Another measurement model for fraction division allows us to make common markings on fraction strips. This model shows the reason for finding a least common denominator. NOTE: both fractions must reference the same size "whole".
EXAMPLE: Model 3/4 -:- 1/2 = ________
On your graph paper, choose an appropriate "whole" fraction strip so that both fractions can be modeled easily. Model 3/4 above and 1/2 below. Now mark the 3/4 strip with halves using dashed vertical lines. Mark the 1/2 strip with fourths using dashed vertical lines. This divides each fraction representation into equal pieces. The ratio of these equal pieces is 3 to 2, or 3/2. This model automatically simplifies the fraction.
EXAMPLE: Model 6/5 -:- 1/3 = ________
On your graph paper, choose an appropriate "whole" fraction strip so that both fractions can be modeled easily.
Model 6/5 on the upper strip (notice this improper fraction extends beyond the "whole" -- the extra length beyond one whole is colored orange).
Model 1/3 on the bottom strip. Now split each of the 6/5 strip sections into 3 parts. Split the 1/3 section into 5 parts. Now both red and yellow pieces are of equivalent sizes.