ฝึกพูดภาษาอังกฤษด้วยเทคนิค Shadowing จากวิดีโอ: Fractions Made EASY!
กำลังสร้างบทเรียน...
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Okay, let's talk about fractions.
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And of course, this is everyone's favorite topic.
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But in actuality, most math students, when they see fractions, they have one or two expressions.
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Either they're very angry, they're like, fractions, just give me regular numbers like two and three.
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You know, I don't mind doing math when the numbers are nice and easy.
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But, you know, some people get upset, then others are just totally just lost.
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They're like, oh my goodness, fractions, anything but fractions.
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I'll do push-ups, but not fractions.
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But here's the deal.
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If you stick with me for a couple minutes, I'm going to give you some outstanding little ways to remember how to deal with fractions.
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You're going to be very, very happy.
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And what we're going to focus on is how to do the following operations with fractions.
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We're going to learn how to add, subtract, divide, and multiply these primary operations.
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Of course, most of you out there probably already learned this, but here's the deal.
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Most students that have learned fractions don't really work with fractions that often, and they get confused, and they struggle because, you know, there's things involved,
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like finding the lowest common denominator, et cetera, et cetera.
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But again, we're going to go ahead and give you a nice quick power lesson in this video.
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So you're going to find fractions much easier by the time you finish this video.
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But I'm going to get to all of this in just one second.
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But first, let me quickly introduce myself.
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My name is John.
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I'm the founder of Tablet Class Math.
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I'm also a middle and high school math teacher.
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I'm going to leave a link to all my information in the description of this video.
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I've been teaching math for decades, and I've come to the conclusion that all students, every single student out there, can be successful in mathematics.
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But it requires two things.
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One, you have to be willing to do the work, practice, take notes, study.
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But that's the first thing.
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The second thing you need is clear and understandable instruction.
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So that's what I can offer you.
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So if you're at the middle school, high school, or even college level, definitely check out my math help program if you need assistance.
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By the way, if you're preparing for any test that has a math section, I'll talk about things like the SAT, ACT, maybe a teacher certification exam, GED.
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I can help you out there.
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If you homeschool, I have fantastic homeschool, middle, and high school math courses you may want to check out.
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And if you need some math notes, I'm going to leave links to my math notes in the description of this video as well.
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Okay, so let's get into fractions.
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And again, if you've been having difficulty with fractions, that's kind of normal.
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A lot of students struggle with this, but we're going to make it easy for you here.
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So let's go ahead and first of all, set this up for us.
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Okay, so I want you to think of the world of fractions in kind of two rules.
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I'm going to break it up as one rule, and then we're going to have another rule.
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So the first rule is super easy.
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We're talking about multiplication and division.
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When I show you how to multiply and divide fractions, you're going to be like, that is so easy.
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So we're already 50% there.
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So think about this.
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Four operations we're talking about, multiplication, division, and then over here, addition and subtraction.
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So I'm telling you right now, you're going to see how we multiply and divide fractions.
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You're going to be like, that is really, really easy.
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So that's like one rule.
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OK, so that's just half of what you need to know about fractions.
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Now, the other half is addition and subtraction.
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And this is where most people, when they think of fractions, they don't like dealing with fractions because this requires a little bit more work.
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This is when you have to do like the LCD, the lowest common denominator and all that kind of good stuff.
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So if you remember that and you're like, oh, I hate finding the LCD.
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Well, listen, I'm going to give you a nice little shortcut.
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I'm going to call it a hack that can bypass you having to find the LCD.
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Now, you still need to know how to find the LCD.
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But if you're confused about this, if you'll get these problems right, adding and subtracting problems every single time by using this nice little shortcut,
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you're going to want to know this for sure.
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And here's the great news.
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Adding and subtracting fractions is basically the same procedure.
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Okay, so here's the deal.
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If you know how to multiply fractions, then you're going to know how to divide.
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It's effectively the same thing.
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If you know how to add fractions, it's the same thing as subtracting.
