Shadowing Practice: Fractions Made EASY! - Learn English Speaking with Video

Okay, let's talk about fractions.

And of course, this is everyone's favorite topic.

But in actuality, most math students, when they see fractions, they have one or two expressions.

Either they're very angry, they're like, fractions, just give me regular numbers like two and three.

You know, I don't mind doing math when the numbers are nice and easy.

But, you know, some people get upset, then others are just totally just lost.

They're like, oh my goodness, fractions, anything but fractions.

I'll do push-ups, but not fractions.

But here's the deal.

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.

You're going to be very, very happy.

And what we're going to focus on is how to do the following operations with fractions.

We're going to learn how to add, subtract, divide, and multiply these primary operations.

Of course, most of you out there probably already learned this, but here's the deal.

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,

like finding the lowest common denominator, et cetera, et cetera.

But again, we're going to go ahead and give you a nice quick power lesson in this video.

So you're going to find fractions much easier by the time you finish this video.

But I'm going to get to all of this in just one second.

But first, let me quickly introduce myself.

My name is John.

I'm the founder of Tablet Class Math.

I'm also a middle and high school math teacher.

I'm going to leave a link to all my information in the description of this video.

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.

But it requires two things.

One, you have to be willing to do the work, practice, take notes, study.

But that's the first thing.

The second thing you need is clear and understandable instruction.

So that's what I can offer you.

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.

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.

I can help you out there.

If you homeschool, I have fantastic homeschool, middle, and high school math courses you may want to check out.

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.

Okay, so let's get into fractions.

And again, if you've been having difficulty with fractions, that's kind of normal.

A lot of students struggle with this, but we're going to make it easy for you here.

So let's go ahead and first of all, set this up for us.

Okay, so I want you to think of the world of fractions in kind of two rules.

I'm going to break it up as one rule, and then we're going to have another rule.

So the first rule is super easy.

We're talking about multiplication and division.

When I show you how to multiply and divide fractions, you're going to be like, that is so easy.

So we're already 50% there.

So think about this.

Four operations we're talking about, multiplication, division, and then over here, addition and subtraction.

So I'm telling you right now, you're going to see how we multiply and divide fractions.

You're going to be like, that is really, really easy.

So that's like one rule.

OK, so that's just half of what you need to know about fractions.

Now, the other half is addition and subtraction.

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.

This is when you have to do like the LCD, the lowest common denominator and all that kind of good stuff.

So if you remember that and you're like, oh, I hate finding the LCD.

Well, listen, I'm going to give you a nice little shortcut.

I'm going to call it a hack that can bypass you having to find the LCD.

Now, you still need to know how to find the LCD.

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,

you're going to want to know this for sure.

And here's the great news.

Adding and subtracting fractions is basically the same procedure.

Okay, so here's the deal.

If you know how to multiply fractions, then you're going to know how to divide.

It's effectively the same thing.

If you know how to add fractions, it's the same thing as subtracting.

So again, just think of the world of fractions as two rules.

Rule one, rule two.

So let's get on to this first rule, multiplying and dividing fractions, because it's super, super easy.

Let's get into it right now.

So our first rule, okay, multiplying and dividing fractions, again, very easy.

So let's go ahead and take a look at a couple examples.

So here we have 2 thirds times 1 fifth.

Now, just a quick review.

The top number in a fraction is called the numerator.

The bottom number is called the denominator, okay?

But here's what you need to know.

When we're multiplying fractions, okay, The way we multiply fractions is we simply multiply the respective numerator.

So in this case, it's going to be 2 times 1.

And then we're going to multiply the respective denominators.

That's 3 times 5.

I mean, it doesn't get much easier than that.

So we're just going to multiply across.

So 2 times 1 is 2.

3 times 5 is 15.

You are done.

There is the answer.

And let's go ahead and give ourselves a nice little happy face for, you know, feeling good about that.

Like, hey, I know how to multiply fractions now.

It's literally as easy as that.

