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### Course: 5th grade foundations (Eureka Math/EngageNY) > Unit 3

Lesson 3: Topic C: Foundations- Intro to adding mixed numbers
- Intro to subtracting mixed numbers
- Add and subtract mixed numbers (with regrouping)
- Comparing fractions: tape diagram
- Comparing fractions: number line
- Visually compare fractions with unlike denominators
- Visually comparing fractions review

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# Comparing fractions: number line

Sal compares fractions on a number line.

## Want to join the conversation?

- Let's see if this helps. 5/3 = 1 2/3 10/7= 1 3/7 you only need 1 more 1/3 to make a whole (3/3) but you need 4 more 1/7 to make a whole (7/7) so 5/3 is larger because it is closer t anot her whole. Let me give you a little trick- 5/3 and 10/7 multiply 7×5=35 on the 5/3 side then multiply 3×10=30 on the 10/7 side so 35 is larger than 30 which means 5/3 is larger than 10/7. Sorry this is so long but I hope it helps.(31 votes)
- it is actually only one more fraction that equals a different fraction.(4 votes)

- is it easy to do fractions on a number line?(12 votes)
- Pretty much. because you can write two consecutive numbers on a nunmber line

(for example 0-I----1 then you count how many spaces between the numbers and start so that example would be 0 2/7(8 votes)

- This video comes up when I search for benchmark fractions. I have watched the full video but still do not know what a benchmark fraction is. Can you please define benchmark fraction? Thanks.(4 votes)
- If you are having trouble try watching the video again but this time take notes,or go to google and search it up or you can even ask your teacher(11 votes)

- Is there any such thing as 5/3? would you do it like this instead... 1 2/3? Or would you just make it 5/3? :) I guess that it would just be an improper fraction...🤪(6 votes)
- There is such a thing called 5/3. It is an improper fraction. An improper fraction is a fraction with a larger numerator(the number on top).(6 votes)

- How are you adding this(5 votes)
- 105 is the answer buddy(0 votes)

- 1 twelfth is closets to 1/2 or 1 whole?(2 votes)
- I already know this(1 vote)
- Lets see if we can comPARE the fractions(1 vote)
- 2/3 5/12 what is the common denominator(1 vote)

## Video transcript

- Let's see if we can compare
the fraction 5/3 to 10/7 or which-- if we can figure out which one of these fractions is larger. And you might notice both of
these are larger than a whole. A whole would be 3/3, this is 5/3. And a whole here would
be 7/7, this is 10/7. So which of these is going to be larger? And to help us with
that, I'm going to plot each of these on a number line and I encourage you to pause this video and try to do the same
before I work it out. Alright, so I have a number line, here. We have zero, one, two and, first, I divide the number line into thirds. You see right over here, this is 1/3, this is 2/3, the thirds
are being marked off in blue right over here. You see that each from
the space from zero to one is split into three equal
sections, one, two, three. And then the space from one to two is split into three equal
sections, one, two, and three, you see that right over here. So I'm marking off all of the-- I'm marking off all of the thirds. So this is 1/3, this is
2/3, this is 3/3, which is, of course, the same thing as one. This is 4/3, and then this right over here is going to be 5/3. And if we were to go over here, two would be the same thing as 6/3. But what we care about
is 5/3, so that's that. Right over there, I don't
want to fill it in so much. So 5/3 is that right over there. Now let's think about sevenths. Now to do sevenths I have
to split the part of the number line between zero and one or between each whole number
into seven equal spaces. So you see that here. One, two, three, four, five, six, seven. You have seven equal sections. So this is 1/7, this is
2/7, 3/7, 4/7, 5/7, 6/7, this is 7/7, I could write that down, this is, one is the same thing as 7/7, 8/7, 9/7, 10/7 right over here. This, right over here is ten over seven. So we see that both 10/7 and 5/3 are between one and two, but which one of these is actually larger? Well we see 5/3 is further to the right on the number line than 10/7. I'm gonna make this a
little bit easier to see. So 10/7 and that is right over there. So 5/3 is to the right of 10/7,
so 5/3 is greater than 10/7. So how do we write the symbol? Well we always want to open
it up to the larger number. 5/3 is the larger number
so we want the larger side or the opening on the larger number. Or the smaller side, or the point, pointing to the smaller number. So we have 5/3 is greater than 10/7.