Fractions
Adding and subtracting fractions with unlike denominators
None
How to add fractions that have different denominators
To solve this problem, we need to find the least common multiple to get at the common denominator. Can you help? We bet you can!
Discussion and questions for this video
 We're asked to add 4/9 and 11/12 and to write our answer
 as a mixed number, and then simplify and write our answer
 as a mixed number.
 So here we have two fractions we're adding together, but we
 have different denominators.
 So whenever you add fractions, the first thing you have to do
 is check the denominators.
 If they're the same, you can add, but if they're different
 like this, you have to make them have the same
 denominator.
 So what we have to do is find a number that both 9 and 12
 will divide into, and that will be our common
 denominator, and you'll see why both 9 and 12 have to
 divide into it.
 So let's think about what that number is, and there's two
 ways of coming up with that what we could call a least
 common multiple, the smallest multiple of both 9
 and 12 that is common.
 One way is just to kind of look at the multiples of 9 and
 see if any of them are divisible by 12.
 So if you start with 9 we can do it over here.
 So you have 9, that's not divisible by 12.
 18 isn't divisible by 12.
 27 isn't divisible by 12.
 36, well, that is divisible by 12.
 That is 12 times 3.
 So 9 goes into 36 and 12 goes into 36.
 So what we want to do is write a common denominator.
 So we're going to write 4/9 as something over 36, and we're
 going to write 11/12 as something over 36.
 Now, to turn your 9 into a 36, you have to
 multiply it by 4, right?
 9 times 4 is equal to 36.
 Now, you can't just multiply the denominator by 4.
 You also have to multiply the numerator by the same thing.
 So if you multiply the numerator by 4, you get 4
 times 4 is 16.
 So 4/9 is the exact same thing as 16/36.
 If you wanted to simplify this one to 4/9, you divide the
 numerator and the denominator by 4.
 Now, we do the same thing over here.
 36, 12 times 3, so we're multiplying 12 by 3 to get 36.
 Well, if we did that to the denominator, we also have to
 do that to the numerator, so 11 times 3 is 33.
 And just like that, we've now rewritten each of the
 fractions so that they have the same denominator.
 Both of their denominators is 36.
 So now we're ready to add.
 If you add these two things, we'll have 36, because we're
 considering kind of parts of 36 or fractions of 36, and
 then we have 16 plus 33 in the numerator.
 Let me write that down.
 16 plus 33 in the numerator.
 And 16 plus 33 is what?
 6 plus 33 would be 39 and then you have
 another 10, so it's 49.
 So it's equal to 49/36.
 Now, can we simplify this?
 49, it's 7 squared, so it has 1, 7 and 49 as factors.
 This has 1 it has a bunch of numbers, but it's not
 divisible by 7, so this is actually in simplest form, but
 this is an improper fraction.
 The numerator is larger than the denominator.
 So let's write it as a proper fraction.
 To do that, we divide 36 into 49.
 36 goes into 49 how many times?
 Well, it only goes one time, so it equals 1.
 And how much will be left over?
 If I divide 36 into 49 one time, or 1 times 36 is 36,
 then I have 13 left over to get to 49.
 So it's 1 and 13/36.
 And you can do that manually, if you like you.
 You'd say 36 into 49.
 36 goes into 49 one time.
 1 times 36 is 36, and then you subtract.
 9 minus 6 is 3.
 4 minus 3 is 1.
 You have a remainder of 13.
 So that's our answer: 1 and 13/36.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

Have something that's not a question about this content? 
This discussion area is not meant for answering homework questions.
why does the denominator have to be the same as the other denominator
It makes the process a lot easier, but you don't have to. Just find the common denominator and multiply, divide, add, or subtract. Using graphs or charts such as the pie chart also helps understand the basic concept of it. Such as 1 3/5 + 1 2/3. A calculator does make this handy if you have one. Just turn it into an improper fraction and add. This process simplifies the complications of this branch of math a lot.
First understand that x/y means "x" parts of a "whole" which is divided into "y" parts..
Now an example:
Suppose a class has 100 students, for a particular task 1/4 students were selected, and other 1/5 students were selected for a 2nd task. Find how many students have been selected from the class in all. [(1/4 + 1/5) * 100] = ?
Solution,
1/4 of the class will be 1/4 * 100 = 25 ; 1/5 of the class will be 1/5 * 100 = 20
25+20 = 45; the answer will be 45 students
But if we directly add both the fractions we get 1/4 + 1/5 = 2/9 ; 2/9 * 100 = 22.22 students; which is not the correct answer.
To solve this problem we need to first find a LCM (Lowest Common Multiple) of the denominators (4 & 5) which is 20.
Now 1/ 4 becomes 5/20 and 1/5 becomes 4/20;
So 1/4 + 1/5 is now = 5/20 + 4/20 = 9/20
9/20 * 100 = "45" the correct number of students.
