction --> use grid model or algorithm
- mixed fraction x improper fraction --> convert both to improper and use algorithm
- mixed fraction x fraction --> convert mixed to improper and use algorithm