Final answer:
After converting all ribbon lengths to meters, the sister will get approximately 0.4666 meters of the 2 2/3 meters long ribbon once the student's 1 1/2 meters and the brother's 7/10 meters shares are removed.
Step-by-step explanation:
The student wants to know how much ribbon their sister will get after they and their brother have taken their shares from a ribbon that is 2 2/3 m long. The student will take 1 1/2 m, and the brother will take 7/10 m. To find out how much ribbon the sister will get, we first need to convert all lengths of ribbon to a common unit, which will be meters in this case.
First, we will add the lengths of ribbon the student and their brother will take:
- Student's share: 1 1/2 m = 1.5 m
- Brother's share: 7/10 m = 0.7 m
Now we add up the student's and brother's shares: 1.5 m + 0.7 m = 2.2 m. Next, we subtract this total from the length of the entire ribbon to find out how much the sister will get:
2 2/3 m - 2.2 m = 8/3 m - 2.2 m = 2.6666 m - 2.2 m = 0.4666 m (or 14/30 m when converted to a fraction, which simplifies to 7/15 m).
Therefore, the sister will get approximately 0.4666 meters of ribbon.