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So again, just think of the world of fractions as two rules.
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Rule one, rule two.
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So let's get on to this first rule, multiplying and dividing fractions, because it's super, super easy.
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Let's get into it right now.
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So our first rule, okay, multiplying and dividing fractions, again, very easy.
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So let's go ahead and take a look at a couple examples.
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So here we have 2 thirds times 1 fifth.
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Now, just a quick review.
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The top number in a fraction is called the numerator.
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The bottom number is called the denominator, okay?
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But here's what you need to know.
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When we're multiplying fractions, okay, The way we multiply fractions is we simply multiply the respective numerator.
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So in this case, it's going to be 2 times 1.
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And then we're going to multiply the respective denominators.
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That's 3 times 5.
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I mean, it doesn't get much easier than that.
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So we're just going to multiply across.
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So 2 times 1 is 2.
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3 times 5 is 15.
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You are done.
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There is the answer.
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And let's go ahead and give ourselves a nice little happy face for, you know, feeling good about that.
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Like, hey, I know how to multiply fractions now.
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It's literally as easy as that.
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Okay, so let's talk about how to divide fractions.
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Now, dividing fractions, what we're going to do is take division problems and we're going to convert them into multiplication problems.
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So we don't really divide fractions per se.
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I mean, technically, yes, that's what we're doing, but we're going to change the problem into a multiplication problem.
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And being that you already know how to multiply fractions, you're going to see how easy this is.
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So let's take a look at this problem, two thirds divided by one fifth.
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Okay, so we're going to change this problem from division to multiplication.
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Okay, but how do we do that?
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Well, you have to pay attention to the fraction to the right of the division symbol.
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Okay, this division operator right there, the fraction to the right of it is one-fifth.
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Okay, now here's how you change this problem to multiplication.
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You simply take the fraction to the right of the division symbol and you flip it upside down.
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So if this is 1 over 5, we're going to flip it upside down to 5 over 1.
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That's called the reciprocal.
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So that's all you do.
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And now this becomes a multiplication problem.
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So again, we're going to go from division to multiplication by flipping the fraction to the right of the division symbol.
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And now you already know how to multiply fractions.
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We're simply going to multiply across.
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So that's going to be 2 times 5, of course, is 10.
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And 3 times 1 is 3.
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And we are done.
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OK, so we'll give ourselves a nice little happy face for this.
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So here you know how to multiply.
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Here you know how to divide.
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Now, of course, you're going to want to practice this, but literally this is how easy this is.
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OK, so I told you this first rule, rule one, which covers multiplication and division, is very easy.
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OK, let's go ahead and add in something here.
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OK, just to make sure we're kind of complete.
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because some of you might be thinking, well, what about when we're dealing with mixed number fractions?
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Something like 2 and 1 5th, and we're going to multiply it by 1 and 1 3rd.
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Well, how does that work?
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Well, what you're going to want to do is rewrite these fractions as improper fractions.
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So, for example, 2 and 1 5th, I can write that as a single fraction by going 5 times 2.
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That's what?
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That's 10.
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Then I add 1.
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So that's going to be 10 plus 1 or 11 5ths.
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OK, and then one
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and one third as an improper fraction is three times one is three plus one is four or four thirds.
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So I'm going to rewrite this problem with mixed number fractions as eleven fifths times four thirds.
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OK, so now I'm just going to simply multiply across.
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So eleven times four, eleven times four is 44 and five times three is 15.
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And we are done.
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OK, again, very, very easy.
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and now we're 50% done with learning fractions.
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Okay, you already know how to multiply and divide.
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Okay, so let's get into our second rule here.
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And our rule number two is going to be focusing in on how to add and subtract fractions.
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And again, this is where you have to be thinking about the lowest common denominator.
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But I am going to give you a lovely hack here in just one second.
