2023 AMC 8 第 10 题

先试着解答 2023 AMC 8 第 10 题,然后核对你的答案与视频与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2023 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

10.

哈罗德做了一个李子派去野餐。他只吃了这个派的 14\frac{1}{4},把剩下的留给朋友。一只驼鹿经过,吃掉了哈罗德留下部分的 13\frac{1}{3}。之后,一只豪猪又吃掉了驼鹿留下部分的 13\frac{1}{3}。豪猪离开后,原来的派还剩多少?
Harold made a plum pie to take on a picnic. He was able to eat only 14\frac{1}{4} of the pie, and he left the rest for his friends. A moose came by and ate 13\frac{1}{3} of what Harold left behind. After that, a porcupine ate 13\frac{1}{3} of what the moose left behind. How much of the original pie still remained after the porcupine left?
112\dfrac{1}{12}
16\dfrac{1}{6}
14\dfrac{1}{4}
13\dfrac{1}{3}
512\dfrac{5}{12}
答案:D
知识点:分数
小提示:
始终用原来整个派的分数来表示剩余量
Work with the fraction of the original pie remaining
大提示:
哈罗德吃完后剩 34\frac34;驼鹿吃完后再乘 23\frac23
After Harold, 34\frac34 remains; after the moose, multiply by 23\frac23
视频讲解:
解答视频缩略图
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文字解答:
哈罗德把整个派的 1−14=341 - \frac{1}{4} = \frac{3}{4} 留给了朋友。
驼鹿吃掉其中 13⋅34=14\frac{1}{3} \cdot \frac{3}{4} = \frac{1}{4},所以剩下 34−14=12\frac{3}{4} - \frac{1}{4} = \frac{1}{2}。
豪猪再吃掉剩余的 13⋅12=16\frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6},所以最后剩下 12−16=13\frac{1}{2} - \frac{1}{6} = \frac{1}{3}。
所以正确答案是 D。
Harold left 1−14=341 - \frac{1}{4} = \frac{3}{4} of the pie for his friends.
The moose ate 13⋅34=14\frac{1}{3} \cdot \frac{3}{4} = \frac{1}{4} of the pie, leaving 34−14=12\frac{3}{4} - \frac{1}{4} = \frac{1}{2} of the pie.
Finally, the porcupine ate 13⋅12=16\frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6} of the pie. This leaves 12−16=13\frac{1}{2} - \frac{1}{6} = \frac{1}{3} of the pie.
Thus, D is the correct answer.
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