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In the first half of a basketball game, Shaundra made 2 of 6 free throws. In the second half, she made 7 of 8. Overall, what was her success rate for free throws in this game?

Suppose a middle school student responded to the above problem by writing: . Evaluate the student's answer.

Is the addition of ratios and fractions comparable? Do the ratios 1:3 and 7:8 add to yield a success rate equivalent to that of 2:6 plus 7:8? Why or why not?

 Extensions

Can you find any non-zero real numbers that would produce this type of equivalent relationship for fractions? That is, does for some case of a, b, c, and d? Explain.

 Related External Resources

Ratio and proportion
A lesson plan in which the students will use the phenomenological approach to complete the activities, calculate ratios and proportions and compare and contrast group data with class data.

Does more wins mean more fans at the ballpark?
Determine an attendance-to-win ratio for each of the 28 major league teams and then study the results to see if winning always leads to good attendance.

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