Okay, so let's talk about how to divide fractions.

Now, dividing fractions, what we're going to do is take division problems and we're going to convert them into multiplication problems.

So we don't really divide fractions per se.

I mean, technically, yes, that's what we're doing, but we're going to change the problem into a multiplication problem.

And being that you already know how to multiply fractions, you're going to see how easy this is.

So let's take a look at this problem, two thirds divided by one fifth.

Okay, so we're going to change this problem from division to multiplication.

Okay, but how do we do that?

Well, you have to pay attention to the fraction to the right of the division symbol.

100

Okay, this division operator right there, the fraction to the right of it is one-fifth.

101

Okay, now here's how you change this problem to multiplication.

102

You simply take the fraction to the right of the division symbol and you flip it upside down.

103

So if this is 1 over 5, we're going to flip it upside down to 5 over 1.

104

That's called the reciprocal.

105

So that's all you do.

106

And now this becomes a multiplication problem.

107

So again, we're going to go from division to multiplication by flipping the fraction to the right of the division symbol.

108

And now you already know how to multiply fractions.

109

We're simply going to multiply across.

110

So that's going to be 2 times 5, of course, is 10.

111

And 3 times 1 is 3.

112

And we are done.

113

OK, so we'll give ourselves a nice little happy face for this.

114

So here you know how to multiply.

115

Here you know how to divide.

116

Now, of course, you're going to want to practice this, but literally this is how easy this is.

117

OK, so I told you this first rule, rule one, which covers multiplication and division, is very easy.

118

OK, let's go ahead and add in something here.

119

OK, just to make sure we're kind of complete.

120

because some of you might be thinking, well, what about when we're dealing with mixed number fractions?

121

Something like 2 and 1 5th, and we're going to multiply it by 1 and 1 3rd.

122

Well, how does that work?

123

Well, what you're going to want to do is rewrite these fractions as improper fractions.

124

So, for example, 2 and 1 5th, I can write that as a single fraction by going 5 times 2.

125

That's what?

126

That's 10.

127

Then I add 1.

128

So that's going to be 10 plus 1 or 11 5ths.

129

OK, and then one

130

and one third as an improper fraction is three times one is three plus one is four or four thirds.

131

So I'm going to rewrite this problem with mixed number fractions as eleven fifths times four thirds.

132

OK, so now I'm just going to simply multiply across.

133

So eleven times four, eleven times four is 44 and five times three is 15.

134

And we are done.

135

OK, again, very, very easy.

136

and now we're 50% done with learning fractions.

137

Okay, you already know how to multiply and divide.

138

Okay, so let's get into our second rule here.

139

And our rule number two is going to be focusing in on how to add and subtract fractions.

140

And again, this is where you have to be thinking about the lowest common denominator.

141

But I am going to give you a lovely hack here in just one second.

142

it's like a shortcut okay

143

that you don't even have to do fraction problems using the lowest common denominator you still need to understand it

144

but i'm going to give you a technique that

145

if you're struggling with fractions you can do addition

146

and subtraction problems right correct every single time okay

147

so let's go ahead and first just review some basic concepts about adding

148

and subtracting fractions again when you're adding fractions or subtracting fractions, you're doing the exact same thing.

149

Okay, that's why I'm going to just classify this as one rule.

150

We'll call it rule number two.

151

All right, so here's the deal.

152

You can add or subtract fractions if you have the exact same denominator.

153

Okay, the denominators must be the same.

154

So let's take a look at this problem here.

155

I have two sevenths plus one seventh.

156

So I'll look at the denominators.

157

I'm like, are they the same?

158

This is seven, that's seven.

159

So our answer is going to have a 7 as a denominator.

160

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.

161

So this is 2, and this is 1.

162

So that's going to be 2 plus 1.

163

Okay, so we're going to add the respective numerators if the denominators are the same.

164

If this was a subtraction problem, I would subtract the numerators.

