Bài 25 Volume of a Cube- Thể tích hình lập phương

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Boys and girls ,

Ladies and gentlemen.

Today  we will be finding the volume of a cube.

First  we should probably talk about what a cube is .

A  cube is basically a box that has six congruent or equal squares.

So  all of the squares that form the cube are exactly the same.

So  what do we mean by volume .

So  here we have a three-dimensional object and this is really the first three dimensional object .

We 've been dealing with when we talk about volume it's .

How  much would fill up the entire cube like if we wanted to pour water into this cube.

How much water would fill up the cube.

So volume is all of the space that's taken up by the inside of the cube.

We're going to use volume when we're talking about any three dimensional object.

So we want to find the volume of this cube .

Now you have to know one of your side lights so.

Here this is six inches.

Now remember because this is a cube this is a three-dimensional object.

That 's created by six identical squares nino and a square.

You are.

Face  in the height of the square exactly the same .

So if that's six inches , this is also six inches .

This 6 inches.

This is six inches really all of the lines you see or six inches.

So when we're finding volume and we first want to find the area of our base which is the square that on the very bottom here.

The first thing we want to do is find the area of the square that is the base of the square.

Remember the space of the square is the square that's on the bottom.

But Now we know that one side length of the square is fixed .

So  the other side length of the square also has to be 6.

And  therefore the area of this square will be 6 times 6 or 36 square inches.

 To  find the volume we're going to multiply the area that is the area of the base.

Times  our height which again in this case is going to be another six inches.

So the volume here of our cube is going to be 216 cubic inches or inches cubed.

Whenever  we're finding the volume of a rectangular prism which

is basically anytime,  you have a three-dimensional figure that's contained by rectangles.

You're going to find the volume by length times width times height now.

Because  this is a cube, our length or width and our height all have the same length.

And  therefore we can say that it is our side length cubed or the side length to the third power.

And  now remember ,because we're talking about volume ,our answer always has to be in our units cubed or to the third power.

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Bài 24 Volume - Rectangular Prisms - thể tích lăng trụ hình chữ nhật.

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Volume is measured by how many cubic units it would take to fill a given space.

The  cube shaded green is a cubic unit .

The amount of cubic units it takes to fill a defined space is what we call volume .

The shown geometric solid is a rectangular prism .

To find the volume of any rectangular prism, we simply multiply the length times the width times the height .

The length and the width of the rectangular prism are always at the bottom of the shape.

These  two dimensions make up the base of the rectangular prism.

In this case the length is 4 in the width is 3.

Multiplying  the length times the width will give you the area of the prisms base .

This is a two dimensional measurement .

After multiplying the length times the width and getting the area of the rectangular prisms base by multiplying it by the rectangular prisms height that will give us the volume.

Multiplying  the area of the prisms base by the height is filling up the prism or adding depth .

This is what gives our rectangular prism a third dimension or gives it volume.

We  can clearly see when multiplying the length times the width of the rectangular prism.

We come up with 12 square units which would be the area of the rectangular prisms base.

Remember this is only a two dimensional measurement.

To  give a depth or volume we must now multiply the area of the rectangular prism space of 12 by whatever the height is to fill up the rectangular prism or to add depth or volume.

 If  we multiply the area of the base which is 12 by a height of 1 that would give us 12 cubic units which would be how many cubes it would take to make one level of our rectangular prism.

Adding  two levels of 12 we would get a total of 24 cubic units three levels of 12 would give us 36 four levels of 12 give us 48 cubic units.

And  of course five levels of 12 would give us 60 cubic units.

We could say that each level of the rectangular prism contains 12 cubes.

There  are five love twelve cubes for a total of 60

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Bài 23 Pie Chart-biểu đồ hình quạt

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LESSON 12

Pie chart .

A  pie chart presents the data in the form of a circle that is

divided into sections .

Each section corresponds to a particular data value.

The area of each section is proportional to the proportion of the category that section represents .

Pie charts are primarily constructed for qualitative data where the relative size of each section depicts the percentage.

So  here is an illustration of a generic pie chart  where like all graphical methods a descriptive title appears at the top.

Then  each individual section is clearly labeled with the corresponding data value and percentage .

The relative size of each section depicts the percentage of each category.

 For  instance, the entire pie or circle accounts for 100% of the data.

 If  we're to cut this 100% in half, we would then show 50 50 % slices .

If  you cut the halves in half ,we then have quarters or 25 percent segments of the pie.

So the overall relative size of each piece corresponds to the percentage that that data value occupies.

