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Low Cost Home | 127m² A Small House On The Hill With Simple Design, Convenient - Duration: 3:32.

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SHSAT Math Strategies & Shortcuts (2018-2019) | 5 Simple Tricks | Bobby-Tariq Tutoring Center - Duration: 18:33.

- Hello guys!

Welcome to Tariq's class.

You all know that SHSAT is a very challenging test.

The biggest challenge is the time.

You get three hours to finish the test.

However, there are 114 questions to finish.

You get approximately 95 seconds to solve each questions.

Now think about it.

If you can finish each question within 50 seconds,

you can save a lot of time.

You can use this time to review your test towards the end

and you can do better at the test.

Now, the only way to save time is

if you know the shortcut techniques.

Today I am going

to show you five amazing math shortcut techniques

that you can use on your exam.

My first shortcut is about Finding Average.

This technique works when there is a common difference

between the numbers.

For example, my first question is,

find the average of the following numbers.

The numbers are two, four, six, eight, 10,

and it goes all the way to 1000.

There is a common difference of two.

If you can see between each and every number,

there is a common difference of two.

Like the difference between two and four is two,

the difference between four and six is two,

and between six and eight is two, and so on.

Now, the traditional way of finding average is

we'll have to add all these numbers and divide it

by the total amount of numbers which is 500.

There are a total of 500 even numbers from two to 1000.

So that's so much work, but the shortcut is,

if you have common difference between the numbers,

then, in order to find the average,

you could just add the first number,

add the last number, and divide it by two.

Add the first number with the last number,

and divide it by two.

So, 1000 plus two is 1002 divided by two, you get 501.

and that's your average.

Is that easy guys?

Now, let's solve another question.

The second question says find the average

of the the following numbers.

This time, the numbers are 15, 20, 25, 30,

and to goes all the way to 50.

Is there any common difference guys?

What is the difference between 15 and 20?

It's five.

What is the difference between 20 and 25?

Also five.

So there you have common difference between the numbers.

So we can use our shortcut technique.

So you can add the first number

with the last number and divide it by two.

So 15 plus 50 divided by two,

that's 65 over two, which is 32.5.

That's it.

Remember, the first plus the last,

divide by two.

That's all you gotta do.

Shortcut number two is about finding the area

of the square, given the diagonal.

Now what is a diagonal, guys?

Now the diagonal is a straight line

that connects the two opposite corner of a square.

For example, A and H, they are two opposite corners.

The straight line

that is connecting them is called diagonal.

Now, my question is, find the area

of the following square math, means M-A-T-H

given that the diagonal A H is four.

Now, the traditional way of finding the area of square is

using the formula.

The formula is area is equal to length times width

or area is equal to any of the sides power of two,

means side squares.

These are the two traditional ways to find the area.

Now, where is the side length?

We don't know any side length.

So how are we gonna find the area?

Now we have the shortcut.

The shortcut is, if you know the diagonal,

in order to find the area,

you could just square the diagonal,

means diagonal power two and divide it by two.

Square the diagonal, divide it by two.

Again, square the diagonal, divide it by two.

What is the diagonal?

Four.

So square of four means four power of two,

divided by two.

Now, four power of two means 16.

Now, 16 divided by two is eight.

Now this is your area.

Now let's try another question.

What is the area of the square A B C D,

given the diagonal D B is three?

Again guys, what is the formula to find the area

of the square knowing the diagonal?

You are correct.

Square the diagonal and divide it by two.

Square the diagonal and divide it by two.

Remember this.

So the diagonal of this square is three.

So three square divided by two.

So that's nine divided by two which is 4.5.

Remember guys.

Square the diagonal and divide it by two.

That's all.

The shortcut number three is

about the divisibility rule for three.

There is a divisibility rule for almost every number.

Now, the question is,

is the number 45,942 divisible by three?

Now, if you want to divide it the traditional way

and then check if it is divisible by three,

it is gonna take you a lot of time

and later you might find out

that it is actually not divisible by three.

So you kinda wasted your time.

So let's check if it is divisible by three.

Now the number is 45,942.

The technique is...

the shortcut is you add the digits,

four, five, nine, four, and two from 45,942.

Your gonna get 24.

Now check.

The sum 24.

Is it divisible by three?

Let's check.

24 divided by three, yes it is divisible by three

because you get eight when you divide.

Since the sum of the digits is divisible by three,

it means the number itself is divisible by three.

It means you can divide 45,942 by three.

Now you can go ahead and divide.

Now let's check another one.

Now the second question.

Let's see if this is divisible by three.

What is the technique guys again?

Add all the digits.

So four plus three plus seven plus four plus five,

what is the sum?

four plus three seven, seven plus seven 14, 18, 23.

The sum is 23.

Now guys, is the sum 23 divisible by three?