165

But in this case, 2 plus 1 is 3, and that would be 3 over 7, and that is it.

166

Okay, so pretty easy to add and subtract fractions, especially if the denominators are the same.

167

OK, so if the denominators are the same, we simply add or subtract the respective numerators, and we'll get our final answer.

168

So again, that's not that difficult.

169

But here is where the fun starts.

170

Okay.

171

So what happens when the denominators are not the same?

172

Well, this is when most people go, oh, this is where I had to think about the LCD and everything else.

173

That is true.

174

Okay.

175

You do need to think about what the LCD is and you have to learn how to find the LCD.

176

This is very, very important.

177

However, what I'm doing in this little lesson is giving you a shortcut.

178

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.

179

So I'm going to have to rewrite this fraction and this fraction such that they do have the same denominator.

180

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.

181

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.

182

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.

183

That is the lowest common denominator.

184

Okay, so if I, most people would say, okay, here, what is the LCD?

185

Most of you would say it's 15.

186

Okay, you would probably know that, and you would be correct.

187

Now, I have additional videos on how to find the LCD.

188

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.

189

So that means I'm going to rewrite each fraction such that the denominator is 15, okay?

190

So here, how do I turn this 5 into 15?

191

Well, I have to multiply it by 3, okay?

192

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.

193

This is 6 over 15.

194

So that's how this first fraction right here I rewrite as 6 over 15.

195

And then a 1 third, how do I get this to be a 15?

196

I multiply by 5, so I'm going to multiply the numerator by 5.

197

So I get 5 over 15.

198

So I'm showing you kind of the long way that we deal with fractions.

199

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.

200

Again, I'm going to show you a nice little shortcut here in a second.

201

But now I rewrote these fractions such that they have a common denominator, the lowest common denominator.

202

So remember the rule, when the denominators are the same, I simply go ahead and add or subtract the respective numerators.

203

So this is 6 plus 5.

204

Of course, that's 11.

205

So I got 11 15ths.

206

Okay, so that is the answer.

207

And this is the way most of you have learned this using the LCD method.

208

Okay, so we'll go ahead and put this here, LCD.

209

But hey, what if you don't want to deal with LCD?

210

Well, you're in luck because you're watching this video.

211

I want you to remember this little symbol right here.

212

Okay, it's called a bow tie.

213

Okay, just like you wear a little bow tie.

214

I don't think too many people wear bow ties anymore.

215

But this is the general pattern I want you to remember.

216

Okay, this is going to be super, super easy.

217

This works with variables.

218

It works with any addition or subtraction fraction problem.

219

You will get the answer right 100% of the time.

220

Okay, so here we go.

221

I want to show you how easy this is.

222

Here's the pattern.

223

You start in the bottom right and you go this way.

224

Okay, you always start from the bottom right and you go this way first.

225

Okay, so we're going to do 3 times 2.

226

We're going to put our answer there.

227

And then you're going to go from the bottom left and you're going to go this way.

228

So you can see it has like a little crisscross pattern.

229

We're going to put that answer there.

230

So let's do that now.

231

3 times 2 is what?

232

6. Now, this is an addition problem.

233

That's going to be plus 5 times 1 is what?

234

5, okay?

235

That's our numerator.

236

So this times this will always start from here, okay, because this will make an impact if you're subtracting fractions.

237

So 3 times 2 is 6, plus 5 times 1 is 5, over our denominator is going to be 5 times 3.

238

So here is our bow tie.

239

5 times 3 is 15.

240

Now we simplify that.

241

6 plus 5 is what?

242

11 over 15.

243

It is exactly the same thing we have right here.

244

But look, I didn't have to mess around and change these fractions, even think about the LCD.

245

I simply just thought about my little bow tie method.

246

I went this times this plus this times this over this times this.

247

Okay.

248

This is the bow tie method.

249

You're going to want to know this not only for arithmetic, but for variable fractions as well.

250

So let's go ahead and practice this right now.

251

Okay.