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it's like a shortcut okay
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that you don't even have to do fraction problems using the lowest common denominator you still need to understand it
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but i'm going to give you a technique that
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if you're struggling with fractions you can do addition
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and subtraction problems right correct every single time okay
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so let's go ahead and first just review some basic concepts about adding
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and subtracting fractions again when you're adding fractions or subtracting fractions, you're doing the exact same thing.
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Okay, that's why I'm going to just classify this as one rule.
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We'll call it rule number two.
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All right, so here's the deal.
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You can add or subtract fractions if you have the exact same denominator.
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Okay, the denominators must be the same.
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So let's take a look at this problem here.
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I have two sevenths plus one seventh.
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So I'll look at the denominators.
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I'm like, are they the same?
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This is seven, that's seven.
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So our answer is going to have a 7 as a denominator.
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So if the denominators are the same, we're going to keep that denominator in our answer, and then we're going to add the numerators.
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So this is 2, and this is 1.
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So that's going to be 2 plus 1.
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Okay, so we're going to add the respective numerators if the denominators are the same.
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If this was a subtraction problem, I would subtract the numerators.
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But in this case, 2 plus 1 is 3, and that would be 3 over 7, and that is it.
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Okay, so pretty easy to add and subtract fractions, especially if the denominators are the same.
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OK, so if the denominators are the same, we simply add or subtract the respective numerators, and we'll get our final answer.
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So again, that's not that difficult.
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But here is where the fun starts.
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Okay.
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So what happens when the denominators are not the same?
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Well, this is when most people go, oh, this is where I had to think about the LCD and everything else.
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That is true.
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Okay.
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You do need to think about what the LCD is and you have to learn how to find the LCD.
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This is very, very important.
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However, what I'm doing in this little lesson is giving you a shortcut.
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All right, so if I have this fraction, 2 fifths plus 1 third, I want to add these together, but they don't have the same denominator.
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So I'm going to have to rewrite this fraction and this fraction such that they do have the same denominator.
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Okay, so I'm going to have to write 2 fifths as, I'm going to have to find an equivalent fraction of 2 fifths.
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Okay, it's the same thing as two fifths, but it has a denominator that's going to be the same as an equivalent fraction here that has the same denominator.
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In other words, I've got to match up these denominators, and we're trying to find that same denominator that these two fractions have in common.
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That is the lowest common denominator.
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Okay, so if I, most people would say, okay, here, what is the LCD?
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Most of you would say it's 15.
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Okay, you would probably know that, and you would be correct.
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Now, I have additional videos on how to find the LCD.
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It's important that you understand that, but for this particular video, let's just assume that you know that, okay, yeah, this is the lowest common denominator is 15.
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So that means I'm going to rewrite each fraction such that the denominator is 15, okay?
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So here, how do I turn this 5 into 15?
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Well, I have to multiply it by 3, okay?
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So if I multiply the denominator by 3, I also have to multiply the numerator by 3, and that's how I get 3 times 2.
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This is 6 over 15.
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So that's how this first fraction right here I rewrite as 6 over 15.
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And then a 1 third, how do I get this to be a 15?
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I multiply by 5, so I'm going to multiply the numerator by 5.
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So I get 5 over 15.
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So I'm showing you kind of the long way that we deal with fractions.
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Okay, this is probably the way most of you have learned this problem or learned how to add or subtract fractions, and that's perfectly fine.
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Again, I'm going to show you a nice little shortcut here in a second.
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But now I rewrote these fractions such that they have a common denominator, the lowest common denominator.
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So remember the rule, when the denominators are the same, I simply go ahead and add or subtract the respective numerators.
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So this is 6 plus 5.
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Of course, that's 11.
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So I got 11 15ths.
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Okay, so that is the answer.
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And this is the way most of you have learned this using the LCD method.
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Okay, so we'll go ahead and put this here, LCD.
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But hey, what if you don't want to deal with LCD?
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Well, you're in luck because you're watching this video.
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I want you to remember this little symbol right here.
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Okay, it's called a bow tie.
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Okay, just like you wear a little bow tie.
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I don't think too many people wear bow ties anymore.
