SOLUTION: Hi. Here is the problem: Rosalie makes 3 sugar cookies and puts blue frosting on 2 of those cookies. She puts yellow frosting on the other one. Ellie makes 4 sugar cookies an

Question 34848: Hi. Here is the problem:
Rosalie makes 3 sugar cookies and puts blue frosting on 2 of those cookies. She puts yellow frosting on the other one. Ellie makes 4 sugar cookies and puts blue frosting on 3 of them. She puts yellow frosting on the other one. If the girls put all of their cookies together, they have 7 cookies, and 5 of those cookies have blue frosting.
The addition sentence looks like: 2/3 + 3/4 = 5/7. But we learn that 2/3 + 3/4 = 17/12 or 1 5/12. Why do we have these discrepancies? How do we fix these differences?
Can you explain this to me? Thanks in advance!!!
Answer by stanbon(57214) (Show Source):
You can put this solution on YOUR website!
"The addition sentence looks like: 2/3 + 3/4 = 5/7."
This sentence is mathematically wrong.
Fractions are not added by adding the numerators
and then adding the denominators as is done in
this sentence.
The rules require that we find a least common denominator,
convert each fraction to that denominator, then add.
The LCM for your problem is 12
The fractions become 8/12 + 9/12
The sum then becomes 17/12 or 1 5/12
Cheers,
stan H.