252

So let's take a look at this problem here.

253

Four ninths minus one half.

254

Okay.

255

So what is the LCD of this problem right here?

256

Okay.

257

Well, everyone, you know, we're looking at this video right now.

258

You can see I kind of wrote it.

259

But most of you, hopefully, could say, well, the LCD is 18.

260

So that's good.

261

If you know that the LCD is 18, that's excellent.

262

So you can, you know, write each of these denominators as 18.

263

You're like, well, I would just multiply this by 2 and this by 9.

264

And now I'm going to go ahead and fix this thing up right here and, you know, use the LCD method.

265

So some of you, you know, may be non-believers in the LCD, this little bow tie method I'm actually saying.

266

You're like, no, I'll just stick with LCD.

267

And that's good.

268

You need to know that.

269

But what about this situation?

270

Okay.

271

What's the LCD between these two denominators?

272

Okay.

273

Now this is where it gets fun because most people are going to be like, all right, I'm not watching your video anymore.

274

I'm not doing this problem.

275

Okay.

276

So to find the LCD of these two denominators, this gets much more interesting.

277

All right.

278

So a lot of you are like, oh, okay.

279

Okay.

280

I'll maybe I'll just use your bow tie method because to do this problem, it's super easy.

281

I would just go this times this plus this times this over this times this.

282

Now I'm going to have big numbers, but I will add these fractions and I will have the exact right answer.

283

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.

284

But your answer will be correct, but you may need to reduce your final answer.

285

But you will have an accurate answer, okay?

286

So that's the main idea.

287

All right, so let's go ahead and practice this bow tie method right now.

288

Okay, so again, let's take a look at this first problem.

289

We're not going to be thinking about the LCD.

290

We're going to go, okay, I'm going to start from the bottom right.

291

I'm going to multiply it this way.

292

Okay, so 2 times 4, that's 8.

293

This is a subtraction problem, so I have a subtraction operator there.

294

And then 9 times 1 is 9.

295

And then my denominator is going to be 9 times 2, which, of course, is 18.

296

Now, when you're subtracting fractions especially, that's why the order is very, very important.

297

And that's why you have to start this way, okay, because we have our 8 there.

298

If you put your 8 right here, you would have a different sign.

299

So when you're subtracting fractions or subtracting any number, you've got to be very, very careful that you have the correct sign.

300

So 8 minus 9 is the same thing as 8 plus negative 9, which is negative 1, okay?

301

So the final answer here is negative 1 over 18, okay?

302

Negative 1 over 18, that is the answer.

303

But again, we're using that bow tie method.

304

I don't have to think about it.

305

I just have to follow the procedure and make sure I do the arithmetic correctly.

306

All right, so how does this work with mixed number fractions?

307

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.

308

So 3 and 1 third is the same thing as 10 thirds.

309

And then 2 and 3 fifths is the same thing as 13 fifths.

310

So now I can go ahead and just do the bow tie method.

311

So that's 5 times 10 is 50.

312

3 times 13 is 39 over 3 times 5, which is 15.

313

And I'm just going to go ahead and add my numerators.

314

50 plus 39, that's 89 over 15.

315

And we are done.

316

Okay, so hopefully your facial expression about fractions went from here, or maybe like it was total confusion from here to here to here,

317

to a big, lovely, happy face, okay?

318

This is the whole idea behind this video, right?

319

I'm giving you years and years and years of experience.

320

Not that it takes years and years of experience or years to learn fractions, but being a math teacher,

321

I'm an observer of where students make a lot of mistakes.

322

And I'm telling you right now, students make a ton of mistakes when dealing with fractions

323

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,

324

we don't do arithmetic as much as hand arithmetic as much as we should, okay?

325

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.

326

You'll be like, oh, I remember that.

327

There's like two rules.

328

Remember that little bow tie method.