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But this is the general pattern I want you to remember.
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Okay, this is going to be super, super easy.
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This works with variables.
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It works with any addition or subtraction fraction problem.
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You will get the answer right 100% of the time.
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Okay, so here we go.
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I want to show you how easy this is.
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Here's the pattern.
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You start in the bottom right and you go this way.
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Okay, you always start from the bottom right and you go this way first.
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Okay, so we're going to do 3 times 2.
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We're going to put our answer there.
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And then you're going to go from the bottom left and you're going to go this way.
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So you can see it has like a little crisscross pattern.
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We're going to put that answer there.
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So let's do that now.
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3 times 2 is what?
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6. Now, this is an addition problem.
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That's going to be plus 5 times 1 is what?
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5, okay?
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That's our numerator.
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So this times this will always start from here, okay, because this will make an impact if you're subtracting fractions.
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So 3 times 2 is 6, plus 5 times 1 is 5, over our denominator is going to be 5 times 3.
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So here is our bow tie.
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5 times 3 is 15.
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Now we simplify that.
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6 plus 5 is what?
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11 over 15.
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It is exactly the same thing we have right here.
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But look, I didn't have to mess around and change these fractions, even think about the LCD.
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I simply just thought about my little bow tie method.
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I went this times this plus this times this over this times this.
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Okay.
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This is the bow tie method.
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You're going to want to know this not only for arithmetic, but for variable fractions as well.
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So let's go ahead and practice this right now.
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Okay.
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So let's take a look at this problem here.
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Four ninths minus one half.
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Okay.
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So what is the LCD of this problem right here?
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Okay.
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Well, everyone, you know, we're looking at this video right now.
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You can see I kind of wrote it.
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But most of you, hopefully, could say, well, the LCD is 18.
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So that's good.
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If you know that the LCD is 18, that's excellent.
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So you can, you know, write each of these denominators as 18.
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You're like, well, I would just multiply this by 2 and this by 9.
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And now I'm going to go ahead and fix this thing up right here and, you know, use the LCD method.
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So some of you, you know, may be non-believers in the LCD, this little bow tie method I'm actually saying.
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You're like, no, I'll just stick with LCD.
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And that's good.
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You need to know that.
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But what about this situation?
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Okay.
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What's the LCD between these two denominators?
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Okay.
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Now this is where it gets fun because most people are going to be like, all right, I'm not watching your video anymore.
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I'm not doing this problem.
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Okay.
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So to find the LCD of these two denominators, this gets much more interesting.
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All right.
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So a lot of you are like, oh, okay.
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Okay.
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I'll maybe I'll just use your bow tie method because to do this problem, it's super easy.
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I would just go this times this plus this times this over this times this.
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Now I'm going to have big numbers, but I will add these fractions and I will have the exact right answer.
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The only thing with the bow tie method is that oftentimes, well, not oftentimes, sometimes you're going to need to reduce, okay, your final answer.
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But your answer will be correct, but you may need to reduce your final answer.
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But you will have an accurate answer, okay?
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So that's the main idea.
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All right, so let's go ahead and practice this bow tie method right now.
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Okay, so again, let's take a look at this first problem.
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We're not going to be thinking about the LCD.
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We're going to go, okay, I'm going to start from the bottom right.
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I'm going to multiply it this way.
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Okay, so 2 times 4, that's 8.
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This is a subtraction problem, so I have a subtraction operator there.
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And then 9 times 1 is 9.
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And then my denominator is going to be 9 times 2, which, of course, is 18.
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Now, when you're subtracting fractions especially, that's why the order is very, very important.
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And that's why you have to start this way, okay, because we have our 8 there.
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If you put your 8 right here, you would have a different sign.
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So when you're subtracting fractions or subtracting any number, you've got to be very, very careful that you have the correct sign.
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So 8 minus 9 is the same thing as 8 plus negative 9, which is negative 1, okay?
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So the final answer here is negative 1 over 18, okay?
