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Lesson 1: Fractions intro

# 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.
•  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?
• 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)
• how did fractions get their name?
(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)