Hey Hey, this is Berwin the lead tutor from
Berleaf Education today we are taking a look at a fraction word problem that can be solved
through the change of numerator method Now, if you are unfamiliar with this method please check out
the video link in the description right below for a detailed explanation Without further ado let's
take a look at the question Sandy had a total of 868 red pens and blue pens after selling an equal number of both types of pants she had one-quarter of the red p
ants and one-fifth of the blue pants
left what was the total number of blue and red pens left Let's start off by identifying the
important information while the problem doesn't explicitly provide the fractions representing each color of pen sold we can however logically infer the equivalence because the information highlighted in red tells us that they are equal. Now, this enables us to apply the
change of numerator method effectively We start off by identifying the equal fractions or we call
it
the equivalent fractions within the problem and that would be the pens that were sold for each of the color Okay, so find the fraction of pen sold we use one hole subtracted by one quarter, which was what was left and we will get 3/4 and as for the blue we will have 1 - 1/5 to give us 4/5 Now, these are the fractions of the
pens sold Now, we have identified the equivalent fractions representing the pens sold for each of the colors and we can now move on to next step which is to get these fr
actions to have common numerators and I call it apply the change of numerator okay, now proceeding with the change of
numerator I will arrange it in this manner Red is to Blue Red pen sold is that of 3/4 and it's equivalent to 4/5 as we have previously found Alright, now to make them the same numerator we have to use this which is 3 x 4 to get a common multiple Here, which is 12 So, this will mean that we have to multiply 4 to each of the numerator and denominator of Red And for blue is 3 to th
e numerator and the denominator So this will give us 12/16 and 12/15 okay Now, at this point is crucial for us to understand all these parts over here what they actually mean So, for the numerators of these fractions, it represents the pens sold for each of these colors that we have previously found which are the red and the blue pens sold Alright, so let me write it down for clarity Units of red pens sold on the other hand, the denominator
actually represents the total units of red pens And of
course for the other one
this fraction over here the numerator means the units of blue pens sold and the denominator means the total number of units of blue pens okay, alright, We know that there were a total of 868 pens and this is represented by the sum of the units found here over here in the denominator okay so the total units we have can actually be found by using 16 + 15 giving us 31 units Now, 31 units represent 868 and therefore 1 unit is actually equals to 868 divided by 31 giving us
28 okay now our next step is to find the
remaining pens to do this we need to determine the number of units that represent the total remaining pens okay So for this, we can actually use the total of each of the pens subtracted by the sold and
that would give us the remaining pens units as follows So, we can find the total units of pens
remaining by using give me a moment, just write it down first We can use 16 -12 which actually means that we are using the total of red pants minus the sold a
nd adding it together with 15 - 12 which is this minus this and that gives us the number of blue pens that were left together, we have seven units in total Since we have previously found 28 so let's find the seven units which are the pens left Simply by using 28 x 7 which gives us 196 pens Awesome all right, et voila And there we go this is how we solve this question And if you have found this helpful please like this video and subscribe to our YouTube channel You can also follow us on our
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ial media Facebook, Instagram and Tik Tok for more Meanwhile keep on practising and I will see you soon to solve the next question Take care
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