So if you had 12/12, would that equal 1 whole?

yes because its like 1/1 which is one whole

wait but what if the 3/7 pieces where much bigger than how sal cut them and the 3/4 where the same so you cant always know. Is there an other operation that tells you what to do with that.

As mentioned in prior discussions, you have to assume the whole units are the same size. If they aren't, the problem will tell you they aren't and you will need to convert them to units that are equal size. For example: We don't compare liters and gallons without converting to a common unit of measure. You need either both numbers in liters or both numbers in gallons to work with them.

How can 3/4 be larger than 3/7? 3/4 has a smaller denominator. Can someone help me?

If you have a bigger denominator it is smaller because then you have more parts, and that makes it smaller. fractions can also be turned into decimals, so 3/7= 3 divided by seven, which is about 0.4285. but 3 divided by 4 is 0.75.

can fractions have decimals?

Yes, and this is common in basketball. For example, a player who attempts 10.6 shots per game and makes 5.3 of them can be represented by the fraction 5.3/10.6 (which, of course, means the player makes half of their shot attempts)

How do you remember that the top is the numerator and the bottom is the denominator?

I can think of it as the top is "New" and the bottom as "Den" The numerator has sprung out of the floor, "New" as ever. The denominator is under the line, so it is in it's "Den"

Can you simplify 5/30?

Yes. If you divide both the numerator and denominator by 5, it will simplify to 1/6. *5/30 ÷ 5/5 = 1/6*

How do you know if a fraction is equivelent to another fraction?

There are a few ways to check: 1) You can fully reduce both fractions. In reduced form, they should be identical to each other. For example: is 5/10 equal to 21/42. Yes because they both reduce to 1/2 2) You can convert them to a common denominator. Once they have a common denominator, it the numerators are the same, then the fractions are equal. 3) You can test to see if they create a proportion. Proportions have a unique characteristic that if you multiply along the diagonals, the results will be equal if the fractions are equal. Example: Is 2/7 = 14/49 ? Multiply 2*49 and see if it equals 7*14. These are equal as both create 98.

I understand what <,>, & = equals, but what does the < and > mean with a line under it?

Do you mean ≤ and ≥? ≥ is equal to or greater than. For example, you could use 2 ≥ 1 or 4 ≥ 4. ≤ is equal to or less than. For example, you could use 5 ≤ 8 or 8 ≤ 8. Hope this helped! <3

Main content

3rd grade

Course: 3rd grade > Unit 6

Lesson 1: Comparing fractions

Comparing fractions with > and < symbols

Name: Comparing fractions with > and < symbols
Uploaded: 2013-10-18T20:58:21Z
Description: When comparing fractions, remember that the numerator is the top number and the denominator is the bottom number. With the same denominator, the larger numerator means a larger fraction. With the same numerator, the smaller denominator means a larger fraction. Two fractions can be equivalent even with different numerators and denominators

Google Classroom

When comparing fractions, remember that the numerator is the top number and the denominator is the bottom number. With the same denominator, the larger numerator means a larger fraction. With the same numerator, the smaller denominator means a larger fraction. Two fractions can be equivalent even with different numerators and denominators. Created by Sal Khan.

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Lilly Brown
Posted 5 years ago. Direct link to Lilly Brown's post “How can 3/4 be larger tha...”
How can 3/4 be larger than 3/7? 3/4 has a smaller denominator. Can someone help me?
Comment on Lilly Brown's post “How can 3/4 be larger tha...”
(5 votes)
- ABHISAB
  Posted 5 years ago. Direct link to ABHISAB's post “If you have a bigger deno...”
  If you have a bigger denominator it is smaller because then you have more parts, and that makes it smaller. fractions can also be turned into decimals, so 3/7= 3 divided by seven, which is about 0.4285. but 3 divided by 4 is 0.75.
  Comment on ABHISAB's post “If you have a bigger deno...”
  (15 votes)
smoeesha
Posted 7 years ago. Direct link to smoeesha's post “How do you know if a frac...”
How do you know if a fraction is equivelent to another fraction?
(1 vote)
- Kim Seidel
  Posted 7 years ago. Direct link to Kim Seidel's post “There are a few ways to c...”
  There are a few ways to check:
  
  1) You can fully reduce both fractions. In reduced form, they should be identical to each other. For example: is 5/10 equal to 21/42. Yes because they both reduce to 1/2
  
  2) You can convert them to a common denominator. Once they have a common denominator, it the numerators are the same, then the fractions are equal.
  