Thus finding LCM means finding a common number of parts; which also keep the ratio same; 1/4 = 5/ 20 and 1/5 = 4/20.
Hope this helps..
Now an example:
Suppose a class has 100 students, for a particular task 1/4 students were selected, and other 1/5 students were selected for a 2nd task. Find how many students have been selected from the class in all. [(1/4 + 1/5) * 100] = ?
Solution,
1/4 of the class will be 1/4 * 100 = 25 ; 1/5 of the class will be 1/5 * 100 = 20
25+20 = 45; the answer will be 45 students
But if we directly add both the fractions we get 1/4 + 1/5 = 2/9 ; 2/9 * 100 = 22.22 students; which is not the correct answer.
To solve this problem we need to first find a LCM (Lowest Common Multiple) of the denominators (4 & 5) which is 20.
Now 1/ 4 becomes 5/20 and 1/5 becomes 4/20;
So 1/4 + 1/5 is now = 5/20 + 4/20 = 9/20
9/20 * 100 = "45" the correct number of students.
Thus finding LCM means finding a common number of parts; which also keep the ratio same; 1/4 = 5/ 20 and 1/5 = 4/20.
Hope this helps..
i agree it is good explanation
1/3+3/7=7/21+9/21=16/21
well its not because it makes it esear its just that it wont work properly
Because the denominator of a fraction can be thought of as a unit and when adding values they have to have the same unit. You can't add inches and centimeters without converting them to the same unit.
it would not make sense if they did not have a common denominator.
Yes, excactly. I'm a fifth grader, and it makes it a lot easier
"yeah" 23 45245 equals that
yes that makes sense
so that the answer can be found faster and simpeler
It's a similar reason to why you need common units to combine measurements. If I had three cups plus two pints, I couldn't add it together and get five cup+pints. That doesn't even make sense, because "cup+pint" is not a unit of measure.
I would first have to convert them both to cups and get three cups plus 4 cups = 7 cups. (Or I could convert them both to pints and get 1.5 pints + 2 pints = 3.5 pints.)
You can think of the denominator of a fraction as being similar to a unit of measure.
I would first have to convert them both to cups and get three cups plus 4 cups = 7 cups. (Or I could convert them both to pints and get 1.5 pints + 2 pints = 3.5 pints.)
You can think of the denominator of a fraction as being similar to a unit of measure.
Then you couldn't add them
you did your math wrong and I don't know were
i definetly agree it
It is like the law of sameness. If you add apples and bananas, it is not bananapples, it is fruit.
Because if not, then you won't be able to add or subtract properly and you will get a completely different answer. but if you multiply or divide fraction, you won't need the same denominators. just for adding and subtracting. Hope this Helps!! :)
If the denominators are not the same, then your answer will come out wrong.
For example, say you had 5/6 and 3/4. If you just added them with different denominators, it would come out as 8/10. (4/5), but instead it would be 10/12+9/12=19/12, or 1 7/12.
For example, say you had 5/6 and 3/4. If you just added them with different denominators, it would come out as 8/10. (4/5), but instead it would be 10/12+9/12=19/12, or 1 7/12.
You can't add or subtract unlike denominators unless you find a common denominator
no this has to be wrong make amixed number takes time dont rush him/her
It needs to be like that so you can subtract the numerators you cant do that with different denominators.
Why do you need to make the denominators the same
In some cases denominators are equal to make some of the questions easier, like
Example: A person bought 8/10 kgs of sugar and another person bought 2/10 of it. So how much is left in the bag
Answer: Nothing
Example: A person bought 8/10 kgs of sugar and another person bought 2/10 of it. So how much is left in the bag
Answer: Nothing
because say you want to add the 2 numbers the nmbers need to be the same in order to add them witch them means that the numbers need to be the same in order to add them but with subtracting you need to find common numbers that still work in order for you to do the subtracting but if you are multiplying the numbers you still need to find denomiters that will work for both. And for dividing then you need to still need find common denimatiors so then you need to dived the numbers the by the top then the bottom
it`s easer to add
The integers would have different values and the numerator would be incorrect.
Because you have to make it a least common denominator so you can subtract or add the fraction.
20140205T20:08:12Z
by
Anonymous
if the denominators are the same it is going to be the denominator in the answer example
3 4ths+2 4ths is going to be 5 4ths but that is a improper fraction
3 4ths+2 4ths is going to be 5 4ths but that is a improper fraction
If the domeator is in the same you can't add it so you need to find what 3 and the 7 have the same multiplies that means you have to multiply 3 times 7 do with the numerator then 7 times 3 then add with numerator then add the numerators and if it is greater then domerator then divided the numerators altogether then tat is you're answer.
Good question.
In mathematics, the concept of adding and subtracting fractions require the denominator to be common. The numerator does not need to be common but the denominator must be.
If the denominator wasn't common how would we work out the question?
E.g. 1/3 + 3/7 = ?
