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### Course: Arithmetic (all content) > Unit 5

Lesson 5: Comparing fractions- Comparing fractions with > and < symbols
- Comparing fractions with like numerators and denominators
- Compare fractions with the same numerator or denominator
- Comparing fractions
- Comparing fractions 2 (unlike denominators)
- Compare fractions with different numerators and denominators
- Comparing and ordering fractions
- Ordering fractions
- Order fractions

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# Comparing fractions with > and < symbols

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.

## Want to join the conversation?

- How can 3/4 be larger than 3/7? 3/4 has a smaller denominator. Can someone help me?(3 votes)
- 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.(25 votes)

- How do you know if a fraction is equivelent to another fraction?(2 votes)
- 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.(1 vote)

- So if you had 12/12, would that equal 1 whole?(61 votes)
- yes because its like 1/1 which is one whole(38 votes)

- Are fractions like division(11 votes)
- 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.(2 votes)

- 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.(6 votes)
- 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.(11 votes)

- I understand what <,>, & = equals, but what does the < and > mean with a line under it?(0 votes)
- 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(9 votes)

- Can you simplify 5/30?(4 votes)
- Yes. If you divide both the numerator and denominator by 5, it will simplify to 1/6.
**5/30 ÷ 5/5 = 1/6**(8 votes)

- can fractions have decimals?(5 votes)
- 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)(6 votes)

- How do you remember that the top is the numerator and the bottom is the denominator?(3 votes)
- 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"(5 votes)

- How can you tell which fraction is greater than or less than without visualizing?(3 votes)
- 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.(3 votes)

## 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.