329

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

330

because they're everywhere and obviously any level of math whether it's elementary math middle school math

331

and high school math and beyond okay fractions are everywhere

332

so hopefully this little video helps you out and if

333

that is the case go ahead and consider smashing that like button

334

and i want to strongly suggest that you follow through in practice okay so i'm going to give you a couple suggestions.

335

I definitely would check out my pre-algebra course.

336

I have a whole chapter on fractions in my math program.

337

And then I have additional videos on my YouTube channel about fractions.

338

I have a ton of videos actually about fractions as well.

339

But if you're new to my YouTube channel, hopefully you'll consider subscribing.

340

I've been on YouTube for 10 plus years.

341

I have over a thousand plus math videos from basic math to advanced math like calculus and everything in between.

342

So if you like my teaching style, please take advantage of my content.

343

I make it for you, but my best math help will always be within my math help program.

344

Okay, so with that being said, I definitely wish you all the best in your mathematics adventures.

345

Thank you for your time and have a great day.

✨ Recomendar Video

The 7 Habits of Highly Successful Students (Part 6) 💯

2,575

11 oraciones

The 7 Habits of Highly Successful Students (Part 6) 💯

Business EnglishDaily ConversationHigh School Students

137 oraciones

Multiplying Fractions - The Easy Way!

High School StudentsUniversity Students

278 oraciones

How to read ALL NUMBERS in English - BIG NUMBERS, Decimals, Dates, Fractions, Phones, Ordinals

Business EnglishDaily ConversationHigh School Students

212 oraciones

How to Speak English Fluently like an American in just 1 Month (Step by step) - Part 1

Business EnglishDaily ConversationHigh School Students

205 oraciones

Let's talk about Money in English

Business EnglishTravel EnglishDaily Conversation

72 oraciones

Math Antics - Percents And Equivalent Fractions

Daily ConversationHigh School StudentsUniversity Students

227 oraciones

I use these phrases Every. Damn. Day... So YOU should probably learn them too! ✌🏻🇬🇧

Daily ConversationHigh School StudentsUniversity Students

32 oraciones

Plan smarter with Claude for Teachers

Business EnglishHigh School StudentsUniversity Students

Vocabulario y notas de pronunciación para esta lección

Este vídeo tiene 345 frases y 3779 palabras para practicar shadowing. La parte hablada dura 21:02. El hablante habla rápido, unas 180 palabras por minuto, así que espera sonidos enlazados y reducidos. El 85 % de las palabras está entre las 3.000 más comunes del inglés; conviene repasar el resto antes de empezar.

Vocabulario clave de este vídeo

15 palabras del vídeo que vale la pena aprender, con su pronunciación y significado:

Palabra	Pronunciación	Significado
fraction sustantivo	/ˈfɹæk.ʃən/	fracción
mathematics sustantivo	/mæθ(.ə)ˈmæt.ɪks/	matemáticas, matemática
divide verbo	/dɪˈvaɪd/	desunir, dividir
respective adjetivo	/ɹɪˈspɛktɪv/	respectivo
symbol sustantivo	/ˈsɪmbəl/	símbolo
flip verbo	/flɪp/	darle vuelta, voltear
improper adjetivo	/ɪmˈpɹɑ.pɚ/	improprio, impropio
confused adjetivo	/kənˈfjuːzd/	confundido
lesson sustantivo	/ˈlɛs.ən/	lección
procedure sustantivo	/pɹəˈsiː.d͡ʒə/	procedimiento
operator sustantivo	/ˈɑpəˌɹeɪtɚ/	operador
seventh adjetivo	/ˈsɛvənθ/	séptimo
variable adjetivo	[ˈvæɹ.i.ə.bl̩]	variable
upside sustantivo	/ˈʌpˌsaɪd/	lado bueno, lado positivo
minus	/ˈmaɪ.nəs/	menos

Phrasal verbs que vas a escuchar

Palabra	Pronunciación	Significado
go ahead verbo	/ˌɡoʊ əˈhɛd/	venga, adelante
check out verbo		investigar, chequear
get over verbo		superar, sobreponerse a
mess around verbo		boludear

Pronunciación a tener en cuenta

El hablante usa 140 contracciones y formas reducidas, como I'm, we're, you're. Dilas en su forma corta, tal como las oyes.