Here  cutting the 100% into thirds, we get 33  33 % sizes.

Or  other various sizes 10%, 15% together make 25%, 20%, 30% together make up 50%.

In  statistics drawing a pie chart by hand is rarely done.

In  practice ,pie charts are constructed using software applications.

To  describe the distribution of qualitative data represented in a pie chart , the various categories observed are merely mentioned along with their associated percentages.

This  is because qualitative data that's at the normal level doesn't follow a particular order and using the conventional terms like bell-shaped or skewed do not apply to this type of data.

So  when describing the pie chart,  you merely just mention the categories along with their associated percentages.

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BÀI 22 : Convert Mixed Numbers to Improper Fractions – đổi hỗ số sang phân số không thực sự

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Converting mixed numbers to improper fraction .

Let 's try and convert one and three fourths to an improper fraction.

Let 's represent this in the form of squares .

Now  let's try representing the squares as a fraction .

Counter  the scraps.

There  are seven fourths that is 7 over 4.

So  1 and 3 fourths equals seven folds.

To change a mixed number into an improper fraction .

Multiply  the old number by the denominator.

And  add it to the numerator of the fractional part.

Let 's do one more and this time without the help of any squares or pictures .

Let 's change 2 and five sixths to an improper fraction.

First multiply 2 by 6 that is multiply the whole number by the denominator .

Then  add it to the numerator of the fractional part which is five.

Hence  17 becomes our new numerator .

The  denominator remains the same which is six .

Hence  our improper fraction becomes  17 / 6.

Let 's look at one more example.

Six  and a half .

So  it is  6 x 2 plus 1 equals 30.

Denominator  remains too.

Hence  the improper fraction is 13 by 2 .

Did n't I tell you it was easy.

Now  let's look at..

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Bài 21 Improper Fraction- phân số không thực sự.

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Improper fractions.

Improper  fractions have  the numerators that are larger than or equal to the  denominators.

 11 / 4    5 over 5  and 13 / 2 are some improper fractions .

Let 's look at an example.

This hexagon has seven pieces .

Hence  this fraction will be written as 7 over 6.

So we see that the numerator is greater than the denominator

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BÀI 20 : Mixed Numbers – Hỗn số

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Shh

Mixed numbers .

Fractions  are used to count a part of something.

Mixed  numbers are used when you need to count whole things and parts of things at the same time .

How  much of these squares is red.

There  are three whole squares and one-fourth of another square.

We  write it like this 3 1/4 and read it like 3 and 1/4 .

It 's really 3 plus 1/4 but we don't put the plus in .

This  is why we say the and.

Hence  we see that mixed numbers have a whole number part and a fraction part.

Examples  2 and 3/4 and 6 and ½.

You  are right .

This  is really getting to be interesting and fun .

Now  let's look at

Ummh

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BÀI 19 : FIND PERCENTAGES OF NUMBERS- TÌM TỶ LỆ % CỦA SỐ

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What is 10% of a million dollars.

exactamente 10% is $100,000 .

go gogo … 

To find 10% of a million dollars, we simply move the decimal point one place to the left.

If  we had 10 stacks of cash on a table and each stack was $100,000 ,we would have a million dollars.

 one stack equals one tenth  which is $100,000.

10 / 10 would be all 10 stacks equals $1,000,000.

wrote…… chut cha chut cha-ching oh yeah.

Let’s try another problem.

 What  is 60% of 80 dollars.

Well, what's 50% of 80 dollars.

 That 's right $40.

Now  what's 10% of 80.

 Remember, To find 10% , we can just move the decimals one place to the left.

So 80 becomes 8.
40 plus 8 equals 48 and that's our answer.

How  about 65% of 80.

We  know that 50% of 80 is 40.
 and we know that 10% of 80 is 8.

5% is half of 10% .

So  half of 8 is 4 .

And  if we add it all up ,we have 52 .

65% of 80 is  52 .

Let 's try a tricky one .

What  is 15% of 70 .

To  solve this,we need to find 10% and 5% to give us  15%.

So  what's 10% of 70.

That 's right.

We  move the decimal one to the left to give us seven .

And   five percent is half of 10%.

So  what's half of seven .

That 's right.

Three  point five .

Seven  plus three point five is ten point five .

So  ten point five is our answer.

 ro room yes hi yeah .

Let 's do one more.

What  is one percent of five million dollars .

ruah thousand dollars.

 So  100 percent of five million dollars is five million dollars.

 To  find 10 percent we just move the decimal one space to the left .

