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Adding & subtracting rational numbers: 0.79 - 4/3 - 1/2 + 150%

Video transcript

so we have 0.79 minus 4/3 minus 1/2 plus 150% so we have four different numbers written in different formats here it's a decimal here we have two fractions and then here we have a percentage so the easiest thing to do would be to write all of these in the same format and for me the easiest format to do this computation in would be to write them all as fractions and the reason why I wanted that in particular is because four thirds when you divide by three when you divide a one-third two-thirds four thirds you're going to have a repeating decimal so to avoid that I want to put all of these I want to rewrite all of these as fractions so let's do them one at a time so zero point seven nine this is the same thing as seventy nine hundredths so I'll just write it that way so this is the same thing as 79 over 100 then of course we have minus 4/3 minus 4/3 then we have minus 1/2 minus 1/2 and then finally we have we don't want to run out of colors here finally we have 150 percent well 150 percent percent literally means per cent per 100 so this is plus 150 per 100 per hundred so now we've written them all as fractions in order to do all the subtraction addition we have to find a common denominator so what's the comment what's the least common multiple of 100 3 2 and 100 well 100 is 'visible by 2 so 100 is actually the least common multiple of 102 so we really have to just find a least common multiple between 100 and 300 and that's just going to be 300 there's no other common factors between 100 and 3 so let's write write all of them with 300 as the common denominator so let me do this in this reddish color so 79 over 100 is the same thing if I were to write it over 300 to go from 100 to 300 in the denominator I'm multiplying by 3 so after multiply the numerator by 3 as well so I'm going to multiply by 3 as well let's see 80 times 3 would be 240 so it's going to be 3 less than that so 200 and 40 minus 3 is 237 now 4/3 well to get the denominator to be 300 we had to multiply the denominator by 100 so we have to multiply the numerator by 100 as well 1/2 1/2 if our denominator is 300 we multiplied the denominator by 150 to go from 2 to 300 so we have to multiply the numerator by 150 and then finally 150 over 300 oh sorry 150 over 100 well we're multiplying the denominator by 3 to get to 300 to go from 100 to 300 so we have to do the same thing in the numerator so 3 times 150 is 450 so now we have the same denominator and we can now add our numerators so this is going to be equal to this is going to be equal to actually I could just do it right over here on the right hand side this is going to be equal to some stuff over 300 so it's going to be 237 237 - 400 - 400 and - 150 - 150 and this actually should be a plus right over here this should be plus plus 450 plus 450 and so let's see what if we could simplify this a little bit we're subtracting 400 and we're subtracting 150 so these two would be the same thing as subtracting 550 and then we are at we have a positive 237 and we're adding it to a positive 450 or actually maybe another easier way to think about this is negative 550 Plus 450 is going to get us negative 100 and so this simplifies things a good bit now we have 237 minus 100 is going to be 137 so it equals 137 in the numerator over over 300 and this is about as simplified as I can think of making it and so this is our final answer 137 over 300