To work out this question, we would have to find the LCM (Lowest Common Multiple) of the denominators; in this case, 3 and 7. Then when we find that it is 21 we can adjust the numerators to 7 and 9. With that done, we can add 3 and 7 to make 10 over the denominator, which is 21.
This is why the denominators have to be common. There was no equation or formula built in the concept of adding and subtracting fractions that do not require the denominators to be common.
I hope this clears everything up. :) GO EVERYONE WHO ANSWERED THIS!
In mathematics, the concept of adding and subtracting fractions require the denominator to be common. The numerator does not need to be common but the denominator must be.
If the denominator wasn't common how would we work out the question?
E.g. 1/3 + 3/7 = ?
To work out this question, we would have to find the LCM (Lowest Common Multiple) of the denominators; in this case, 3 and 7. Then when we find that it is 21 we can adjust the numerators to 7 and 9. With that done, we can add 3 and 7 to make 10 over the denominator, which is 21.
This is why the denominators have to be common. There was no equation or formula built in the concept of adding and subtracting fractions that do not require the denominators to be common.
I hope this clears everything up. :) GO EVERYONE WHO ANSWERED THIS!
It's much better to have them the same denominator because it's way less complex (which means easier). I don't know if there is a way you can add up fractions with unlike denominators but if there is without all the abracadabra, then I'll let you guys know :) But, like I said, it's way less complex if their the same denominator :D Hope this helped. By the way, that's just the way somebody invented fractions _
why? Okay.
You can add 3/8+5/8=8/8
fairly easily because the denominators are the same.
However, if you did not change the denominators then this is what it would be like:
2/8+3/5=?
You cant do it because the denominators are not equal. You can't add 2+3=5
and 8+5=13 and get 5/13. They aren't equal fractions and you don't add denominators.
You can add 3/8+5/8=8/8
fairly easily because the denominators are the same.
However, if you did not change the denominators then this is what it would be like:
2/8+3/5=?
You cant do it because the denominators are not equal. You can't add 2+3=5
and 8+5=13 and get 5/13. They aren't equal fractions and you don't add denominators.
There arae denominator
You cannot add the denominators and when you get the answer you cannot chose a denominator
because it needs a common denominator or the answer will be wrong
i listen the video carefully . the answer is in video
it has to be the same because then we need same denominators for adding fractions with an unlike denominator.
The denominator has to be the same so you can add evenly and so you get the right answer. Hoped it helped
if you add the fractions with unlike denominators it will not be the same as if you change them!
The denomentar has to be the same because if you want to add , you have to have the same equal sized pieces.
the common factor would me 70 because if you don't find a common factor like the video said its 70
This is a very necessary thing to learn....now I am not as smart as the guy on the videos, but
it is easy to add them when they are alike! It makes it way way way easier! :)
it is easy to add them when they are alike! It makes it way way way easier! :)
I think it's in 0:19
Because to add them they need to have like denominators so you cant just subtract the numerator
It would be like going to the store and saying I want 2/grapes plus 2/apples. They cant bring you out 4/apples or 4/grapes and say that they have satisfied your order. Same thing with fractions with differing denominators. Nor could they say that grape flavored/apples is the same thing as an apple flavored/grapes. They have totally different tastes and sizes depending on what is on the top/bottom ;)
So that you can get the wright number
Imagine we'v got 2 identical apples: apple A and apple B (The denominator is the total number of pieces in each case and the numerator is the number of pieces out of the whole we are working with in each case) :
1.We cut apple A into 2 pieces of the same size and we cut apple B into 8 pieces of the same size.
2. You will agree with me that the one piece of apple A will be larger in size than one piece of apple B.
3. If we represent one piece of apple A in terms of fraction, we'll get 1/2. (Meaning 1 piece of apple out of the 2 pieces. The denominator represents the total no. of pieces)
If we represent one piece of apple B in terms of fraction, we'll get 1/8. (Same logic. Remember we cut apple B in 8 pieces)
4. Since one piece of apple A is not of the same size as one piece of apple B, we cannot add them and get a number directly. We cannot say 1/2 + 1/8= 2/10. (meaning we cannot say that a piece of an apple divided by 2 and another of an apple divided by 8 when added will give us 2 identical pieces out of 10 identical ones. Remember the denominator represents the number of pieces)
5. To get a number, we need to get the pieces of apple A of the same size as those of apple B. For that, we'll need to reduce apple A to 8 pieces too. Only then can we get identical pieces everywhere and thus add effectively.
6. To reduce apiece of apple A to the same size as one of apple B, we need to divide 1/2 by 1/8. This will give us 4. Each of the 2 pieces of apples in apple A will be cut into 4, thus getting 8 identical pieces. One piece of apple A will therefore represent one eighth of the whole apple.
