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“This lesson. We re going to talk about equivalent ratios. So let s say if if we have the ratio 8 to 6 and 12 to 9 are the two equivalent to each other what would you say how can we tell how can we find the answer well there s two ways in which we can do so first we need to convert the ratio into a fraction and then we could simplify the two fractions and see if they re equal to each. Other if they are then the ratios are equivalent to each.
Other the second option is to convert them to fractions set. The fractions equal to each other and check to see if the cross products are the same. So let s start with the first method. 8 2.
6. Can be written as 8. Over. 6.
As a fraction now how can we reduce this fraction. 8. Is basically 4 times 2 6. Is 3 times.
2. So if we cancel a 2. We can reduce 8 over 6 to 4 over 3. Now let s do the same with the other fraction or the other ratio 12 to 9.
Is the same as or we can write it as 12 over 9. Now both numbers are divisible by 3 12..
Divided by 3 is 4 9. Divided by 3 is 3. So notice that both fractions simplify to the same result so this means that these two ratios are equivalent to each other now. Let s talk about the second method.
So let s convert the ratios into fractions and let s put an equal sign between the two fractions now. What i want you to do is i want you to cross multiply. So first we re going to multiply 8. By 9 8 times.
9. Is 72 next we re going to multiply. 6. And 12.
What is 6 times 12. If you add 12 6 times ward you get 10 times. 6. Is 60 2 times.
6. Is 12 60 plus. 12. Is 72.
So notice that these two are the same so therefore. These two ratios are equivalent to each other..
And so that s two ways in which you can tell if two ratios are equivalent let s look at another example for the sake of practice. So let s say if we have the ratio 4 to 5 and let s say. 7 to actually let me change this let s say 12 to 8. And 16 to 12 use both methods to see if the two ratios are equivalent.
So first let s begin by reducing the fraction 12 over 8. We could divide both numbers by 4 12. Divided by 4 is 3 8. Divided by 4 is 2 now 16 over 12 how can we reduce it we can write.
16 as 4 times 4 12. Is 4 times stream and so we could cancel a 4. And so this gives us a simplified fraction of 4 over 3. So notice that these two are not the same so therefore.
These ratios are not equivalent to each other now let s use the other technique. Let s write the two fractions and let s put an equal sign between them so let s begin by multiplying. 12. By 12 12 times.
12. Is 144. Now what about 8 times. 16.
Well let s use the old fashioned multiplication a times. 6 is 48..
So we ll write the 8 carry over the 4 8 times. 1. Is 12 plus. 4.
So that gives us 128 128 does not equal 144. So the two ratios are not equivalent to each other now let s work on a math. Problem. Let s say that 15 2 x.
Is the same ratio as 21 to 28. So what is the value of x. That will make these two ratios equivalent to each. Other what would you do in a problem like this how should we begin well what i recommend is writing the two fractions and put in an equal sign between them in order for these two ratios to be equivalent to each other we know that the cross products have to be the same so that means that 15 times 28.
Must equal 21 times x. So now that we have the equation. We can calculate the value of x. Now using a calculator you could do 15 times 28.
Divided by 21 and you ll get the answer. But let s see if we can do this mentally. If you don t want to use the calculator. I recommend rewrite in 15 as 5 times 3 break it down into smaller numbers.
28. You can write that as 7 times 4 21..
Is 7 times. 3. Now if you divide both sides by 7. You could cancel the 7 on both sides.
Now we could do the same with the 3. So notice that we only have the x variable on the right side. So. The answer is gonna be 5 times.
4. Which is 20 so x is 20. So 15 to 20 is the same ratio as 21 to 28. Now let s check the work by simplifying.
The ratios. So this is 15 over 20 and if we divide both numbers by 5. This will reduce to 3 4. For the other fraction.
We could divide both numbers by 7. And so this is going to be the same thing. 3. Over 4.
So the two ratios are ” ..
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