now what would you do if you need to solve an equation that has fractions so what would you do to solve this one so here's what we can do let's multiply both sides by three that will get rid of the three on the bottom if we do that these will cancel and so we're going to have on the left is 2x on the right 8 times 3 is 24 and now all we need to do is divide both sides by 2. so 24 divided by 2 is 12. now another way in which you can solve this if you wish to do it faster can also do it this way you can multiply both sides by the reciprocal of this fraction that is by three over two and so notice that the twos will cancel and also uh the threes will cancel as well and so you're gonna have x on the left side now what is eight times three over two now there's two ways you can do this you can multiply then divide or divide the multiply 8 times 3 is 24 24 divided by 2 is 12. or you could say 8 divided by 2 is 4 4 times 3 is 12. either way you'll get the same answer but when dealing with larger numbers it's better to divide first and then to multiply let's try another example that's similar to this one let's say 5 over 8x plus four is equal to fourteen go ahead and try it now before we multiply by eight let's get rid of the four let's subtract both sides by four you can multiply by 8 but 8 times 14 is going to be a large number so let's avoid doing that for now these will cancel and so 5 over 8x is equal to 10. now let's multiply both sides by 8. so we're going to have 5x is equal to 10 times 8 10 times 8 is 80. and now let's divide both sides by 5. 80 divided by 5 is 16. and so that's the value of x now what if we have an equation that contains two fractions in this case it might be better to clear away all the fractions and the best way to do that is to multiply both sides by the common denominator of the two fractions you can use any common denominator ideally you want to use the least common denominator but all common denominators will work if you're not sure what to multiply by multiply three and five and just use fifteen that technique will always work so now let's distribute the fifteen to everything on the inside so what's 15 times one third 1 3 times 15 is the same as 15 divided by 3 and so that's 5. now what about 15 times 2x that's simply going to be 30x now 15 times 2 over 5. we could say 15 times 2 is 30 30 divided by 5 is 6 or we could say 15 divided by 5 is 3 3 times 2 is 6. now let's subtract both sides by five so 30x is equal to one now our last step is to divide by thirty so x is a fraction it's one over thirty here's the next example x divided by two plus five is equal to one over four what is the value of x so what should we do here well just like the last example let's clear away all fractions we have a two and a four now we don't need to multiply and use eight we could use a it'll still work but we can use a small number four two and four both go into four so let's multiply everything by four so what is x over two times four if you're not sure simply multiply them four times x is four x so right now we have four x over two next four times five is twenty and one fourth times four is basically one the fours cancel so this is what we now have now four 4x divided by 2 is 2x so 2x plus 20 is equal to 1. now let's subtract both sides by 20. therefore 2x is 1 minus 20 and so 1 minus 20 is negative 19. now the last thing we need to do is divide both sides by 2. so x is equal to negative 19 divided by 2.