7. With both apple A and apple B being divided into 8 pieces of the same size, calculations can be effectively carried out. We can easily add 1 piece of apple A with one piece of apple B. We can say 1/8 (of apple A) + 1/8 (of apple B)= 2/8 (meaning 2 identical pieces of apples out of 8 identical ones)
1.We cut apple A into 2 pieces of the same size and we cut apple B into 8 pieces of the same size.
2. You will agree with me that the one piece of apple A will be larger in size than one piece of apple B.
3. If we represent one piece of apple A in terms of fraction, we'll get 1/2. (Meaning 1 piece of apple out of the 2 pieces. The denominator represents the total no. of pieces)
If we represent one piece of apple B in terms of fraction, we'll get 1/8. (Same logic. Remember we cut apple B in 8 pieces)
4. Since one piece of apple A is not of the same size as one piece of apple B, we cannot add them and get a number directly. We cannot say 1/2 + 1/8= 2/10. (meaning we cannot say that a piece of an apple divided by 2 and another of an apple divided by 8 when added will give us 2 identical pieces out of 10 identical ones. Remember the denominator represents the number of pieces)
5. To get a number, we need to get the pieces of apple A of the same size as those of apple B. For that, we'll need to reduce apple A to 8 pieces too. Only then can we get identical pieces everywhere and thus add effectively.
6. To reduce apiece of apple A to the same size as one of apple B, we need to divide 1/2 by 1/8. This will give us 4. Each of the 2 pieces of apples in apple A will be cut into 4, thus getting 8 identical pieces. One piece of apple A will therefore represent one eighth of the whole apple.
7. With both apple A and apple B being divided into 8 pieces of the same size, calculations can be effectively carried out. We can easily add 1 piece of apple A with one piece of apple B. We can say 1/8 (of apple A) + 1/8 (of apple B)= 2/8 (meaning 2 identical pieces of apples out of 8 identical ones)
Or you can think of it in an easy way. Let's say the denominators are very special. Each one is unique. Let's say the denominator 4 is an orange, and the denominator 8 is an apple. You can't add apples and oranges because their values are different in the market. 4 oranges may be $5, but 4 apples could be $6.50.
it is this way so it will be easy
They have to be the same becuase to add or subtact them they have to be equivalent
you can only add fractions with same denomenator
Good help now to make another math problem adding multiple fractions eg)1/2 + 3/5 + 4/7= Actually Mom knows the method but the 15 year old can't figure out w/ a lot of examples from a good book. However KHAN makes an excellent teaching explanation!!!
watch the video stupid
so you can divide
at 2:33 what did he that you have to do mr.
so that you can add it evenly
61 it is don't say it's wrong just think about it how about 11x11=4
22x22=16
Now 33x33=?
22x22=16
Now 33x33=?
It makes it easier to add the fractions.
because you can't add apples and oranges!
we cannot add the denominator,,,,, so we shall have the denominators same
because if you dont then you are not ready to add them. They need to be the same unlike when you are multiplying fractions
What does it mean to simplify the problem?
Simplifying a fraction just means putting it into the simplest form. For example, 3/6 can be simplified to just 1/2. They are the same thing, but 1/2 is simplified.
To simplify means to reduce the fraction. Like for example, simplify: 4/8.
So you simplify 4/8 to 1/2.
So you simplify 4/8 to 1/2.
Simplifying is just making the fraction smaller
ok when he says to simplify he means that u need to make the fraction into its lowest terms lets say u have 10/20 it becomes 5/10 then it becomes 1/2 it just means to make it small like break it up and to do so u need to make a factor rainbow i believe
Bingo your right k?
You just divide the numerator (top number) and the denominator (bottom number) by the same umber until you can divide no more. Remember you can not have decimals.
It works like this. And I'll use a fraction OTHER than 1/2.
If you have a fraction like 40/120 in a problem on Khan Academy, it won't accept it as an answer. It has to be in simplest form, simply because it's easier to grade for teachers, the website, and you. It simplifies to 1/3 because you can break it down.
If you have a fraction like 40/120 in a problem on Khan Academy, it won't accept it as an answer. It has to be in simplest form, simply because it's easier to grade for teachers, the website, and you. It simplifies to 1/3 because you can break it down.
Simplifying is to take, say 2/4, and to make it into its simplest form which in this case, would be 1/2
well its like 50/100 is half is written like 1/2 and 100 divided by 50=2
50 divided by 50=1
so the numerator is 1 and the demonator is 2 (1/2(half))
50 divided by 50=1
so the numerator is 1 and the demonator is 2 (1/2(half))
When you simplify you have to make the fraction into the lowest possible fraction. If you have 4/12 you can simplify it. You can divide them both by two. So that would make the fraction now 2/6. You can simplify it lower by dividing it by two again to 1/3. If the fraction is 5/8 you can't divide it any lower because 5 is a prime number. A prime number can only be 1 and itself. Like five. You can't divide it any lower.
Are you Lauren Davidson ?
It means to make the problem simpler.
Or fraction simpler.
For example if you have 6/8,
6 out of 8 simplifies to 3/4.