No it is not.

It means 43,745,

this number cannot be divided by three.

The shortcut number four is about fraction simplification.

Question number one.

Simplify the fraction multiplication.

So the traditional way would be multiplying

all the numerators of this fraction and divide the product

by the product of all the denominators.

Right here.

The question that should come in your head is,

why don't you do it?

Now, I'm not gonna do it in traditional way.

I'm gonna use my shortcut.

Before learning the shortcut, let's learn

about fraction simplification.

Let's say you have a fraction.

In the fraction, you have a numerator and a denominator.

We can always simplify a numerator and a denominator

if they are both divisible by the same number.

Now, if another fraction is multiplied

with the previous fraction,

then we can simplify the numerator of the previous fraction

with the denominator of the next fraction

and this simplification is called cross simplification,

means we are simplifying cross.

Now let's use this cross simplification technique

into our fraction multiplication.

Now let's look at it.

4,020 and 8,040, we can see there in one to two ratio,

means if I divide 8,040 by 4,020, then I get two.

It means both 4,020 and 8,040 are divisible by 4,020.

Now, 4,020 is a numerator and 8,040 is a denominator,

and there is a multiplication in the middle

so I'm allowed to use cross simplification.

So if I divide 4,020 by 4,020 itself,

the quotient will be one.

What do I get when I divide 8,040 by 4,020?

I'm gonna get two.

Now that was a cross simplification.

Now let's do another cross simplification

between three and 15.

Is there a number by which you can divide

both three and 15?

Yeah, we can divide both three and 15 by three.

Let's divide three by three.

Then the three would become one

because three divided by three is one.

Now let's divide 15 by three,

15 divided by three is what, guys?

Five.

Okay.

Now, can we simplify the six and nine?

Yes, as I said, every fraction you can always divide,

you can always simplify the numerator and the denominator.

If you want to simplify, you can simplify six and nine

or you could simplify two and six.

That would be a cross simplification.

What do you like guys?

Cross simplification or the numerator divided

by denominator?

Let's use another cross simplification.

So I can divide this two by two, I get one,

and divide this six by two as well.

What do I get, guys?

Three.

Now I can simplify this three and this nine.

As I said, you can always simplify one numerator

with another denominator if it is divisible.

So divide three by three.

You get one.

Divide this nine by three.

What do you get, guys?

Three.

Okay.

Now we have this five surviving,

this three surviving, and that 60 surviving.

Can we simplify this five and three guys?

No.

Two reasons.

First of all, they are both denominators

and the second reason is they are not divisible by any...

They don't have any common factor

means you cannot divide both of them

by any numbers except for one.

Hey, wait a minute, I can divide three by three

and I can divide 60 by three.

That will be a cross simplification.

Let's divide this three by three,

you get one.

Divide this 60 by three,

what do you get, guys?

20.

Can we do anymore cross simplification?

Well, we have a five surviving and we have a 20.

20 is a numerator and five is a denominator.

Can we simplify cross?

Yes.

So divide five by five we get one.

Divide 20 by five, we get four.

Finally, as you can see, all the survivors,

we have one times one, times one, times four,

which is four in the numerator.

At the bottom we have one times one,

times one, times one, which is one.

So we just forward the numerator,

one is the denominator, so answer is four.

Much easier.

Isn't it guys?

Now let's try one more.

Well, let's see if we can do cross simplification

between four and eight.

Look.

Four, We can divide both four and eight by four.

four divided by four is what, guys?

One.

Eight divided by four is two.

Well, let's see.

Hey, we can divide nine by nine, we get one,

nine by nine we get one.

Can we cross simplify anything else?

Yes, 10 and 10.

Simplify this 10 by 10 and that by 10 as well

so we get the same thing.

321 and 642.

They look like one to two ratio.

So I can divide 321 by 321, I'm gonna get one.

If I divide 642 by 312, we get two

and finally we can see that this two

and this two can be simplified to one and one,

means we divide both of them by two,

and the final answer would be just one

because that's all is surviving.

One.

So if you know the simplification,

your multiplication will be much easier

unless you want to do it the traditional way.

The shortcut number five is about finding LCM.

The least common multiple.

Now the questions is, find the LCM of 15 and 18.

The traditional way would be using the tree method

like the 15 can be factored, the two factors of 15

is three and five, 18 can be factored,

the two factors are three and six,

six can be further prime factor to two and three.

My question is, then what?

It's pretty messy.

Now the shortcut is and the fun method is the cake method.

C-A-K-E, cake method.

So we can draw a cake, means draw a box.

Let's start with the box and let's put the

both numbers 15 and 18 in the box using a comma.

15 comma 18.

Now let's divide by any prime numbers in there,

the smallest and the only even prime number is two.

So let's divide by two.

