 Now let's go back to adding fractions, right? Let's say you have one over two plus one over three Let's do a visual of this right if you're doing a visual of this Simplify us simplify us if you're doing a visual of this a Fraction is part of a whole so one over two means take an object a whole object You have and break it up into two pieces right so we're breaking up in this into two pieces And you're taking one of the pieces so one out of two, right? That's one out of two For this one plus Take a whole thing right and break it up into three pieces and you're taking one out of three, right? Here's one out of three Now we want to add one over two plus one over three, right? What is it? We will we'll do it simplest form of this, right? So if you're gonna add this plus this we need to Like we can't do it right now because they're not broken into Compatible parts right so what we need to do is take each one of these holes and break them into Equal parts and see what one out of that looks like right? So the common denominator or the lowest common multiple for two and three is six So what we can break a whole thing into when we're dealing with one over two and one over three Is to break that whole thing into six parts because both two and three go into six Five out of six perfect, right? But here's the visual. So we're gonna take this whole thing and break it into six pieces right And one out of two means a half means we're taking three Out of six, right? So this becomes three over six plus This guy we're gonna break at the six pieces So we're gonna go this this this and we're taking This many which is two So this becomes plus two out of six and Three over six plus two out of six because they have the same Number of pieces now we can just add them up just add them one two three four five five pieces five over six right Good math teacher. What about this guy's good math teacher, right? five out of six Okay, now, how do you do? How do you do this just algebraically without the visuals because you're not going to go through visuals all the time, right? What you do you find the lowest common multiple you say That's six and you ask yourself. What did you multiply two by to give you six you multiply two by three So you multiply the top by Three as well. So you multiply the bottom by three you multiply top by three and by the way Do you know why you can do this? Because you can multiply any number by one without changing its value and three over three is One right so you're not changing the value of one out of two. You're making it look different Right You just that's all you're doing first thing Understood Trust me that look mathematics each there's only five axioms. Everything else is built on that, right? So what happens is Two times three is six which is what we had one times three is three Plus what do you multiply three by to give you six you multiply three by two right, but you can't just Multiply the bottom by two you're going to multiply the top by two because you don't want to change the Value the weight of one over three. You just want to make it look different So we're going to multiply the top by two and the bottom by two Right because two over two is one. We're just multiplying it by one So one times two is two three times two is six six cool They have the same number of they broken the same size pieces now. You just add them up you get Five over six that's adding fractions