Solving Ratio Problems with Tables Question

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Tito Warren

2018. március 22. 19:21

I am attempting to enhance my (rudimentary) grasp of mathematics. It's a subject that I, sincerely, have an extremely difficult time understanding. I cannot stress enough just how frustrating the subject is. I'm only adding this prelude to my question because I've found that the video instructions assume a level of mathematical comprehension that I do not always possess and I suspect that is the root of my concern here.

In the snip above, you can see that the narrator has filled in the answers. I'm well into the tutoring session but I keep coming back to the same confusion - if the ratios shown are equivalent, why did he use different common numbers to alter them?

For instance, the narrator halved the given values to discern that 12 is half of 24. So half of 40 is 20. But then he divined 4 as a relevant input (somehow) to get his answer of 5. And finally, to discern the last value the narrator doubled the 24.

To the narrator, this makes obvious sense but to me... how do I know when to use half and when to use 4? How do I know when to double and when to use a 4? This seems completely arbitrary.

There must be some step that I am missing.

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ikrik72

2018. április 10. 17:38
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Try not to think too much in arbitrary actions but try to reason your steps in order to match the ratios.

So you start off with two given values, you write both down with a line between them. The thing with the ratio is, that whatever happens to the left value should also happen to the right value (perform the same operations means keeping the same ratio).

Let's take your given example:

24 | 40

Now the first question is to get the denominator matching 3 as a numerator (for this specific ratio).

24| 40

= 3| ?

as you can see, we need to perform operations to lower the 24 in order to get to 3. An easy first step would be to split it in halve. Remember: the same operation has to be performed on both sides!

24 split in halve will become 12, and 40 split in halve becomes 20. so we get:

24|40

12|20

3|?

We still have to go even lower to get to 3. Now we can keep splitting in halve, but we can also try to speed things up a little. In this case, in order to get from 12 to 3, we would have to divide by 3 (because 12/4 = 3).

Again, the same operation has to be performed on both sides. So when we divide 12 by 4, we also divide 20 by 4:

12/4 = 3 and 20/4 = 5

so we get:

24|40

12|20

3|5

The trick is to keep performing division and multiplication actions on both sides untill you get to the desired ratio!

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Solving Ratio Problems with Tables Question

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