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## 6th grade (Eureka Math/EngageNY)

### Course: 6th grade (Eureka Math/EngageNY) > Unit 1

Lesson 1: Topic A: Representing and reasoning about ratios- Intro to ratios
- Ratio review
- Basic ratios
- Part:whole ratios
- Basic ratios
- Equivalent ratios
- Equivalent ratios: recipe
- Equivalent ratios
- Equivalent ratio word problems
- Equivalent ratios with equal groups
- Equivalent ratio word problems
- Equivalent ratios in the real world
- Understanding equivalent ratios
- Understand equivalent ratios in the real world

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# Understanding equivalent ratios

Sal discusses what it means for two ratios to be equivalent.

## Want to join the conversation?

- At3:18Sal said "the order matters". Why does the order matter?(16 votes)
- Hey Ashi, to respond to your question,the order matters,a lot with ratios. If I had four bananas and fifteen apples and I had to put the amount of apples to bananas, I would have to put 15:4. If I put4:15without being told to put bananas to apples, the problem wouldn't work. I hope this answered your question.(15 votes)

- In the first question, why didn't he multiply both? like, doesn't that mean they ain't equivalent?(7 votes)
- I think what you mean is when he is multiplying one of the stores recipe and not the other one. The thing is, is that when he multiplied the ratio 2:2/1 he multiplied both sides by 2 yes? Which means the value of the ratio hasnt changed but how it is presented is. For example say you were actually making something, and you had the ratio 1:1 (this is mainly because I DONT WANNA DO MATH cough* anyways) and then you multiplied both sides by 4, making 4 servings. the ratio itself is still the same its just presented differently. (this is confusing i know) Basically its like its 1 to 1 yeah? then its 4 to 4. The ratio still means the same its just making more servings. The same goes for the problem Sal is showing, the two when brought to the same amount of servings as the other makes them both equal.
**If you dont get it might wanna comment and ask for someone else to explain**. Keep in mind though that this doesnt apply to all equations. (I cant really explain these examples either because there are none or i just havnt the care to research them. Maybe both). Hope this helps!(19 votes)

- i get the concept, but when I take the tests it says what he's doing is WRONG which does not make sense, does anyone have an explanation?(6 votes)
- There is an explanation for every question on the tests on Khan. Try following those.(11 votes)

- can i add the two values in two ratios and see if they are equivalent?for example in the ration 4:3 , if i add them i would get 7 and in the ratio 20 : 15 , if i add them i would get 35. So can i say that 7 times 5 is 35 , so in each value of the ratio 4:3 , i need to multiply with 5 to get 20 : 15?(6 votes)
- You're making it more complicated than it needs to be.

Why don't you just look at 4 and 20. 4*5 = 20. Then, look at 3 and 15. if 3*5=15 (which it does), then you have an equivalent ratio.

Or, think of ratios as fractions (which they are). Fully reduce 20/15 by removing a common factor of 5 and you get 4/3. So, the ratios are equivalent.

For more complicated ratios, you can use cross multiplication.

If 4/3 = 20/15, then 4(15) must equal 3(20).

Hope this helps.(7 votes)

- I AM KINDA CONFUSED BC WHEN I DO THE WORD PROBLEMS FOR EXAMPLE: Victoria's favorite cookie recipe uses 170 grams of butter for every 250 grams of flour. Victoria's daughter made cookies using 340 grams of butter for every 400 grams of flour.

What will Victoria think of her daughter's cookies? IT DOESNT MAKE ANY SENCE FOR ME BC I DONT KNOW IF I AM SUPPOSED TO MULTIPLY OR DIVIDE AND I DIDNT UNDERSTAND THE VIDEO...(7 votes)- is 340 divisible by 170 if so by how much then do the same with the other ration 250 divide 400 by 250 then see if you get the same quotient if you dont then its not equivalent if you want to knwo which is higher and which is lower in a certain substance or which substance is lower or higher then multiply the first ratio by the quotient that was revealed when youdivided it by the second ratio's first number with and if the resulting ratio is lower or higher you can answer it in the question(3 votes)

- 2:11to2:15is understood, but is the question not state :

"Which dipping sauce hasmustard flavour?"**stronger**

Firstly: It's written stronger MUSTARD flavour, and we can clearly see that Burgur Barn uses 1/2 or 0.5 or one-half spoonful mustard, and Sandwhich Town uses 1 spoonful of mustard. So isn't it clear that Sandwhich Town has a stronger mustard flavour?

Secondly: Even if we look at it as a whole or one dipping sauce, we would find that Sandwhich Town has stronger mustard flavour.

