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Lesson 1: Week 4

# Intro to fractions

Sal divides wholes into equal-sized pieces to create unit fractions. Created by Sal Khan.

## Want to join the conversation?

• Why isnt it 3 fourths instead of 1 fourth.. because one is shaded.. and 3 arent.
• When he shaded it, he meant it like he was taking away
• i keep hearing denominators and numerators, what are they?
• 1
_ is a fraction, right?

2

so the number on the top of the bar, which is 1 is the numerator
and the number on the bottom of the bar, which is 2 is the denominator

kathyc's rule for remembering this is easy, and you should use it :)
• I dont understand fractions because how is it that if you add 1/4+1/4 you get 1/2 the number is now shorter
• Let's see if I can clear this up for you. If you have a pizza, and you cut that pizza into four big slices, each slice is 1/4 of a pizza. Now, here's where you might have been confused. 2 of those 4 slices is the same as 1/2 of a pizza. 1/2 is the same as 2/4. If you had only cut the pizza in half, you would have 2 equal halves. I hope this was helpful, because I know how it is to be confused by fractions.
• Can every shape represent unlimited fractions?
• yes since you can always divide it further into more parts.
• At , why did they use the shapes a rectangle and a square?
• Since both squares and rectangles have congruent (similar) sides, then they can be easily cut into integer (whole number) pieces that make it easier to understand in terms of the overall lesson.
• then if the triangle is not 1/4th as its not equal. Then how much it is?
timestamp == around min
• Hey,

What a great question! Let's go think about it using geometry. I'm gonna assume that that triangle is equilateral. Equilateral means the triangle has all the sides of the same length and all the angles of the same size. Looking at the video we can see that one of the sides is devided into four 1/4ths. Therefore we might think that the area of each part is 1/4th of the whole triangle as well, but unfortunately we're looking for equal area not equal parts of a side.

Let's leave calculations aside - when we look at the small triangle and the whole triangle, we have to ask ourselves: "How many times would that small triangle fit into the whole?" Try imagining having infinite amount of these small triangle to play with and your goal is to build a copy of the whole triangle. How many triangles would you need? The answer is excatly 8 - meaning that the small triangle is just a 1/8th.

CALCULATIONS

So what is the area of that small triangle compared to the whole shape? Let's do some calculations: Let's say each side of the whole triangle is excatly 1 cm (you can also use inches or no units as well if that helps). So how big is the whole triangle? The formula for area of any triangle is half of base times it's heigth also known as bh/2. Don't worry if you don't understand right now. We can find the height using the pythagorean theorem, which tells us that the heigth will be approximetly 0,87 cm or to be exact the half of the square root of 3.

So we know the whole triangle is approximetly 0,435 cm squared large. So how big is the smaller triangle? Using the same ways of calculations we get that the area of the small triangle is approximetly 0,05 cm squared.

To summarize:
WHOLE triangle ≈ 0,435 cm squared.
Smaller triangle ≈ 0,05 cm squared.

Smaller triangle ÷ Whole triangle ≈
0,05 ÷ 0,435 ≈
50 ÷ 435 ≈ 0,115 ≈ 1/8 th
• Can I use fractions with money?
• Yes you can! With American money, we have half dollars (1/2), quarters (1/4), dimes (1/10), nickels (1/20) and pennies (1/100). So, what would the number look like if you had \$3.27 - it would be 3 and 27/100 dollars.

As an interesting tidbit - pennies are called CENTS. That word CENT stands for 100. 100 pennies in a dollar - 100 years in a CENTury, etc.
• Why does Sal cut the square into 4th and not 8th's or 16th's?
(1 vote)
• He could have cut the square into any number of pieces. When fractions are initially taught, smaller numbers are used until students grasp the concepts.
(1 vote)
• how did fractions get their name?
(1 vote)
• It is a late Middle English word coming from Old France. It is derived from Fractio, a Latin word that means "breaking (bread)". Fractio comes from the Latin word frangere, which means "to break".

This makes sense because fractions, in math, are broken sections of objects.
(1 vote)
• whats the point in making a whole piece of something a fraction like 9/9 instead of doing 1?
(1 vote)
• One of the uses of this comes in multiplying fractions. Say you wish to multiply 1 2/9 by 4 5/6.

The first step to do this is converting both mixed numbers to improper fractions. To convert 1 2/9 to an improper fraction, you need to know that 9/9 = 1 that way you can convert 1 2/9 into 11/9. You can convert the second one into 29/6. That way you can multiply 11/9 by 29/6 to get 319/54. You can then convert that back to a mixed number, 5 49/54.

Other examples include comparing fractions. If you were to compare 8/9 to 1 it might be slightly difficult to know which one is bigger. However if instead you have 8/9 and 9/9, 9 > 8 so 9/9 > 8/9.
(1 vote)

## Video transcript

What we're going to talk about in this video is the idea of a fraction. And we'll see there's many ways to think about a fraction. But first, we'll think about the most fundamental. So let's say that I have this square. And we can consider this a whole. So let me write that down. This is a whole. It is a complete square. Now, what I'm going to do is divide this into 4 equal parts. So with one cut like that, I've divided it into 2 equal parts, and then with another cut like this, I could divide it into 4 equal parts. So there are 4 equal parts. And now what I'm going to do is I'm going to select one of those equal parts, so let's say this part right over here. I am going to select that. So the question is, what fraction of the whole is the part that I have shaded in red? Well, it is 1 out of the 4 equal parts, right? I've shaded in 1 out of 1, 2, 3, 4 equal parts. So we write this as this fraction. This piece represents 1/4 of the whole. And there's two ways that you can think about this. You could view this as 1 of the 4 equal parts, or you could view this as a whole divided by 4 would get you exactly this much. Now let's do another one. And this time, let's think about how we could represent 1 over 8, so 1 over 8. Well, we could divide this whole, in this case, the whole is this rectangle-looking thing. We could divide the whole into 8 equal parts. So let's do that. So here I've divided into 2 equal parts. That looks pretty good. And now I can divide each of those into 2 equal parts to get me 4 equal parts. And then if I were to divide each of those into 2 equal parts, I will have 8 equal parts. And it's not exact. Obviously, I've drawn it by hand, but hopefully this gets you a sense. So now I have 8 equal parts. And now I'm going to select exactly one of them. And that'll represent 1/8. And I could select any one of these, but I'll just do this one to show you it does not have to be necessarily the first one. So once again, this square right over here that I'm shading in red represents 1/8 of the whole. Now, let's look at a few more examples where I've shaded them in ahead of time. And what I want you to do right now is pause the video, and either in your head or a piece of paper write down if you consider this purple thing, the whole, what fraction does this red part represent? If you consider this blue part the whole, what fraction does this red part represent? If you view this yellow triangle as a whole, what fraction does this red part represent? And so I encourage you to pause the video now. Well, let's look at each of these. So in this case, for this rectangle, we have 3 equal parts, and we've shaded in one of them. So this red rectangle right over here represents 1/3 of the whole. Now, Over here, in this kind of pie-looking thing, this circle-looking thing, we have 1, 2, 3, 4, 5 equal parts. And we have shaded in 1 of those 5 equal parts. So this little slice of the pie, this represents 1/5. This right over here is 1/5 of the entire pie. Now, this one's interesting. You might be tempted to say, well, I've got 5 parts, and then I've shaded in 1. That must represent 1/4. But remember, it needs to be 4 equal parts. And it's pretty clear looking at this that this part right over here is not equal in size to this part right over here or this part right over here. These are not 4 equal parts. So we cannot say that this is 1/4 of the triangle. So you cannot say that.