Fraction

In t Let'say if we have 3 divided by 5 plus 4 divided by 7. How can we add these two fractions? Well here's a simple technique. First multiply 5 and 7. T Next multiply 3 and 7. 3 times 7 is 21. And also there's a plus in between. Multiply 5 times 4 w 21 plus 20 is 41. So the answer is 41 divided by 35. Let's try another example. Let'say if we want to subtract 7 over 8 minus 2 over 9. Let's use the same technique. Let's multiply the two denominators 8 and 9 w And then the next one is going to be 7 times 9 w Minus 8 times 2 w Now let'subtract. What is 63 minus 16? T Now 47 is not divisible by 2 nor is it divisible by 3. So that's the final answer. So now what if we wanted to add or subtract let'say three fractions instead of two? What should we do in t So let'say we wish to combine 3 over 4 plus 5 over 3 minus 7 over 2. Whenever you wish to add or subtract fractions the denominator has to be the same. The denominator is the bottom part of the fraction. And right now they're all different. So how can we make them the same? How can we get the commons down there? If you want to find the least commons denominator make a list. All of the multiples of 2 are 2, 4, 6, 8, 10, 12, 14 and so forth. Multiple of 3 are 3, 6, 9, 12, 15, 18 and so forth. And multiples of 4 are 4, 8, 12, 16, 20. What is the least common multiple? We'll look at for a multiple that is common to all three n The least common multiple is 12. 12 is common to 2, 3 and 4 and it's the lowest of such now granted, 24 is also a common multiple and if you use 24 you can get the right answer. You just got to simplify at the end. So if you're ever unsure about how to find the least common denominator you can find any common denominator. One simple technique is simply to multiply these three. 4 times 3 times 2 is 24 and you could use 24 and still get the right answer. So now that we know the least common denominator is 12, let's multiply each fraction in such a way to get 12. The first fraction, let's multiply the top and the bottom by 3 because 3 times 4 is 12. Now for the second one, let's use 4 and for the last one, let's use 6. So looking at the first one, 3 times 3 is 9, 3 times 4 is 12. 4 times 5 is 20, 4 times 3 is 12. 7 times 6 is 42, 2 times 6 is 12. Now that we have the same denominator we can combine the n 9 plus 20 is 29 and 29 minus 42 is negative 13. So t It's negative 13 divided by 12. So now it's your turn. Go ahead and try t 8 over 5 minus 2 over 3 plus 9 divided by 4. So go ahead and add these three fractions. So t It may not be the least common multiple but it is a common denominator just so If we multiply 5 times 4 times 3, t So 60 is going to be the common denominator that we're going to try to get. So we're going to multiply the first fraction by 12 because 12 times 5 is 60 and the second one by 20 because 20 times 3 is 60. By the way, if you want to find out the n 60 divided by 5 will give you the 12. 60 divided by 3 will give you the 20 and 60 divided by 4 will give us the now 12 times 8, that's 96, 5 times 12, we know it's 60. 2 times 20 is 40, 3 times 20 is 60, and 9 times 15. 15 times 10 is 150. So if you take away 15 from that, you'll get 15 times 9, so that's 135. And 4 times 15 is 60. Now 96 minus 40, that's positive 56. And 56 plus 135, let's go ahead and add those two n 5 plus 6 is 11, carry over the 1. 1 plus 3 plus 5 is 9 plus 1. So the final answer is 191 divided by 60. In t Whenever you need to multiply, multiply the n 3 times 7 is equal to 21. And 5 times 2 is equal to 10. And so the answer is 21 over 10. That's all you need to do when multiplying fractions. But sometimes the n Let'say if we have large n What should we do in t Now we can multiply across. We can multiply 24 and 45, which will give us a big n But do we really want to do that? When multiplying fractions with large n For instance, 24 is basically 6 times 4. 27 is 9 times 3. 45 is 9 times 5. And 30 is 6 times 5. You want to break it in such a way that you cancel some n Here we cancel a 5 because we have one on top and the other on the bottom. The same is true for the 9. And we cancel a 6. So therefore, the final answer is 4 over 3. So were able to get the final answer without multiplying 24 by 45. That step was necessary. Plus it's going to take some time and you need a calculator. Doing it try t Multiply 56 divided by 77 by 35 over 40. Now 56 is 8 times 7. 77 is 11 times 7. 35 is 7 times 5. And 40 is 8 times 5. So we cancel an 8. We cancel a 7. And we cancel a 5. Leave in the final answer of 7 over 11. So now In t Let's use 8 over 5 as an example. And let's divide it by 12 over 7. Now, perhaps you heard of the expression keep change flip. It's useful when dividing fractions. Keep the first fraction the same way. Change division to multiplication and flip the second fraction. And now you can do it. So 8 times 7 is 56. But we can simplify it before we multiply. 8 is basically 4 times 2. And 12 is 4 times 3. So we cancel a 4. And now we can multiply. 2 times 7 is 14. And 5 times 3 is 15. So the final answer is 14 over 15. Try t What's 4 divided by 3? Divided by 9 over 5. So using the expression keep change flip, let's keep the first fraction the same. Let's change division to multiplication. And let's flip the second fraction. Now there's not So let's multiply across. 4 times 5 is 20. 3 times 9 is 27. And so we can't reduce that's the answer. Now, what if you see a problem that looks 36 over 54 divided by 64 over 48. If you have a fraction written t And then we can use the keep change flip principle. Let's keep the first fraction the same. Let's change division to multiplication. And then let's flip the second fraction. And now let'simplify. So 36 is basically 9 times 4. 54 is 9 times 6. 48 is 16 times 3. And 64 is 16 times 4. So right now we cancel a 9. We cancel a 16. And we cancel a 4. So what we have left over is 3 over 6. Now 3 over 6 can be reduced. We can divide both n 3 divided by 3 is equal to 1. 6 divided by 3 is 2. So the final answer is 1 over 2.