Los sonidos de “th”: mathematics /mæθ(.ə)ˈmæt.ɪks/, seventh /ˈsɛvənθ/, ninth /naɪnθ/, arithmetic /æɹɪθˈmɛtɪk/
Los sonidos de “sh” y “zh”: fraction /ˈfɹæk.ʃən/, conclusion /kənˈkluːʒən/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, suggestion /səˈd͡ʒɛst.ʃən/, confusion /kənˈfjuːʒən/
Palabras largas — cuida el acento: mathematics /mæθ(.ə)ˈmæt.ɪks/, operator /ˈɑpəˌɹeɪtɚ/, difficulty /ˈdɪfɪkəlti/, elementary /ˌɛləˈmɛntəɹi/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/

Cómo practicar con este vídeo

Escucha el vídeo entero una vez sin hablar y anota las palabras que no conoces.
Empieza a velocidad 0,75×, haz shadowing frase por frase y vuelve a la velocidad normal cuando te resulte fácil.
Grábate y compara con el original, prestando atención a palabras como fraction, mathematics, divide.

Gramática en este vídeo

Las estructuras que más usa el hablante, con las palabras exactas del vídeo:

Estructura	En el vídeo
Oraciones condicionales if + oración, will/would + verbo — una condición y su resultado	if you're confused about this, if you'll get · if I, most people would say
Present perfect continuous have/has been + -ing — una acción que empezó antes y continúa	I've been teaching · you've been having
Voz pasiva be + participio pasado — importa lo que ocurre, no quién lo hace	is called · are done · being said
Present perfect have/has + participio pasado — una acción pasada que sigue importando ahora	have learned · I've come · I've been

¿Qué es la Técnica de Shadowing?

Shadowing es una técnica de aprendizaje de idiomas respaldada por la ciencia, desarrollada originalmente para la formación de intérpretes profesionales y popularizada por el políglota Dr. Alexander Arguelles. El método es simple pero poderoso: escuchas audio en inglés nativo y lo repites en voz alta de inmediato, como una sombra que sigue al hablante con solo 1-2 segundos de retraso. A diferencia de la escucha pasiva o los ejercicios de gramática, el shadowing obliga a tu cerebro y músculos de la boca a procesar y reproducir simultáneamente patrones de habla reales. Las investigaciones muestran que mejora significativamente la precisión de la pronunciación, la entonación, el ritmo, el habla conectada, la comprensión auditiva y la fluidez al hablar, convirtiéndola en una de las metodologías más efectivas para la preparación del IELTS Speaking y la comunicación en inglés en el mundo real.

Técnica de shadowing: lee la guía completa paso a paso →

Shadowing Practice: Fractions Made EASY! - Learn English Speaking with Video

The 7 Habits of Highly Successful Students (Part 6) 💯

Multiplying Fractions - The Easy Way!

How to read ALL NUMBERS in English - BIG NUMBERS, Decimals, Dates, Fractions, Phones, Ordinals

Practica tu inglés conmigo en este video

Elements | Middle school chemistry | Khan Academy

The Easy Way to Remember Every English Word

My Back to School Favorites

How to Speak English Fluently like an American in just 1 Month (Step by step) - Part 1

Let's talk about Money in English

Math Antics - Percents And Equivalent Fractions

I use these phrases Every. Damn. Day... So YOU should probably learn them too! ✌🏻🇬🇧

Plan smarter with Claude for Teachers

Vocabulario y notas de pronunciación para esta lección

Vocabulario clave de este vídeo

Phrasal verbs que vas a escuchar

Pronunciación a tener en cuenta

Cómo practicar con este vídeo

Gramática en este vídeo

¿Qué es la Técnica de Shadowing?