Because 6=2*3
8=2*4
The 2s cancel out to be just 1.
So there is just 3/4 left.
Hope this helps:)
Or fraction simpler.
For example if you have 6/8,
6 out of 8 simplifies to 3/4.
Because 6=2*3
8=2*4
The 2s cancel out to be just 1.
So there is just 3/4 left.
Hope this helps:)
You have to find the greatest common factor of the numerator and the denominator of the fraction you are simplifying (GCF). Like in the example 4/8 = 1/2, I listed the factors of four and eight. Four: 1,2,4 and eight: 1,2,4,8. Then I listed the common factors. Those are the factors that both numbers have. In this case, 1,2, and 4. Then I select the largest one(4), so as to make the fraction in simplest form. Then I divide both the numerator and the denominator of the original fraction; 4/4=1, 8/4=2. And there you have the fraction in simplest form; 4/8=1/2.For more info see http://www.mathisfun.com/simplifyingfractions.html
Hope this helped,
Tesla
Hope this helped,
Tesla
One reason is the simplicity principle, keep it simple.
So isn't 1/2 easier to remember and deal with that 108/216 ?
So isn't 1/2 easier to remember and deal with that 108/216 ?
Ex. 4/8 can be simplified into 1/2
4 and 8 can be divided by 4
4 divided by 4 = 1
8 divided by 4 = 2
= 1/2
Remember to divide both the numerator and the denominator by the same number :)
4 and 8 can be divided by 4
4 divided by 4 = 1
8 divided by 4 = 2
= 1/2
Remember to divide both the numerator and the denominator by the same number :)
simplifying is just means to make the problum easier like you divide the nuemerator and denomenatr by the same number.hope it any body who does not know what it means.
thanks but can u tell me how it works
to simplify a number u have to either divide it by 2,4 etc..It depends on wat both numbers can divide by!For instance 12/24? to simplify it u make the 12 a 6 and the 24 a 12
it makes it easy. make simple
simplifying a fraction means to make it smaller or less value so it is easier to work with
Well if you wanted to simplify 3/6 you would see that 3 is half of 6 so simplify it to 1/2 which is one half
It means that you make the answer as small as possible. You reduce the answer to the lowest term.
Just what Isaac said. It also means that you need to make it into the smallest fraction as possible. For example, 4/8 would be simplified into 2/4 which would then, make it into 1/2. Then you're done
Simplifying means that you put a number that can be multiplied evenly to get the simplest answer.
You divide the numerator and the denominator by the same number. If the numerator or the denominator don't share any common factors, you're done. If not, divide them both by another (or the same) number until you run out of factors. Just remember that both of the numbers have to stay as whole numbers.
when im adding uncommon fractions, i keep getting it wrong. what im saying is i dont understand. please tell me the steps.
Well, let's do 17/10 + 3/2.
The first step is to find the least common multiples of the denominators ( 10 and 2).
The LCM of 10 and 2 is 10.
You have to multiply 10 1 time to get 10 so you also multiply the numerator by 1. The left side becomes 17*1/10*1
You have to multiply 2 5 times to get 10 so you also multiply the numerator by 5. The right side becomes 3*5/2*5
Your expression is now 17*1/10*1 + 3*5/2*5. 17*1=17. 10*1=10. The left side is now 17/10. 3*5=15 and 2*5=10. The right side is now 15/10.
Your final equation becomes 17/10 + 15/10. Now you add the numerators. 17 + 15 = 32. Your answer is now 32/10.
Now, you simplify. 32/2=16 and 10/2=5. Your final improper answer is 16/5.
The reason it may say you got the question wrong is because you have to convert to a mixed number. 16 goes into 5 3 times. 5*3=15. 16  15 = 1.
Your final mixed answer is 3 1/5.
I hope this was not too confusing :)
The first step is to find the least common multiples of the denominators ( 10 and 2).
The LCM of 10 and 2 is 10.
You have to multiply 10 1 time to get 10 so you also multiply the numerator by 1. The left side becomes 17*1/10*1
You have to multiply 2 5 times to get 10 so you also multiply the numerator by 5. The right side becomes 3*5/2*5
Your expression is now 17*1/10*1 + 3*5/2*5. 17*1=17. 10*1=10. The left side is now 17/10. 3*5=15 and 2*5=10. The right side is now 15/10.
Your final equation becomes 17/10 + 15/10. Now you add the numerators. 17 + 15 = 32. Your answer is now 32/10.
Now, you simplify. 32/2=16 and 10/2=5. Your final improper answer is 16/5.
The reason it may say you got the question wrong is because you have to convert to a mixed number. 16 goes into 5 3 times. 5*3=15. 16  15 = 1.
Your final mixed answer is 3 1/5.