I understand that the answer was same because we are doing equivalent ratios so the answer is "same", but is this answer not wrong for this question? Or is my understanding wrong?(6 votes)- actually is it my eyes being dumb or does burger barn have half the serving as sandwich town(4 votes)

- how do you get 9:5 please tell me(2 votes)
- you take18:10and divide both of them by 2.(10 votes)

- Please comment if you are forced to do this for school(6 votes)
- how do u do this

please help me with really big numbers(6 votes)- just practise your times tables and didvshon ones to but first you times your number times what is there number than x your other number the same number or divide what ever you want. I hope this helps someone(1 vote)

- how do you change the ratio to a total number(5 votes)

## Video transcript

- [Voiceover] We're told that Burger Barn makes dipping sauce by
mixing two spoonfuls of honey with one half spoonful of mustard. Sandwich Town makes dipping sauce by mixing four spoonfuls of honey with one spoonful of mustard. Which dipping sauce has a
stronger mustard flavor? So pause this video and see if you can work through that on your own. All right, now let's
think about the ratios of honey to mustard at
each of these restaurants. So first let's think about
the scenario with Burger Barn. So I'll just say BB for
short, for Burger Burn. So they have two spoonfuls of honey for every one half spoonful of mustard, so the ratio of honey to mustard in terms of spoonfuls is
two spoonfuls of honey for every one half spoonful of mustard, so this is the ratio of honey to mustard. Let me write this. This is honey, and this
right over here is mustard. Now, let's look at Sandwich
Town, so I'll call that ST. So Sandwich Town makes dipping sauce by having four spoonfuls of honey for every one spoonful of mustard. So the ratio of honey to mustard is four spoonfuls to one spoonful, so once again, that is
honey and that is mustard. Now, can we make these equivalent ratios or can we compare them somehow? Well, let's see. We have one half spoonful of mustard here. We have one spoon of mustard here, so what if we multiplied both the mustard and the honey spoonfuls by two? That still would be an equivalent ratio because we're multiplying
by the same amount. So if we multiply by
two in both situations, you have four spoonfuls of honey for every one spoonful of mustard. Well, that's the exact same ratio that we have at Sandwich Town. So it actually turns out that they have the same concentration of mustard. They have the same ratio
of honey to mustard. Four spoonfuls of honey for
every spoonful of mustard in either situation. Let's do another example. So here, we are asked or
we are told, we are told, Patrick's favorite shade of purple paint is made with four ounces of blue paint, so underline that in blue,
four ounces of blue paint, for every three ounces of red paint, for every three ounces of red paint. So the ratio of blue paint to red paint is four ounces of blue,
four ounces of blue, for every three ounces
of red, so four to three. Which of the following paint mixtures will create the same shade of purple? All right, pause this video and see if you can figure
it out on your own. So this is three ounces of blue paint mixed with four ounces of red paint. Well, this is a ratio
here of three to four, and even though it's dealing
with the same numbers, this is a different ratio. The order matters. This is four ounces of blue
for every three ounces of red. This is saying three ounces of blue for every four ounces of red,
so we could rule this one out. Eight ounces of blue paint mixed with six ounces of red paint. So here, this ratio is
eight ounces of blue for every six ounces of red. Well, are these equivalent ratios? Well, the difference, or you can go, if you multiply by two in either case, you will get to eight to six. Four times two is eight,
three times two is six. So this is indeed an equivalent ratio, so we would select this one. All right, here they say
six ounces of blue paint mixed with eight ounces of red paint. So this is, they've swapped
the blues and the red relative to this one, so this
is a ratio of six to eight, so let me write this down. So this is a ratio, six
ounces of blue paint for every eight ounces of red paint. So just like we ruled out that first one, this is dealing with the same numbers but in a different order
and the order matters, so we'll rule that out. 20 ounces of blue paint,
20 ounces of blue paint, for every 15 ounces of red paint. So are these equivalent? Well, let's think about it. To go from four to 20,
you can multiply by five, and to go from three to 15,
you could multiply by five, so we can multiply by the same factor to go from four to three to 20 to 15, so this is indeed an equivalent ratio. 12 ounces of blue paint mixed
with 16 ounces of red paint. All right, so this is a ratio here of 12 ounces of blue for
every 16 ounces of red. So let's think about this. To go from four to 12, you
would multiply by three. Now, if you multiplied three by three, you would have a nine here, not a 16, so this is definitely
not an equivalent ratio. Another way of thinking about it, you have, in terms of ounces, you have more ounces of
blue than you have of red for any of the equivalent ratios, but here you have more
ounces of red than blue, so once again, another way of realizing that that is not equivalent, so only B and D are
the equivalent mixtures that will provide the
same shade of purple. To have that same shade, you need the same ratio of blue to red.