 Okay, one of the biggest issues, one of the biggest problems people have is dealing with fractions. So let's start with adding and subtracting fractions, show you how you do that, okay? Let's start small. Let's go two over five plus three over four. Now the way you do this is, you take the biggest number in the bottom, you try to find a common denominator, the lowest common denominator between them. So whenever you have any fractions being added up, you take the biggest number in the bottom, which is five. Okay, and you see if the other number goes into it. Now four doesn't go into five. So multiply five by two, you're gonna get 10. Does four go into 10? It doesn't go into 10. So you gotta continue with this. Five times three is 15. Does four go into 15? No. So go to the next one, five times four is 20. Now obviously five, four goes into 20. So your common denominator here is 20. Now what did you multiply five by to give you 20? You multiply five by four. So you multiply the top by the same number that you multiply this guy. So two times four is eight. What did you multiply four by to give you 20? Well you multiply four by five, so you multiply top by the same number. Times five, five times three is 15. So plus 15. 15 plus 15 is 23. Over 20. That's how you add fractions, okay? Now what we're gonna do is do a bigger number and I'm gonna add subtraction in there so you see that doesn't really make a difference, okay? Let's move on to another section of walk. Let's say we have seven over five minus three over four plus three over four plus four over... Let's make it five again. And plus seven over 12, okay? So right now you've got the biggest number you have is 12. So you're gonna try to find the biggest or the smallest number that five, four and five go into. So you're gonna take 12. Obviously five doesn't go into 12, okay? So you're gonna multiply 12 by two. You're gonna get 24. Now does five go into 24? No, four goes into it but five doesn't. So you gotta continue. 12 times three is 36. Four goes into it but five doesn't. So you continue. 12 times four is eight, four, 48. Obviously four goes into it but five doesn't. So one more. 12 times five is five times two is 10. You carry the one, five times one is five plus one is six. Now four goes into 60, five goes into 60 and 12 goes into 60. So your common denominator is 60. What did you multiply five by to give you 60? You multiply it by 12. So you multiply seven by 12, okay? Let's do this by hand. Seven times 12, two times seven is 14. One, seven, eight, 84. Then you got minus. What did you multiply four by to give you 60? Well, I'm not sure. So let's do a division. Four goes into six once. That's four, bring the two down. Bring the zero down. Four goes into 25 times. So you multiply four by 15. So what you gotta multiply three by is 15. Three times 15 is 45. So it's minus 45. So right now we've got 84 minus 45. We multiply five by 12. So 12 times four, well we already did it over here, it's 48. So what it's gonna be is gonna be plus 48. And we've got 12 here. Well we multiply 12 by five to give us 60, okay? So we multiply seven by five as well. Seven times five is 35. Now what you gotta do is do all these things down here. Now, we got negative 45 plus 48. If you combine these guys, you're gonna have three left over. Three plus 35, so this plus this gives you 38. And it's positive. So all you gotta do now is add 84 plus 38. Let's do this up here. 84 plus 38. Eight plus four is 12. You carry the one up. Eight plus one is nine. Nine plus three is 12. So all of this turns out to be 122 over 60. Now what you have to do is you cannot leave it like that. You have to break that down into its lowest form. Now, they're both even, so you know two goes into these. Okay? So 60, if you break this down, it becomes two times 30, right? If you break down 122, two goes into 12, six times, two goes into one, two goes into two, once. So two times 61 is 122. So what we got here is two times 61, and we've got two times 30 in the bottom. Two times 30. So what happens is anything from the top can cancel out anything from the bottom. So two kills two. So your final answer is 61 over 30, okay? So what we had here was all these fractions, you find the lowest common denominator is 60, whatever you multiply the bottom by to give you 60, you multiply the top by, you do the operations, addition, subtraction, you get to this number here, and then from here you gotta reduce it to its lowest form, which is breaking it down to its prime numbers. You cancel whatever you need to cancel, and that's your final answer. Simple as that, but it includes breaking numbers down to their prime numbers, adding, subtracting, multiplying, okay? Try it out. I'm gonna have the exercises on the website.