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Math 7 - Simplifying a Complex Ratio

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Simplifying a Complex Ratio aka a Complex Fraction. A Complex Ratio is a Ratio to a Ratio To Simplify a Complex Ratio, convert the complex ratio into a division expression The division expression will be dividing two fractions Dividing two fractions is to convert the division into multiplication and multiply by the Reciprocal aka the Multiplicative Inverse

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simplifying complex fractions using the ideas that we just had in the other examples prior to this the unit rate anytime or simplifying a fraction or whole goal to say let's make our denominator A1 whatever we have up here that is what it's equal to our unit rate trying to make a unit rates simplify a complex fraction what's maker denominator of 1 but look at this we have a fraction now how does 3/7 b, 1 we could well 3/7 / 3/7 that's the one that works but what you do on the bottom you do to the top 4/15 / 3/7 now let's take a second look at this 3/7 / 3/7 that's a complex fraction of 137 or 3/7 the same thing over the same thing is one so for dividing this complex fraction by a one we're not changing the value we're just changing the way it looks we're changing it to look like over 1 what's look at this right here 3/7 / 3 seconds this one but look at this this is 4/5 / 3/7 but isn't that the same thing with these two are these the ones written in Black for 15 / 3/7 remember we went over this before a fraction line over is another way of saying divide 4/15 divided by 3/7 450 / 3/7 we just went in a circle by making the not the denominator a 1 by dividing by itself we just referred it as a division problem like the last time I said writing a frac fractions another way of writing division so let's look at this right here let's pull this out for $0.15 / 3/7 remember we went over review of this dividing fractions is the same thing as multiplying by the reciprocal so when you're dividing fractions keep the first fraction the same change the division to multiplication and you take the reciprocal of 3/7 the reciprocal of 3/7 is just it flipped upside down 7/3 and how do you multiply directions you just multiply straight across numerator times numerator over denominator times denominator multiply fractions 4 * 7 is 2815 * 345 is there anything we can simplify top and bottom by there is no common factor with the fact that this is our answer 28 / 45 and that's what it is so 28 / 45 28/45 / 1 with anything over just that anything so the answer is 28 / 45 we just simplified our complex fraction we turned to fractions into one simple looking fraction another way of looking at it look at this right here this 3/7 / 3/7 is 1 some people say let's clear this up why do we multiply by the reciprocal what happens when you have this so 3/7 multiply by the reciprocal 3 * 7 is 21 7 * 3 is 2121 / 21 that is a one so in a sense we can substitute in a dividing by a fraction as multiplying by the reciprocal let's look at it this way let's rewrite it I'll put it off to the side right here so we can see let's go 4/15 / 3/7 so knowing right now that we get a 1 by multiplying by the reciprocal or dividing by itself so it's pretty much dividing by the reciprocal is the same thing as dividing by a fraction is the same thing as multiplying by the reciprocal set up instead of dividing by 3/7 to get one how about I multiply by the reciprocal take the fraction flip it over 3/7 * 7/3 doing the bottom you do the top * 7/3 * 7/3 * 7/3 / 7 / 3 that is a one we took this and multiplied it by a factor of 1 made up of 7/3 / 7 / 3 what is this 7 * 321 3 * 72017 * 32121 / 21 that is over and look at this right here for * 72815 * 3 4528 / 45 dividing by a fraction is the same as multiplying by the reciprocal so instead of writing / 7/3 we can write multiply instead of writing / 3/7 * 7/3 * the reciprocal you can substitute it in because they are the same thing to each other they create a 1 I multiply together they're called the multiplicative inverse fractions simplify a complex fraction let's do one more instead of a fraction let's say we have mixed numbers let's go 3 2/5 / 2 + 3 8 this is a complex fraction because we have a fractional component over another fraction with component but because it's a mixed number so first things first let's change our mixed numbers into a an improper fraction how do I do that first let's rewrite the denominator so the denominator is 5 so we don't forget that that is going to be over so what do we have to do we have to convert this mixed number into a fraction one number only up top so how do we do that we take our denominator times are whole number which is 15 and then we added to the numerator cuz there are three whole units which is very much a whole unit is made up of five 5/3 of those that's 15 so that's why 5 * 3 makes 15 and then we have the other one which is not a whole onion got two more so we have 15/5 we got to add it to 2/5 so that's why it's 17 5 * 3 is 15 50 + 217 same thing you down here there are two whole units the units for this one is made up of eight so there are two whole units made up of eight that's 8/8 / 8 that's pretty much sick 2 * 8 * 216 at it with three cuz this is not a home Unit 16 + 319 so don't forget the 819 / 8 we have our two fractions 17/5 to 19/8 but again this right here means divided so we can rewrite this ask 17/5 / 19/8 dividing fractions is the same thing as multiplying by the reciprocal of the reciprocal of 19/8 is 8/19 I can't ejaculations off the top of my head so let's do the work out to the side so we're going to multiply 17 * 8/5 * 19 what do the work off to the side 17 * 8 8 * 7 is 56 carat 5/8 * 28 + 5 is 13 so it is 136 over let's look at this 5 * 19 what's the name of this one that's deep that's that's pretty much break it apart make a little decomposition so five time that's 45 and then 5 x 10 that's 50 where did I get the 10 from so you have think this is 10 + 9 and then 5 * 94055 * 1050 so that's still 19 so we add those together was that 95 so 136 / 9 Define is there a common number we can simplify the backdrop for both of these are simplify this fraction know we can change it to a mixed number if we want what's the short form if it does not ask free to change it to a mixed number leave it but if you want to change it to mixed number to do this division problem let's do long division so stupid work off to the side so it's 136 / 95 how many 90 times are in 136 round 99 is 180 that's two of them this is figure that so that's 18190 that's larger than that so that's only one let subtracting 576 - 5 is a 113 - 941 we're not changing it to a decimal we're changing to a mixed number so you look at the remainder so there's one hole 95 one whole units made out of 95 and we have a remainder 41 but what are the units made up of 95 so that's where the 41 over 95 comes in 1 and 41/95 that is our mixed number as an improper fraction simplifying complex fractions

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Math 7 - Simplifying a Complex Ratio

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