To  find one percent ,we would move the decimal two spaces to the left.

 So $50,000 is one percent of five million dollars .

Roku Mulla Mulla Mulla hey yeah hey yeah .

Good job.

 Hopefully  these tricks make it easier keep practicing and you'll get

better and fast.

 bang bang Koston

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BÀI 18 : DIVIDING DECIMALS.

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Alright guys .

Now  let's look at dividing decimals .

Ooh  sounds scary but it's really not okay.

 So  we have two point four five divided by one point five .

And the first thing you want to do is take that second number or the divisor and make it an integer .

So  to do that we want to move the decimal.

 One  place to the right or multiply by ten it's another way of thinking about it.

But  ultimately we just want to make one point five into 15 .

Now  you'll notice we moved it one decimal place to get it into an integer .

And  we want to do the exact same thing with the first number.

So  we had two point four five .

We 're gonna make that twenty four point five because we move the decimal place one time in the first number .

We 're gonna do that now with this number .

Okay  so now the problem reads.

 Twenty  four point five divided by fifteen .

Okay so let's look at that and make that long division .

Okay  so we have twenty four point five.

 Now  this is the real tricky part you want to make sure that the first Number that we had before.

 Twenty four point five goes inside the house .

So it kind of looks like it's doing this criss-cross thing right .

Twenty  four point five goes in the house .

The division house as we say.

 And  fifteen goes out front .

The  other really important thing here is that you make sure to put the decimal place .

Right above where it is inside the house.

 So twenty four point five ,the decimal place is right after the four .

Make  sure the decimal point is right above that in your answer .

Now  we just divide left to right just the way that we do long division.

Okay  so we ask ourselves how many times does fifteen go into twenty four .

We  don't go over that now.

 But you'll recall there's a lot of different strategies how to figure that one out.

 15 goes into 24 one time.

 So  15 times one is 15 .

24 minus 15 is nine .

Okay  so that's our remainder there step.

 We 're gonna go ahead and bring that five straight down .

So  we're left with a remainder of 95.

 Okay  so how many times does 15 go into 95 .

We  ask ourselves again .

We 're not going to go over that particular concept now.

 But  you'll see that if you work it out ,you'll get 6.

 Ok so 15 times 6 is 90.

 95 minus 90 is 5.

 Ok so now what do we do.

 Well  we're gonna imagine that there's zeros going on for.

You  tell infinity after 24.5 .

Because remember there actually are zeros that go on to infinity after twenty four point five .

So  it's twenty four point five zero zero zero zero zero and so on.

So  we're gonna bring that zero down and we get 50 .

So  how many times is 15 go into 50.

Well  again if you work it out ,it's three so 15 times 3 is 45.

Now  watch out 50 minus 45 is five .

Now  check it out.

That 's exactly what we got on the step before .

Okay  now that's interesting .

What happens if we bring down that next zero.

Well  you'll see that you get this unending stream of 50 minus 45.

And you're gonna get three on to infinity .

So this is one of those cases where.

We  can stop.

We  can stop and say this decimal is going to keep repeating.

So  we have one point six three repeating.

As  our answer.

And  that's it .

That 's how you divide decimals.

You  just move the decimal in the divisor enough times to get an integer.

And  then move the decimal the same number of times in the dividend .

And  then do long division the way you normally do it.

And that my friends is how you divide decimals.

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BÀI 17 : MULTIPLYING DECIMALS.

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To multiply decimals .

Sixteen  point one times two point four.

First  line up the numbers .

Then  multiplies though we were multiplying whole numbers .

So  we can think of this problem .

As  161 times 24.

Now multiplying 4 times 1 is 4.

 4 times 6 is 24 .

So  we bring down a 4 and carry the 2 .

4 times 1 is 4 plus 2 is 6.

Now starting a new row and beginning in the tens column .

We  have 2 times 1 which is 2.

2 times 6 which is 12 .

So  we bring down a 2 and carry the 1 .

2 times 1 is 2 plus 1 is 3.

Now  we add the rows together 4 plus 0 is 4 .

4 plus 2 is 6 .

6 plus 2 is 8 .

And we bring down the 3 so that we have 3860 for .

Our  final step is to determine where the decimal point goes in our final answer.

 Notice  that since there's one digit to the right of the decimal point

and 16 point one and one digit to the right of the decimal point in 2.4.

We have the total of two digits to the right of the decimal point in our original numbers.

 This  means we'll have two digits to the right of the decimal point in our final answer.

 So  16 point one times two point four is thirty eight point six four.

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