Get ready for 5th grade
Sal adds 3/15+7/15. Created by Sal Khan and Monterey Institute for Technology and Education.
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- Does GCD mean greatest common divider. If so than how is it any different from LCM?(2 votes)
- Why do the denominators have to be the same?(2 votes)
- The denominators have to be the same so you can add the numerators together without worrying about the denominators being different sizes, because that affects the value of the fraction.
It's like trying to count the number of pieces you can get out of different cakes. If the cakes are different sizes, it wouldn't be fair because some people would get larger pieces than others. By making cakes that are the same size and then counting the number of pieces, you can be sure that everyone is getting a fair amount of cake.
In order to add fractions correctly, the "cakes" need to be the same size, which is why the denominators (bottom numbers in the fractions you are adding) need to be the same value.(24 votes)
- at0:17, Sal said that if the denominator is the same, you just add the numerator and then the denominator stays the same? I just dont get it. Is it the same on the problems without the same denominators?(3 votes)
- What if your sum goes over the denominator? Say, 7/14 + 9/14. How do you deal with that?(7 votes)
- you still add the numerator together. Like 16/14.But this will become an improper fraction, the actual answer is 1 2/14. A mixed fraction.(2 votes)
- Does GCF mean greatest common factor ?(5 votes)
- Does the GCM equal the LCM when the BCM Is divided by the WCM?(4 votes)
- What would you do if a mixed number had an improper fraction in it?(2 votes)
- he can just say the denominator stays the same and you add the nominator but instead hes making it confusing by reducing everything(3 votes)
- How and why does this work ?(1 vote)
- The top number represents the amount you have, and the bottom number represents the total needed to form a whole item. so if you have 4 slices of pizza on one plate and another 4 slices of pizza on another plate, and 8 slices form a whole pizza, you now know the denominator is 8, because that is the amount you need to make a whole pizza. Now, if you take the numerator (The actual amount) and add it, you aren't changing how many slices you need to make a pizza, but how many you actually have. When you put all slices together on a plate, you have a whole, or 8/8 pizza.(7 votes)
So we're asked to add 3/15 plus 7/15, and then simplify the answer. So just the process when you add fractions is if they already-- well, first of all, if they're not mixed numbers, and neither of these are, and if they have the same denominator. In this example, the denominators are already the same. The denominator is 15. So if you add these two fractions, your sum is going to have the same denominator, 15, and your numerator is just going to be the sum of the numerator, so it's going to be 3 plus 7, or it's going to be equal to 10/15. Now, if we wanted to simplify this, we'd look for the greatest common factor in both the 10 and the 15, and as far as I can tell, 5 is the largest number that goes into both of them. So divide the 10 by 5 and you divide the 15 by 5, and you get-- 10 divided by 5 is 2 and 15 divided by 5 is 3. You get 2/3. Now, to understand why this works, let's draw it out. Let's split something up into 15 sections. So let me split it up into 15 sections. Let me see how well I can do this. Well, actually, even a better way, an easier way might be to draw circles. So let me do the 15 sections. So let me draw. So that is one section right over there. That is one section and then if I copy and paste it, that is a second section, and then a third section, fourth section, and then we have a fifth section. Let me copy and paste this whole thing. So that's five sections right there. Let me copy and then paste that. So that is 10 sections, and then let me do it one more time. So that is 15 sections. So you can imagine this whole thing is like a candy bar or something, and we have now split it up into 15 sections. Now, what is 3/15? Well, it's going to be 3 of the 15 sections. So 3/15 is going to be one, two, three: 3/15. Now, to that, were adding 7 of the 1/15 sections, or 7 of the sections. So we're adding 7 of those to it. So that's one, two, three, four, five, six, seven. And you see now, if you take the orange and the blue, you get one, two, three, four, five, six, seven, eight, nine, ten of the sections, or 10 of the 15 sections. And then to see why this is the same thing as 2/3, you can just split this candy bar into thirds, so each third would have five sections in it. So let's do that. One, two, three, four, five, so that is 1/3 right there. One, two, three, four, five, that is another third right there. And notice, when you do it like this, we have filled out exactly two-- one, two-- of the thirds. This is the third third, but that's not filled in. So 10/15 is the same thing as 2/3.