Roger has played basketball for 5 3/4 years. Cindy has played for 2 5/6 years. What us a reasonable estimate for how much longer Roger has played than Cindy?

5 3/4 is almost 6

2 5/6 is almost 3

What do you think is a reasonable estimate?

3 years?

Right. We'd naturally say that Roger has played for about three years longer than Cindy.

5 3/4=5+(3/4)=5+(9/12)=(60/12)+(9/12)=69/12

2 5/6=2+5/6=2+(10/12)=(24/12)+(10/12)=34/12

(69/12)-(34/12)= 35/12=(24/12)+(11/12)
=2+(11/12)= 2 11/12

To find a reasonable estimate for how much longer Roger has played basketball than Cindy, we need to subtract their playing durations.

First, let's convert the mixed numbers to improper fractions:
- Roger has played for 5 3/4 years, which is (4 * 5 + 3)/4 = 23/4 years.
- Cindy has played for 2 5/6 years, which is (6 * 2 + 5)/6 = 17/6 years.

Next, subtract the fractions:
Roger - Cindy = (23/4) - (17/6)

To simplify the problem, we need to find the least common denominator (LCD) between 4 and 6, which is 12. Then we convert the fractions:
Roger - Cindy = (23/4) - (17/6)
= (23/4) * (3/3) - (17/6) * (2/2)
= (69/12) - (34/12)
= 35/12

Therefore, a reasonable estimate for how much longer Roger has played than Cindy is approximately 35/12 years.