I hope this was not too confusing :)
1/2+3/4=? lets try that. well the denominator needs to be the same so we have to find a common mutiple of 2 and 4. they both go into 4. so, 1/2 becomes 1/4. but, since 2x2=4,we have to mutiply 1 by to also. so, we end up with 2/4. 3/4 stays the same because we are using 4 as the denominator. 4x1=4, and 3x1=3. so, we end up with 2/4+3/4=? well, you only add the numorators, so that would be 5/4. but, the numorator is larger than the denominator. so, you look at the denominator,which is 4, and subtract the numorator,which is 5. so, the final answer is 1 1/4. hope this helps. if not, please comment me about it.
shut the hell up
17/10+3/2=17/10+15/10=32/10=3 2/10=3 1/5
help adding and subtracting
Well it has to equal 1.So say 2/4 and 4/6 jbj;sgkdxf
Why do the denominators have to be the same?
You do not have to make them the same but it makes it far easier to do.
Because the denominator of a fraction can be thought of as a unit and when adding values they have to have the same unit. You can't add inches and centimeters without converting them to the same unit.
The denominators "denote" what the fraction is counting by (who many is in a whole). This is how we know what portion of a group is selected. For example: I have 10 marbles and 5 of them are blue. What fraction of marbles are blue? 5/10. The denominator being the total number in the group and the numerator being how many.
Now if I were asking to add the number of blue marbles to the number of marbles that you don't know the color of, you would say 5/10 + 5/10 = 10/10 or 1.
This being true we can see that we are adding numerators of the same grouping.
IF this were not true, i.e. adding numerators without like denominators we would get an answer that didn't make sense.
ex. 1/10 + 2/100= ? if you said 3/100. Let's think of money with this example. It would be the same as saying 1 dime plus 2 pennies equals 3 pennies and we know that's incorrect. Therefore, we have to trade the dimes in for pennies giving us 10/100 + 2/100= 12/100. Which makes sense because we know that 1 dime can trade in for 10 pennies and 10 pennies + 2 pennies would equal 12 pennies. I hope this helps.
Now if I were asking to add the number of blue marbles to the number of marbles that you don't know the color of, you would say 5/10 + 5/10 = 10/10 or 1.
This being true we can see that we are adding numerators of the same grouping.
IF this were not true, i.e. adding numerators without like denominators we would get an answer that didn't make sense.
ex. 1/10 + 2/100= ? if you said 3/100. Let's think of money with this example. It would be the same as saying 1 dime plus 2 pennies equals 3 pennies and we know that's incorrect. Therefore, we have to trade the dimes in for pennies giving us 10/100 + 2/100= 12/100. Which makes sense because we know that 1 dime can trade in for 10 pennies and 10 pennies + 2 pennies would equal 12 pennies. I hope this helps.
a fraction with the same denominator makes adding or subtracting the fraction A LOT easier!!It also takes less time to figure out the answer while on the other had different denominators can take time to answer cuz in different denominators u usually have to find the LCD
Because if you add them it messes up the question
They have to be the same because if you imagine it just drawn in your head then that would not make sence! LIke, for ex:3/5+8/11. Then really if you do it that way then the awenser would be 11/14.
so that you can subtract or add them together
if you do not make the denominators the same.... it will be hard to do.
if you make them the same...it will be eaiser
if you make them the same...it will be eaiser
because it wont make scene.
Speeds up the process.
how is he correct?
they make the adding process much easier. and drawing pie charts also helps to grasp the concept.
0:00 to 4:05 he is correct!
yeah id do it because its easyer
Imagine we'v got 2 identical apples: apple A and apple B (The denominator is the total number of pieces in each case and the numerator is the number of pieces out of the whole we are working with in each case) :
1.We cut apple A into 2 pieces of the same size and we cut apple B into 8 pieces of the same size.
2. You will agree with me that the one piece of apple A will be larger in size than one piece of apple B.
3. If we represent one piece of apple A in terms of fraction, we'll get 1/2. (Meaning 1 piece of apple out of the 2 pieces. The denominator represents the total no. of pieces)
If we represent one piece of apple B in terms of fraction, we'll get 1/8. (Same logic. Remember we cut apple B in 8 pieces)
4. Since one piece of apple A is not of the same size as one piece of apple B, we cannot add them and get a number directly. We cannot say 1/2 + 1/8= 2/10. (meaning we cannot say that a piece of an apple divided by 2 and another of an apple divided by 8 when added will give us 2 identical pieces out of 10 identical ones. Remember the denominator represents the number of pieces)
5. To get a number, we need to get the pieces of apple A of the same size as those of apple B. For that, we'll need to reduce apple A to 8 pieces too. Only then can we get identical pieces everywhere and thus add effectively.
6. To reduce apiece of apple A to the same size as one of apple B, we need to divide 1/2 by 1/8. This will give us 4. Each of the 2 pieces of apples in apple A will be cut into 4, thus getting 8 identical pieces. One piece of apple A will therefore represent one eighth of the whole apple.
