1995 AMC 8 Problem 3

Attempt Problem 3 of the 1995 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

3.

Which of the following operations has the same effect on a number as multiplying by 34\dfrac34 and then dividing by 35?\dfrac35?
dividing by 43\dfrac43
dividing by 920\dfrac{9}{20}
multiplying by 920\dfrac{9}{20}
dividing by 54\dfrac54
multiplying by 54\dfrac54
Answer: E
Concepts:fraction
Small hint:
Dividing by 35\dfrac35 is the same as multiplying by 53\dfrac53
Big hint:
Combine 34×53\dfrac34 \times \dfrac53 into a single fraction
Solution:
Dividing by 35\dfrac35 is the same as multiplying by 53,\dfrac53, so the two operations together multiply by
34×53=54.\dfrac34 \times \dfrac53 = \dfrac54.
So the combined effect is multiplying by 54\dfrac54.
Thus, the correct answer is E .
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