  3) You can test to see if they create a proportion. Proportions have a unique characteristic that if you multiply along the diagonals, the results will be equal if the fractions are equal.
  Example: Is 2/7 = 14/49 ? Multiply 2*49 and see if it equals 7*14. These are equal as both create 98.
  (2 votes)
jamal.turrell
Posted 7 years ago. Direct link to jamal.turrell's post “So if you had 12/12, woul...”
So if you had 12/12, would that equal 1 whole?
Comment on jamal.turrell's post “So if you had 12/12, woul...”
(58 votes)
- elizabeth.pearce
  Posted 4 years ago. Direct link to elizabeth.pearce's post “yes because its like 1/1 ...”
  yes because its like 1/1 which is one whole
  Comment on elizabeth.pearce's post “yes because its like 1/1 ...”
  (35 votes)
20175027
Posted 3 years ago. Direct link to 20175027's post “Are fractions like divisi...”
Are fractions like division
Comment on 20175027's post “Are fractions like divisi...”
(8 votes)
- Stephen White
  Posted 3 years ago. Direct link to Stephen White's post “Fractions and division ha...”
  Fractions and division have some things in common. For instance, if you want to convert a fraction into a decimal, you would divide the two numbers.
  
  Example: 1/4 (spoken one quarter) To convert 1/4 into a decimal, you would take 1 divided by 4 and you would get 0.25
  
  If you look at that as money, it would be $0.25 and that is also what we call "one quarter." Looking at it another way, one quarter is 1/4 of a dollar.
  (0 votes)
buttonboxx2321
Posted 6 years ago. Direct link to buttonboxx2321's post “wait but what if the 3/7 ...”
wait but what if the 3/7 pieces where much bigger than how sal cut them and the 3/4 where the same so you cant always know. Is there an other operation that tells you what to do with that.
Comment on buttonboxx2321's post “wait but what if the 3/7 ...”
(6 votes)
- Kim Seidel
  Posted 6 years ago. Direct link to Kim Seidel's post “As mentioned in prior dis...”
  As mentioned in prior discussions, you have to assume the whole units are the same size. If they aren't, the problem will tell you they aren't and you will need to convert them to units that are equal size. For example: We don't compare liters and gallons without converting to a common unit of measure. You need either both numbers in liters or both numbers in gallons to work with them.
  Comment on Kim Seidel's post “As mentioned in prior dis...”
  (10 votes)
Joanna Ni
Posted 7 years ago. Direct link to Joanna Ni's post “I understand what <,>, & ...”
I understand what <,>, & = equals, but what does the < and > mean with a line under it?
Comment on Joanna Ni's post “I understand what <,>, & ...”
(0 votes)
- Elysia Du
  Posted 7 years ago. Direct link to Elysia Du's post “Do you mean ≤ and ≥? ...”
  Do you mean ≤ and ≥?
  
  ≥ is equal to or greater than. For example, you could use 2 ≥ 1 or 4 ≥ 4.
  
  ≤ is equal to or less than. For example, you could use 5 ≤ 8 or 8 ≤ 8.
  Hope this helped! <3
  Comment on Elysia Du's post “Do you mean ≤ and ≥? ...”
  (8 votes)
Eric Ye
Posted 3 years ago. Direct link to Eric Ye's post “can fractions have decima...”
can fractions have decimals?
(4 votes)
- TJ
  Posted 3 years ago. Direct link to TJ's post “Yes, and this is common i...”
  Yes, and this is common in basketball. For example, a player who attempts 10.6 shots per game and makes 5.3 of them can be represented by the fraction 5.3/10.6 (which, of course, means the player makes half of their shot attempts)
  Comment on TJ's post “Yes, and this is common i...”
  (5 votes)
LucasNuss
Posted 9 years ago. Direct link to LucasNuss's post “How do you remember that ...”
How do you remember that the top is the numerator and the bottom is the denominator?
Comment on LucasNuss's post “How do you remember that ...”
(3 votes)
- TrinCat
  Posted 9 years ago. Direct link to TrinCat's post “I can think of it as the ...”
  I can think of it as the top is "New" and the bottom as "Den"
  The numerator has sprung out of the floor, "New" as ever.
  The denominator is under the line, so it is in it's "Den"
  Comment on TrinCat's post “I can think of it as the ...”
  (5 votes)
Eric Ye
Posted 3 years ago. Direct link to Eric Ye's post “Can you simplify 5/30?”
Can you simplify 5/30?
Comment on Eric Ye's post “Can you simplify 5/30?”
(3 votes)
- emmy <3
  Posted 3 years ago. Direct link to emmy <3's post “Yes. If you divide both t...”
  Yes. If you divide both the numerator and denominator by 5, it will simplify to 1/6.
  5/30 ÷ 5/5 = 1/6
  (5 votes)
Mahi
Posted 8 years ago. Direct link to Mahi's post “How can you tell which fr...”
How can you tell which fraction is greater than or less than without visualizing?
Comment on Mahi's post “How can you tell which fr...”
(2 votes)
- Walks on the Clouds
  Posted 8 years ago. Direct link to Walks on the Clouds's post “All you need to do is to ...”
  All you need to do is to make sure that the bottom numbers (denominators) of the fractions you're comparing are the same.
  As long as the denominators are the same, you just look at the top numbers (numerators) and see which is bigger and which is smaller.
  For example: 7/10 is greater than 4/10.
  Another example: 1/8 is less than 5/8.
  The trick is having the same denominators. Then, it's easy to see which fraction is bigger.
  (1 vote)