Wait a minute.

We cannot divide 15 by two.

But can we divide 18 by two?

Yes.

As long as you can divide one of them,

you are allowed to divide by two.

So what we do with the 15, we keep it as it is.

We cannot divide 15 by two so we keep it as it is.

But 18 divided by two,

the answer is nine.

Now, you make another box on top of it

like we are building up a cake.

Now can I divide both of them

or either one of them by two?

No.

So let's use another prime number.

Three.

I can divide both of them by three actually.

15 divided by three is five

and nine divided by three is three.

Now, let's make another cake, another layer of the cake.

Now can I divide by three again?

Yes. Let's divide by three.

Can I divide five by three?

No.

so I keep the five as it is.

Remember, if you cannot divide, you keep it as it is.

Can I divide the three by three?

Yes.

Then you get a one.

Now, can I divide five and one by five?

Yes, I could divide this five by five.

Remember, you can only divide by prime numbers.

So, five is a prime number so I can divide by five.

So I get a one and this one stays as it is.

This is my candle.

Look at this.

My candle.

Now cut the cake, Happy Birthday, and this is you LCM.

So your LCM

is equal to five times three, times three,

and the last one is two.

So five times three is 15.

15 times three, 45 times two, 90.

So that's your LCM.

So let's do another one.

Find the LCM of 20, 25, and 15.

So let's draw a cake.

Put all the three numbers, 20, 25, and 15.

Now think about a prime number.

It could divide either one of them

or two of them or all three of them.

So if you can divide all three of them,

it will be faster.

So let's divide by five.

Five is a prime number so I get four,

25 divided by five is five, 15 divided by five is three.

Now let's make another layer of the cake.

Now can I divide by four?

Yes you can divide this four by four but you're not allowed

to do it because four is not a prime number.

So what number can we use now, guys?

Let's use two.

Then I get four divided by two is two

but can I divide five by two?

No.

So I will keep it as it is.

Three is not divisible by two as well.

Keep three as it is.

Now another layer of the cake.

Remember, you keep building the layers

until you get your candles.

Now let's divide by two again.

You get one, five stays as it is, three as it is.

Now let's divide by three.

You get one, stays as it is.

Five stays as it is.

Three divided by three is one.

Now what is the last number you want to pick, guys?

Now divide by five.

You get one, one, and one, these other three candles,

Happy Birthday, and this is your LCM.

So the LCM is equal to the product of all these numbers.

I have two twos, so two times two,

I have one three and two fives.

So what do you get, guys?

That's 25, 50, 100, 300.

And that's your LCM.

Hope you guys enjoyed and understood

all my shortcut techniques, guys.

These shortcut techniques can help you go

through many exams.

You can save a lot of time

unless you say traditional way for life.

For more videos, guys trust me.

This is just a drop of the ocean.

There are a lot more to learn,

lot more shortcut techniques

that I want to share with you guys.

For more videos, subscribe

to Bobby-Tariq Tutoring Center, my channel,

or leave a comment underneath the video.

If you want me to make a video on a particular topic.

For more infomation >> SHSAT Math Strategies & Shortcuts (2018-2019) | 5 Simple Tricks | Bobby-Tariq Tutoring Center - Duration: 18:33.

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Hello Friends... Welcome to my channel.. My name is Shital..

Today i will show you how to make Macrame Keychain

If you like the video LIke SHARE & SUBSCRIBE

So lets start todays video

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A Home Is Super Small, Super Simple And Super Crazy For Christmas Eve - Duration: 2:16.

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Simple Covers 1: An Introduction. Tokyo - RM (BTS) + Uh Good - RM (BTS) + Eastside - benny blanco - Duration: 0:59.

I can't sleep homesick babe

I just wanna stay right next to you

If I could choose my dreams

I just wanna stay right next to you

Falling short is such a painful thing

If you don't go through it

You can't know it

My ideals and reality

So very far, but still

By crossing that bridge

I want to reach you

The real you

The real me

He used to meet me on the Eastside

In the city where the sun don't set

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Simple Covers 2: 천사 / Angels. Everything's an Illusion + Sea + The Good Left Undone - Duration: 1:05.

Sleep well my friend

There will be another moment we'll meet again

Just let it go

Sleep well goodnight

You're something to remember

I wish that you were here by my side

Where there is hope

There is also despair

Where there is hope

There is also despair

We need to be in despair

For all our hardships

We need to be in despair

For all our hardships

All because of you, I believe in angels

No, not the kind with wings

No, not the kind with halos

The kind that bring you home

When home becomes a strange place

I'll follow your voice

All you have to do is

Shout it out

For more infomation >> Simple Covers 2: 천사 / Angels. Everything's an Illusion + Sea + The Good Left Undone - Duration: 1:05.

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