About this video
Sal compares 3/4 and 4/5 using two same-size rectangles, one split into fourths and one into fifths. Shading 3 fourths and 4 fifths shows that 4/5 covers more, so 3/4 < 4/5. The wholes must be the same size for the comparison to work.
You'll be able to
- use same-size tape diagrams to compare two fractions.
- explain why the wholes must be the same size when comparing fractions.
- write a comparison using the < or > symbol.
Key words
- tape diagram
- A rectangle (bar) split into equal sections to show a fraction.
- whole
- The complete rectangle that the fraction is part of.
- less than (<)
- A symbol whose open side faces the bigger number, like 3/4 < 4/5.
Transcript
- [Voiceover] What I wanna do in this video is compare the fractions 3/4 and 4/5, and I wanna do this visually. So what I'm gonna do is I'm gonna have two copies of the same whole, so let me just draw that, but I'm gonna divide the first one, so this is one whole right over here, this rectangle, when we draw the whole thing.
So this is a whole, and right below that, we have the same whole. We have a rectangle of exactly the same size. Now you might notice that I've divided them into a different number of equal sections. In the top one, I've divided it into four equal sections because I am concerned with fourths so I've divided this top whole into fourths and I've divided this bottom whole, or this bottom bar or this bottom rectangle, into fifths, or five equal sections.
So let's think about what 3/4 represent. So that's gonna be one of the fourths, right over here, two of the fourths, and then three of the fourths. And what is 4/5 going to be? Well, 4/5 is going to be one fifth, two fifths, three fifths, and four fifths. So when you look at them visually, remember, we're taking fractions of the same whole.
This is 3/4 of that rectangle, this is 4/5 of a same-sized rectangle. It wouldn't make any sense if you're doing it for different shapes or different sized rectangles. We just divided them into different sections and you see that if you have four of the fifths, that that is going to be more than three of the fourths, and so 4/5 is greater than 3/4 or you could say 3/4 is less than 4/5, or any way you wanna think about it.
The symbol you wanna use always opens to the larger number. 4/5 is larger than 3/4, so the large end of our symbol is facing the 4/5, so we would say 3/4 is less than 4/5.
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