7. With both apple A and apple B being divided into 8 pieces of the same size, calculations can be effectively carried out. We can easily add 1 piece of apple A with one piece of apple B. We can say 1/8 (of apple A) + 1/8 (of apple B)= 2/8 (meaning 2 identical pieces of apples out of 8 identical ones)
1.We cut apple A into 2 pieces of the same size and we cut apple B into 8 pieces of the same size.
2. You will agree with me that the one piece of apple A will be larger in size than one piece of apple B.
3. If we represent one piece of apple A in terms of fraction, we'll get 1/2. (Meaning 1 piece of apple out of the 2 pieces. The denominator represents the total no. of pieces)
If we represent one piece of apple B in terms of fraction, we'll get 1/8. (Same logic. Remember we cut apple B in 8 pieces)
4. Since one piece of apple A is not of the same size as one piece of apple B, we cannot add them and get a number directly. We cannot say 1/2 + 1/8= 2/10. (meaning we cannot say that a piece of an apple divided by 2 and another of an apple divided by 8 when added will give us 2 identical pieces out of 10 identical ones. Remember the denominator represents the number of pieces)
5. To get a number, we need to get the pieces of apple A of the same size as those of apple B. For that, we'll need to reduce apple A to 8 pieces too. Only then can we get identical pieces everywhere and thus add effectively.
6. To reduce apiece of apple A to the same size as one of apple B, we need to divide 1/2 by 1/8. This will give us 4. Each of the 2 pieces of apples in apple A will be cut into 4, thus getting 8 identical pieces. One piece of apple A will therefore represent one eighth of the whole apple.
7. With both apple A and apple B being divided into 8 pieces of the same size, calculations can be effectively carried out. We can easily add 1 piece of apple A with one piece of apple B. We can say 1/8 (of apple A) + 1/8 (of apple B)= 2/8 (meaning 2 identical pieces of apples out of 8 identical ones)
shut the hell up
if they arent the same you cant add or subtract
Because when you add or subtract you only add or subtract the numerator, and not the denominator. If you have a different denominator for each fraction, say you had 3/4 + 18,
you can, not, add the denominator AND numerator, because if you do, you get 6/12, which is the wrong answer and if that was the way we added fractions it would be way too easy.
So you need to find the common denominator, by listing the two denominators for each fraction:
4:
8:
then writing out the multiples,
4: 4, 8,
8: 8,
then once you find a common multiple, that common multiple becomes the denominator:
3/8 + 1/8
And since you changed the denominator for one of the fractions, you change the numerator for that fraction, according to the difference for what that fraction's denominator used to be, to what it now is:
3/4 > 3/8
4 x 2= 8
So then you do that change to the numerator to even it out:
In 3/4, the numerator is= 3
So you do 3 x 2, which equals 6, so your new fraction and numerator is 6/8.
Now you have 6/8+1/8, and since you ONLY add the numerator, you get 7/8 for your answer.
you can, not, add the denominator AND numerator, because if you do, you get 6/12, which is the wrong answer and if that was the way we added fractions it would be way too easy.
So you need to find the common denominator, by listing the two denominators for each fraction:
4:
8:
then writing out the multiples,
4: 4, 8,
8: 8,
then once you find a common multiple, that common multiple becomes the denominator:
3/8 + 1/8
And since you changed the denominator for one of the fractions, you change the numerator for that fraction, according to the difference for what that fraction's denominator used to be, to what it now is:
3/4 > 3/8
4 x 2= 8
So then you do that change to the numerator to even it out:
In 3/4, the numerator is= 3
So you do 3 x 2, which equals 6, so your new fraction and numerator is 6/8.
Now you have 6/8+1/8, and since you ONLY add the numerator, you get 7/8 for your answer.
I don't know why I think it's easier
they have to be the same or else you are doing the problem incorrectly. and if you do it incorcorrectly you get an F
they have to be the same or else you can't do it correctly ok patterson?
still not sure have problem 12/18 + 5/6 = Not sure of answer 1 9/18
You're correct! Just make sure to reduce 9/18 to 1/2, so your final answer is 1 1/2.
Thanks for your help now i understand. :)
shut the hell up
Why did he say to turn the nine in to a 36 and why multiply by 4 what.]
nine times four is thirty six but why cant the nine just be nine. I'm confused ):
and why do we have to multiply the numerator by 4 too.~_~
nine times four is thirty six but why cant the nine just be nine. I'm confused ):
and why do we have to multiply the numerator by 4 too.~_~
to add fractions, you need to have the denominator the same. these two fractions have denominators of 9 and 12. The lowest common multiple of these two numbers is 36. That requires multiplying by x4 and x3 respectively. We multiply the numerator and denominator by the same number so the number does not change.