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Negative 1 over 18, that is the answer.
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But again, we're using that bow tie method.
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I don't have to think about it.
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I just have to follow the procedure and make sure I do the arithmetic correctly.
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All right, so how does this work with mixed number fractions?
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So basically the same way we did with multiplication and division, we want to rewrite each of these respective mixed number fractions as improper fractions.
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So 3 and 1 third is the same thing as 10 thirds.
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And then 2 and 3 fifths is the same thing as 13 fifths.
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So now I can go ahead and just do the bow tie method.
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So that's 5 times 10 is 50.
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3 times 13 is 39 over 3 times 5, which is 15.
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And I'm just going to go ahead and add my numerators.
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50 plus 39, that's 89 over 15.
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And we are done.
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Okay, so hopefully your facial expression about fractions went from here, or maybe like it was total confusion from here to here to here,
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to a big, lovely, happy face, okay?
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This is the whole idea behind this video, right?
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I'm giving you years and years and years of experience.
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Not that it takes years and years of experience or years to learn fractions, but being a math teacher,
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I'm an observer of where students make a lot of mistakes.
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And I'm telling you right now, students make a ton of mistakes when dealing with fractions
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because they forget how to deal with fractions because we have this little thing called a calculator that we use, and we don't really do a lot of,
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we don't do arithmetic as much as hand arithmetic as much as we should, okay?
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So when you get away from working with fractions, you're going to forget, but hopefully this video you'll be, you know, you'll remember it.
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You'll be like, oh, I remember that.
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There's like two rules.
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Remember that little bow tie method.
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And, of course, it doesn't mean that you don't have to learn the LCD because you do, but again you're going to have to know how to deal with fraction problems
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because they're everywhere and obviously any level of math whether it's elementary math middle school math
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and high school math and beyond okay fractions are everywhere
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so hopefully this little video helps you out and if
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that is the case go ahead and consider smashing that like button
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and i want to strongly suggest that you follow through in practice okay so i'm going to give you a couple suggestions.
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I definitely would check out my pre-algebra course.
