跟读练习: Math Antics - Percents Missing Total - 通过视频学习英语口语
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Hi! Welcome to Math Antics. In our last lesson about percents, we learned that there’re three main types of percent problems because there’s three different numbers that could be missing.
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Those three numbers are the ‘part’, the ‘total’, and the ‘percent’.
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They’re just the three variable in the percentage equation.
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The forth number is always 100, since that’s what percent means: per 100.
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In the last two videos, we learned how to solve problems where the ‘part’ was unknown and where the ‘percent’ was unknown.
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In this video, we’re gonna learn how to solve problems where the ‘total’ is unknown or missing.
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With this type of problem, you’ll be told what the percent is, and you’ll be told what part of the total you have.
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But you’ll need to figure out what that total itself is.
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Here’s an example of a problem like that: Your friend has a bag of marbles, and he tells you that 20% of the marbles are red.
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If there’s 7 red marbles, how many marbles does he have altogether?
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Okay, so how do you know that it’s the total that’s missing in this problem?
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Well, the word “altogether” is a big clue because it means almost the same thing as “total”.
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So, if the question has words like, “altogether”, or “in all”, or “total”, or “whole”, or “entire” those can help you know that you need to find the total.
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And another way that we can tell is by the numbers that we ARE given.
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In this problem, we know that the percent is 20, and we’re also told that PART of the marbles are red, so we know that the PART is 7.
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So that means that it must be the total that’s missing!
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Alright then, so how do we figure out what the total is?
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Well, using a little algebra we can re-arrange our percent equation like this: What this new form of the equation tells us is that, if we take the ‘part’ and multiply it by 100, and then we divide that by the ‘percent’, we’ll get the ‘total’.
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That seems simple enough. It’s just two steps!
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Let’s try it out on our word problem about the marbles.
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We know that the ‘part’ is 7, so step one is to just multiply that part by 100.
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7 × 100 is 700.
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And in step two, we take that 700 and divide it by the ‘percent’, which we’re told is 20.
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Okay, 700 divided by 20…. hmmm….
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Well, we could use a calculator to divide, but this doesn’t seem too hard, so I’ll just do the division the long way.
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20 is to big to divide into the first digit so we’ll need to include the digit next to it as well.
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Now we ask, “How many ’20’s does it take to make 70 or almost 70”.
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That would be 3 because 3 × 20 is 60.
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70 minus 60 leaves 10 as the remainder.
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And then we bring down the zero and then we ask, “How many ’20’s will divide into 100?” Ah-ha… 5, because 5 × 20 is 100, so that leaves no remainder.
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So 700 divided by 20 is 35.
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And that means that the total number of marbles is 35.
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And in a problem like this, you can always check your answer by making sure that the fraction of the ‘part’ over the ‘total’ would give you the correct percent.
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For example, in this case, you could make sure that the fraction 7 over 35 would really be 20%.
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Now that wasn’t so tough, was it?
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Let’s see one more example to make sure you’ve got the procedure down before you try some on your own.
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The next problem says: A high school marching band has 12 flute players.
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If 8% of the band members play the flute, then how many members are in the entire band?
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Okay, so the smaller ‘part’ in this problem is 12 since there’s 12 flute players.
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And we’re told that they make up 8 percent of the band, so the ‘percent’ is 8.
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Again, it’s the ‘total’ that’s missing, and to find it, we just need to follow our 2-step procedure.
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For step one, we multiply the ‘part’ by 100: 12 × 100 = 1,200 For step two, we divide that 1,200 by the percent, which is 8.
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1,200 divided by 8 equals 150.
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Great… that means that the total number of band members is 150.
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And again, you can always check your answer the way we did in the last example.
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Alright… that does it for this lesson.
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Remember… the key to getting really good at math is to do it yourself.
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Doing practice problems on your own will help you become a great problem solver.
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Good luck! Thanks for watching Math Antics and I’ll see ya next time.
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Learn more at www.mathantics.com
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上下文与背景
在这段视频中，主持人欢迎观众来到数学课堂，讨论关于百分比的问题。这一课主要关注在解决含有缺失总量的百分比问题。通过具体的例子，如朋友的弹珠袋和高中乐队的情况，讲解思路使得复杂的数学概念变得易于理解。掌握这些概念不仅可以帮助观众解决数学难题，还能提升他们的逻辑思维能力。
日常沟通的五个关键短语
- 总计 (altogether)
- 部分 (part)
- 百分比 (percent)
- 全部 (total)
- 如何解决 (how to figure out)
逐步跟读指南
在学习如何解决缺失总量的百分比问题时，您可以遵循以下步骤，这将有助于您提高英语口语能力，特别是通过shadow speech技术来增强语言的流畅性：
- 收听与理解: 观看视频时，务必全神贯注，试图理解每个数学概念如何关联到实际问题。
- 分段跟读: 使用shadow speak技巧，暂停视频，模仿视频中的语调与节奏，临摹彼此的表达方式。
- 分析问题: 在视频讲解后，练习分解相似的数学题，尝试自己找出总量。在这种情况下可以使用shadowspeak技巧来反复练习。
- 重复与自主练习: 反复观看这个视频并尝试解答类似的问题，以加深理解。同时，可使用看YouTube学英语的方式学习更多相关内容。
- 自我检查: 最后核对您的答案是否正确，习得解决问题的思维方式，掌握数学与语言的结合。
通过这样有条理的学习方式，不仅可以提高数学能力，还能在口语表达上获得质的提升，成为更加自信的英语学习者。提升您的技能，欢迎您访问相关的shadowing site，获取更多资源！
什么是跟读法？
跟读法 (Shadowing) 是一种有科学依据的语言学习技巧，最初开发用于专业口译员的培训，并由多语言者Alexander Arguelles博士普及。这个方法简单而强大：您在听英语母语原声的同时立即大声重复——就像是一个延迟1-2秒紧跟说话者的影子。与被动听力或语法练习不同，跟读法强迫您的大脑和口腔肌肉同时处理并模仿真实的讲话模式。研究表明它能显着提高发音准确性，语调，节奏，连读，听力理解和口语流利度——使其成为雅思口语备考和真实英语交流最有效的方法之一。