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### Course: 3rd grade > Unit 5

Lesson 2: Fractions in contexts# Fractions in contexts

Sal uses fractions to represent real-world contexts.

## Want to join the conversation?

- Can you multiply fractions?(25 votes)
- Yes you can multiply fractions.(10 votes)

- how do you divide fractions(5 votes)
- Good question! There are at least two methods.

1) Invert the second fraction (the fraction you are dividing by) and then multiply the fractions.

2) Replace the fractions with equivalent fractions that use the same denominator. Then divide the new numerators and cancel out the denominators.

Note: an advantage of using two methods to solve a math problem is that you can use the second method to check your answer.

Example: let’s do 2/3 divided by 3/4.

Method 1):

2/3 divided by 3/4

= 2/3 x 4/3

= (2x4)/(3x3)

= 8/9.

Method 2):

2/3 divided by 3/4

= 8/12 divided by 9/12

= 8 divided by 9

= 8/9.

Have a good day!(1 vote)

- Are fraction unsolved division problems?(3 votes)
- Yea, that could make sense, but try keeping in mind that fractions are still numbers just like 1, 2 and 3.

Try imagining fractions as simplified division, because sometimes we don't need to know the exact value and sometimes we can't write out the whole value, like in the equation: 1 ÷ 3 answer is something along the lines of 0,3333333 and so on. So to simplify such numbers we use fractions like 1/3th.(4 votes)

- can you multiply fracion(3 votes)
- Yes, you can add, subtract, multiply, and divide any fractions (except for division by zero).

To multiply fractions, multiply numerators together, and multiply denominators together.

A shortcut called cancellation can be used, if any numerator and any denominator have a common factor other than just 1. In this shortcut, first divide the numerator and denominator by the common factor (almost like reducing fractions). Then multiply numerators and multiply denominators.

Example: let’s do 3/5 x 10/11.

Without shortcut:

3/5 x 10/11 = (3x10)/(5x11) = 30/55 = 6/11.

With shortcut: the numerator 10 and denominator 5 have a common factor of 5. So divide them each by 5. So 10 changes to 2, and 5 changes to 1, but the answer stays the same.

3/5 x 10/11 = 3/1 x 2/11 = (3x2)/(1x11) = 6/11.

Caution: using this cancellation shortcut for a numerator and denominator belonging to different fractions only works for multiplication! So for example, we cannot say that 3/5 + 10/11 = 3/1 + 2/11. Clearly 3/5 + 10/11 is less than 2, while 3/1 + 2/11 is greater than 3.

Have a good day!(3 votes)

- can you divide fractions?(3 votes)
- Hepful,understandable but could use more time on the diver one.(3 votes)
- What does Sal mean by one eighth?(2 votes)
- one eighth or 1/8 is like one slice of a pizza cut into 8 slices, hope that helps :)(2 votes)

- why does sal use divers?🤷(2 votes)
- could u help me do something(2 votes)
- I saw the video.(2 votes)

## Video transcript

- [Instructor] In this video we're going to think about
how fractions can be used to represent things in the real world. So here we're told that
on the Sharks dive team there are three divers in third grade. There are eight total divers on the team. What fraction of Sharks
dive team is in third grade? So pause this video and see
if you can figure that out. All right, so first of all they tell us there are eight total divers on the team. So maybe I'll represent each diver with a little circle like this, I'll try to make it look
kind of like a diver, so that's not quite a
circle but you get the idea, it looks like something
kind of diving down. So one, two, three, four,
five, six, seven, and eight. Now if we were to talk
about just one diver here, just like that, that would
be one out of the eight. Or we would often call that one eighth, so eight with a h at the end. That is one eighth right over there, or I could represent it like this, I could say this is an eighth, an eighth, or I could say that this is equal to 1/8. This is one of the eight
members of our dive team. Now they tell us that there are
three divers in third grade, what fraction of Sharks
dive team is in third grade? So that is, let's say it these three, so there's three out of the eight. So if you wanted to
represent that as a fraction you could represent it as 3/8 like this, or you could represent it as, if you wanted to write it out as a word, three, instead of having
it three over eight, you could write three eighths like that. If you were doing this on Khan Academy there'd be some choices out there where you'd pick one
of the correct choice, but you could represent the
fraction of Sharks dive team that is in third grade either
as three over eight, 3/8, or three and then spell
out the word eighths. Let's do another example. Here we are told Yuma divided his clay into four equal parts. He made clay animals out
of three of the parts. What fraction of the clay did
Yuma use to make clay animals? So one again, pause this
video, and think about it. All right, so let's just imagine that this is his clay, initially, and he divides it into four equal parts. And so let's say he divides it like this. And let's say that I've divided
it into four equal parts, that these all have the
exact amount of clay in it, it's hand drawn so it's
not going to be perfect the way I drew it but
let's assume they all have the exact same amount of clay. Now it says that he made clay animals out of three of the parts. So maybe, this part right over here, he was able to make a clay animal out of, this part right over here,
he made a clay animal out of, and then that part, right over there, he made a clay animal out of. So what fraction of the clay did he use to make clay animals? So what would you call
each of the equal parts? So if I were to just focus
on that right over there, you would call that a fourth, a fourth. You could also represent it
as one fourth, like that, or you could represent it as 1/4. That's if you were to just
circle one of these equal parts, that one, or that one,
or that one, or that one. Now if you're talking
about all of his clay, what are you talking about? Well you could view it as
four fourths, four fourths, or four over four, this would
also be read four fourths. That would be referring to all one, two, three, four of his clay. Now if you wanted to say
what fraction of the clay did Yuma use to make clay animals, we can see that three of the fourths, were used to make clay animals. So to answer that question, we would say three of the fourths, so three fourths were
used to make clay animals. You can also express that as a fraction. You could also write
that as 3/4 like this. You would read these the same, three fourths, or three fourths. Three out of the four
equal sections of clay were used to make the clay animals.