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I have a whole chapter on fractions in my math program.
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And then I have additional videos on my YouTube channel about fractions.
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I have a ton of videos actually about fractions as well.
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But if you're new to my YouTube channel, hopefully you'll consider subscribing.
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I've been on YouTube for 10 plus years.
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I have over a thousand plus math videos from basic math to advanced math like calculus and everything in between.
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So if you like my teaching style, please take advantage of my content.
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I make it for you, but my best math help will always be within my math help program.
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Okay, so with that being said, I definitely wish you all the best in your mathematics adventures.
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Thank you for your time and have a great day.
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คำศัพท์และข้อสังเกตด้านการพูดสำหรับบทเรียนนี้
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คำศัพท์สำคัญในวิดีโอนี้
คำที่ควรเรียนรู้ 15 คำจากวิดีโอ พร้อมคำอ่านและความหมาย:
| คำศัพท์ | คำอ่าน | ความหมาย |
|---|---|---|
| fraction คำนาม | /ˈfɹæk.ʃən/ | เศษส่วน |
| mathematics คำนาม | /mæθ(.ə)ˈmæt.ɪks/ | คณิตศาสตร์ |
| symbol คำนาม | /ˈsɪmbəl/ | สัญลักษณ์ |
| confused คำคุณศัพท์ | /kənˈfjuːzd/ | สับสน |
| lesson คำนาม | /ˈlɛs.ən/ | บทเรียน |
| procedure คำนาม | /pɹəˈsiː.d͡ʒə/ | วิธี, กรรมวิธี |
| seventh คำคุณศัพท์ | /ˈsɛvənθ/ | ที่เจ็ด |
| minus | /ˈmaɪ.nəs/ | ลบ |
| topic คำนาม | /ˈtɑpɪk/ | หัวข้อ, กระทู้ |
| technique คำนาม | /tɛkˈniːk/ | เทคนิค, กลเม็ด |
| adventure คำนาม | /ədˈvɛn.t͡ʃə/ | การผจญภัย, การเสี่ยงภัย |
| founder คำนาม | /ˈfaʊ̯n.dəː/ | ผู้สร้าง, ผู้ก่อตั้ง |
| introduce คำกริยา | /ˌɪntɹəˈdus/ | แนะนำ |
| examination คำนาม | /ɪɡˌzæm.ɪˈneɪ.ʃən/ | ไต่สวน |
| suggestion คำนาม | /səˈd͡ʒɛst.ʃən/ | ข้อเสนอ, ข้อเสนอแนะ |
การออกเสียงที่ควรระวัง
ผู้พูดใช้รูปย่อและรูปลดเสียง 140 ครั้ง เช่น I'm, we're, you're ให้พูดแบบสั้นตามที่ได้ยิน
- เสียง “th”: mathematics /mæθ(.ə)ˈmæt.ɪks/, seventh /ˈsɛvənθ/, ninth /naɪnθ/, arithmetic /æɹɪθˈmɛtɪk/
- เสียง “sh” และ “zh”: fraction /ˈfɹæk.ʃən/, conclusion /kənˈkluːʒən/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, suggestion /səˈd͡ʒɛst.ʃən/, confusion /kənˈfjuːʒən/
- คำยาว — ลงเสียงหนักให้ถูกพยางค์: mathematics /mæθ(.ə)ˈmæt.ɪks/, operator /ˈɑpəˌɹeɪtɚ/, difficulty /ˈdɪfɪkəlti/, elementary /ˌɛləˈmɛntəɹi/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/
วิธีฝึกกับวิดีโอนี้
- ฟังวิดีโอให้จบหนึ่งรอบโดยยังไม่ต้องพูด แล้วจดคำที่ยังไม่รู้จัก
- เริ่มที่ความเร็ว 0.75× พูดตามทีละประโยค แล้วกลับไปใช้ความเร็วปกติเมื่อเริ่มคล่อง
- อัดเสียงตัวเองแล้วเทียบกับต้นฉบับ โดยสังเกตคำอย่าง fraction, mathematics, symbol เป็นพิเศษ
ไวยากรณ์ในวิดีโอนี้
โครงสร้างที่ผู้พูดใช้บ่อยที่สุด พร้อมคำพูดจริงจากวิดีโอ:
| โครงสร้าง | ในวิดีโอ |
|---|---|
| ประโยคเงื่อนไข if + อนุประโยค, will/would + กริยา — เงื่อนไขและผลลัพธ์ | if you're confused about this, if you'll get · if I, most people would say |
| Present perfect continuous have/has been + -ing — การกระทำที่เริ่มก่อนหน้านี้และยังดำเนินอยู่ | I've been teaching · you've been having |
| Passive voice be + กริยาช่อง 3 — เน้นสิ่งที่เกิดขึ้น ไม่ใช่ผู้กระทำ | is called · are done · being said |
| Present perfect have/has + กริยาช่อง 3 — เหตุการณ์ในอดีตที่ยังเกี่ยวข้องกับปัจจุบัน | have learned · I've come · I've been |
เทคนิค Shadowing คืออะไร?
Shadowing เป็นเทคนิคการเรียนรู้ภาษาที่ได้รับการรับรองทางวิทยาศาสตร์ พัฒนาขึ้นสำหรับการฝึกนักแปลมืออาชีพ วิธีการนี้เรียบง่ายแต่ทรงพลัง: คุณฟังเสียงภาษาอังกฤษจากเจ้าของภาษาและพูดตามทันที — เหมือนเงาที่ตามผู้พูดด้วยช่วงเวลาห่าง 1-2 วินาที การวิจัยแสดงว่าเทคนิคนี้ปรับปรุงความแม่นยำในการออกเสียง ทำนองเสียง จังหวะ การเชื่อมเสียง การฟังเข้าใจ และความคล่องแคล่วในการพูดได้อย่างมีนัยสำคัญ