Video transcript

When you write a fraction, there are actually words for the top number and the bottom number. And the words are a lot more fancy than the word "top number" and "bottom number." What mathematicians typically use is the word "numerator" for the top number and "denominator" for the bottom number. And what I want to do now that we know that the top number is the numerator of the fraction and the bottom number is the denominator, I want to compare pairs of fractions that have either the same denominator or the same numerator. So let's look at this first pair. I want to compare 4/7 to 3/7. And I have two wholes right over here. They're the same hole, and I've divided them into sevenths. I've divided them into 7 equal chunks. And I want to see what's larger, 4/7 or 3/7. So what I can do is, I can fill in 4/7. Let me select 4 out of the 7. So, that's 1, 2, 3, 4. And the fact that trying to even get to 4/7 I had to have 3/7 first gives you good clue that 4/7 is probably larger, or it is larger. But now let's color in 3/7, just so we can compare. So 1, 2, 3/7. And so it's pretty clear that on the left-hand side, we are shading in more of the whole than on the right-hand side. So, 4/7 represents a larger fraction, more of the whole than 3/7. And the way that we can state that comparison mathematically is with the greater than symbol. We can write 4/7 is greater than 3/7. Now, the greater than and less than symbols can sometimes be confusing. This is greater than. This is less than. And the way that I remember it is that the greater than symbol, either symbol, the small pointy side is always on the side of the smaller number, and the big open side is always on the side of the larger number. So here, big open side is opening towards the 4/7, small pointy side opening to the 3/7. 4/7 is greater than 3/7. Now, what about 3/7 and 3/4? So, here I have different denominators, but I have the same numerator. And so I encourage you to pause this video and draw maybe little boxes like this and try to judge for yourself which of these is a larger fraction, represents a larger number. Well, let's color them in. So, let's think about 3/7 first. And we actually already drew it here, but I can do it really fast right over here. So that is 3/7. I've colored in 3 of the 7 equal groups. And what would 3/4 be? Well, that's 1/3, 2/4, and 3/4. And so it's pretty clear that 3/4 represents a larger fraction of the whole, that 3/4 is larger, or that 3/7 is smaller. So we could write that 3/7 is less than 3/4. So, notice, same exact numerator. When I divided it-- because this fraction symbol could also be viewed as division. When I have it as more equal groups, so it's a fraction of more equal groups, so 3 out of 7 versus 3 out of 4, this is a smaller number, which which makes sense. Now, let's compare these two. We have the same denominator, different numerators-- 3/4 versus 2/4. Well, 3/4 we've already looked at. We can just shade in 3 of these. So 3 of these fourths. So that's 3/4 right over there. And then 2/4, well, we're going to only have 2 of the fourths, 1, 2. So 2/4 is clearly the smaller number. 3/4 is the greater number. So, once again, we could write 3/4 is greater than 2/4. And then finally, I encourage you to pause the video. Try to come up with whether 2/4 or 3/6 is a larger number. Well, let's color it in again. We've already seen 2/4. We just have to color in 2 of our fourths. So let's just color in 2 of our fourths right over there. And then 3/6, we've split our whole into 6 equal sections-- 1, 2, 3, 4, 5, 6. We need to color in 3 of them. And as you see, we're coloring in the exact same amount of the whole. These two fractions are equivalent. These are equivalent fractions. 2/4 is equal to 3/6. And as you see here, they're both filling in half of the whole. If we were to just draw the whole and split it only-- let me do this in a different color. If we have our whole, and we were to split it only into two sections, we are shading in exactly 1 out of the 2 sections. So you could say that 2/4 is equal to 3/6, and they both equal 1/2. So 1/2 is equal to 2/4 is equal to 3/6.