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# More on equivalent fractions

CCSS.Math:

## Video transcript

what I want to do in this video is really digest the idea that if we have some fraction as long as we multiply the numerator and the denominator of the fraction by the same number that we're going to have an equivalent fraction so let's think about that let's say we multiply the denominator here by two so let's say we multiply the denominator here by two I'm claiming that as long as we multiply the numerator by two that we are going to get an equivalent fraction so here the denominator was six so here our denominator will be twelve if our numerator here is four what we've got to multiply by two again multiply our numerator by 2 to get 8 so I'm claiming that eight twelve is the same fraction as four six and to visualize that to visualize that let me redraw let me redraw this whole but instead of having six equal sections we now have 12 equal sections so each of the six we can divide we can turn into two that's essentially what multiplying by two does we now have twice as many equal sections now that we have twice as many equal sections literally one two three four five six seven eight nine ten eleven twelve how many of them are actually shaded in yellow well it's one two three four five six seven eight eight 12 so there's no magic here if each of if if we have twice as many sections we're going to have to shade in twice as many of them in order to have the same fraction of the whole and it goes the other way too this isn't just true with multiplication it's also true that if we divide the numerator and the denominator by the same quantity that we are going to have an equivalent fraction so that's another way of saying well what happens if I were to divide by two so if I were to divide by two so let me divide by two I'm going to have 1/2 half the number of equal of sections or I will only have three equal sections and I'm claiming if I do the same thing in the numerator that this is going to represent the same same fraction so 4 divided by 2 is 2 so I'm claiming that 2/3 is the same fraction as 4 six as the same fraction is 8:12 well let's visualize that so here this is six equal sections but now we're going to have only three equal sections so we can merge we can merge some of these equal sections so we can merge these two right over here and we can merge these two right over here and then we can merge and then we can merge these two right over here so our whole is where it's still the same hole but now we've only we only have three equal sections and two of them are actually shaded in so these are all equivalent fractions so the big takeaway here is start with a fraction if you multiply the same if you multiply the numerator and the denominator by the same quantity you're going to have an equivalent fraction if you divide the numerator and the denominator by the same quantity you are also going to have an equivalent fraction so with that in our brains let's tackle a little bit of an equivalent fractions problem let's think about if someone says okay I have 5 over 25 and I want to write that as some as some value let's call that value T let's call that T over over 100 what would t be well we can see in the denominator to go from 25 to 100 you had to multiply by 4 so if you want an equivalent fraction you have to multiply the numerator by 4 as well so T will need to be equal to 20 so T is equal to 25 over twenty fifths is the same thing is the same thing as 20 as 20 over 100 but what if someone says well 5 over 25 is equivalent is equivalent to the lank let's say question mark over 5 well now what would you do actually let's do it the other way is equal to is equal to 1 over question mark well you could say look to go get our numerator from 5 to 1 we have to divide by 5 we have to divide by five to go from five to one and so similarly we have to divide the denominator by five so if you divide the denominator by five 25 divided by five is going to get you is going to get you five going to get you five so these are all equivalent fractions 1/5 is equivalent to five 25th