yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Ratios with tape diagrams


3m read
·Nov 11, 2024

We're told Kenzie makes quilts with some blue squares and some green squares. The ratio of blue squares to green squares is shown in the diagram. The table shows the number of blue squares and the number of green squares that Kenzie will make on two of her quilts.

All right, this is the table they're talking about. Based on the ratio, complete the missing values in the table. So why don't you pause this video and see if you can figure it out?

Well, first let's think about the ratio of blue to green squares. So for every three blue squares—let me do that same, a similar color—for every three blue squares, we are going to have one, two, three, four, five green squares. So the ratio of blue to green is three to five.

In quilt A, she has 21 blue squares. So she has 21 blue squares. How many green squares would she have? Well, to go from 3 to 21, you have to multiply by 7. And so, you would take 5 and then multiply that by 7, so you'd multiply 5 times 7 to get to 35. As long as you multiply both of these by the same number, or divide them by the same number, you're going to get an equivalent ratio. So 21 to 35 is the same thing as 3 to 5.

Now we have a situation in quilt B; they've given us the number of green squares, so that's 20. Well, how do we get 20 from 5? Well, we would multiply by 4. So if you multiply the number of green squares by 4, then you would do the same thing for the number of blue squares: 3 times 4, 3 times 4 is going to be equal to 12.

Twelve blue squares for every 20 green squares is the same ratio as three blue squares for every five green squares. Let's do another example here. We are told the following diagram describes the number of cups of blue and red paint in a mixture. What is the ratio of blue paint to red paint in the mixture? So try to work it out.

All right, so let's just see. We have one, two, three, four, five, six, seven, eight, nine, ten—ten cups of blue paint for every one, two, three, four, five, six cups of red paint. So this would be a legitimate ratio: a ratio of 10 cups of blue paint for every 6 cups of red paint.

But this isn't in, I guess you could say, lowest terms or most simplified terms because we can actually divide both of these numbers by two. So if you divide ten by two, you get five—do that blue color; and if you divide six by two, you get three. So one way to think about it is for every five blue squares you have three red squares in this diagram, in this tape diagram—that's sometimes called—or you could say for every five cups of blue paint you have three cups of red paint in our mixture.

And you can even see that here: three cups of red paint and one, two, three, four, five—five cups of blue paint, and you see that again right over here. Let's do another example here.

We're told Luna and Ginny each cast magic spells. The ratio of spells Luna casts to spells Ginny casts is represented in this tape diagram. All right, based on the ratio, what is the number of spells Ginny casts when Luna casts 20 spells? Pause this video and see if you can work it out.

All right, so let's just see the ratio here. For every one, two, three, four spells that Luna casts, Ginny casts one, two, three, four, five spells. So the ratio is four to five. But if Luna casts 20 spells—so if Luna casts 20 spells—well, to go from 4 to 20, we had to multiply by 5.

And so we would do the same thing with the number of spells Ginny casts: you'd multiply that by 5. So it's 25. So 4 Luna spells for every 5 Ginny spells is the same thing as 20 Luna spells for every 25 Ginny spells.

And so how many spells does Ginny cast when Luna casts 20 spells? She casts 25, and we're done.

More Articles

View All
How To Embody A MILLIONAIRE'S Lifestyle | Kevin O'Leary
I keep telling everybody every time we talk about investing, the key is diversification. I feel good about the expense, but I also feel good from an investment strategy that it’s not just frivolous and stupid; that I needed to get my money back out of it.…
Henderson–Hasselbalch equation | Acids and bases | AP Chemistry | Khan Academy
The Henderson-Hasselbalch equation is an equation that’s often used to calculate the pH of buffer solutions. Buffers consist of a weak acid and its conjugate base. So, for a generic weak acid, we could call that HA, and therefore its conjugate base would …
From the Hunted to the Hunter | The Great Human Race
It’s thought that Homo erectus became the first early humans to actively hunt their prey, elevating themselves from scavenger to predator. “Bring it!” “Yeah, that’s absolutely dead sure! This is her first kill. We’re gonna make the most of this entire a…
How Are Businesses Applying Digital Currencies? | Anthony Pompliano
What is Circle? And then talk to us about the suite of products that you guys have built for various financial organizations to use. Yeah, no problem, thank you! Yeah, so Circle is a global financial technology firm. We’ve been operating in the crypto an…
Ecosystem dynamics: Clark’s nutcrackers and the white bark pine | Khan Academy
What’s that? That sound, that call, sounds like something a crow would make but not quite. That’s actually the call of a really interesting bird called Clark’s nutcracker. These birds are cousins of the American crow, which you might see and hear around …
Eaten by Jaws and Big Wave Surfing| Edge of the Unknown on Disney+
JUSTINE DUPONT (VOICEOVER): [SPEAKING FRENCH] FRED DAVID: Four years ago, we moved to Nazaré. And we decided to focus on big wave surfing. Every big wave is different. But I think Nazaré is probably the best place to learn how to deal with big waves. MA…