4/9 * 4/4 = 16/36. 4/4 is the same as 1, so the number doesn't change
4/9 * 4/4 = 16/36. 4/4 is the same as 1, so the number doesn't change
at first i felt like you so i know what you mean. If you are multiplying with unlike denominators then you need to multiply the denominators by each other so that they are the same. Then you have to multiply the numerator by the other denominator as to make the number not change. If you didn't , it would be a totally different fraction!
shut the hell up
the reason why is because in order for the fractions to add ,the denominator has to be the same as the other and so that is why the numerator has to change because the denominator is increasing and so it only makes sense that the numerator increase to
well, you can't really add two uncommon fractions if they don't have a common denominator. And also 12 isn't a multiple of 9! but, they're both multiples of 36 so that's their common denominator!
Why do you have to get the common denominator, can't you just add?
No. If the denominators are unlike you are comparing two completely different things. Think of fractions like pizza. The total number of slices is the denominator. What happens when you increase the total number of slices while keeping the pizza the same size? The slices get smaller. A pizza with 4 slices will have smaller slices than a pizza with just 3 slices. So if you don't keep the denominator (or number of slices) the same your definition of what constitutes a slice (or fraction) changes and your answer no longer makes sense. It maybe easier to comprehend if you see it visualized, checkout http://mathmistakes.info/facts/AlgebraFacts/learn/fr/add.html
You can only add like terms. When you make the denominator and numerator same, the 2 terms are alike. If you know algebra, you must know that you can't add 2 and x unless x has a defined value.
Well, you can but it will become very hard to add something like 5/8+3/16 it's hard right? But with 1/3+2/3, it's one, easy right!
No because if you add you answer would be way off.
shut the hell up
The more slices you have, each slice becomes smaller.
What about this but for subtracting where is that?
If you understand about adding the fractions together, and changing the denominators, see the video on subtracting fractions. (http://www.khanacademy.org/math/arithmetic/fractions/v/subtractingfractions). There isn't one specifically on subtracting fractions with unlike denominators.
You have to do the same thing, for instance, take 1/3  4/5.
First, list the multiples.
3= 3, 6, 9, 12, 15, 18, 21, 24
5= 5, 10, 15, 20, 25, 30, 35
The least common multiple is 15. So the problem would become ?/15  ?/15. Since 3 times 5= 15, you have to multiply 1 by 5, which = 5. The problem becomes 5/15  ?/15. Since we also multiplied 5 times 3= 15, we have to do that to 4. 4 times 3= 12.
The problem becomes 5/15  12/15.
Because the answer is going to come out negative, here is a trick.
Subtract 12  5. (answer is 7)
Stick a negative sign in (7) and your answer is  7/15.
Hope I Helped! ;D
First, list the multiples.
3= 3, 6, 9, 12, 15, 18, 21, 24
5= 5, 10, 15, 20, 25, 30, 35
The least common multiple is 15. So the problem would become ?/15  ?/15. Since 3 times 5= 15, you have to multiply 1 by 5, which = 5. The problem becomes 5/15  ?/15. Since we also multiplied 5 times 3= 15, we have to do that to 4. 4 times 3= 12.
The problem becomes 5/15  12/15.
Because the answer is going to come out negative, here is a trick.
Subtract 12  5. (answer is 7)
Stick a negative sign in (7) and your answer is  7/15.
Hope I Helped! ;D
yeah, there isn't one for subtracting one with unlike denominators, cuz you do the same thing, but subract . . .
why do we use the same denominators, when we are doing the adding when we have a different denominators.
Hi there, I will show an example because this is better than explaining. If I explained it to you would be lost. So an easier way is easier to understand.
Mr. McFattenMeUp has 4/8 of a chocolate cake in his refrigerator. Later his friend Mr. MeFillMyTummy gave him 3/4 of a vanilla cake. How many cakes does Mr. McFattenMeUp has all together?
(0)(0)(0)(0)( )( )( )( ) 4/8
( 0 )( 0 )( 0 )( ) 3/4
I got this diagram ready. now if I were to add them both without converting them you would get 7/12 and the answer would look like this
[][][][][][][]00000 7/12
And this would be false since if you combine my previous diagram you would get this
[(0)(0)(0)(0)( 0 )( 0 )] ( 0 ) 1 and 1/4
The reason why we change the denominator is because the pieces of chocolate and vanilla cake have different size. So to get the correct answer, we change the denominator to make the pieces of chocolate and vanilla cake have same size. I showed you the answer but lets do the math anyways.
(0)(0)(0)(0)( )( )( )( ) + ( 0 )( 0 )( 0 )( )
4/8 3/4
( 0 )( 0 )( 0 )( ) > (0)(0)(0)(0)(0)(0)( )( )
3/4 times 2 on both sides is 6/8 and 2 x 4 is 8 so the slice changes from ( 0 ) to (0)
So...
(0)(0)(0)(0)( )( )( )( ) + (0)(0)(0)(0)(0)(0)( )( )
4/8 6/8
And we add them up which we get:
[(0)(0)(0)(0)(0)(0)(0)(0)] (0)(0) 10/8 which is 1 2/8
Now we must simplify them.
2/8 factor> (2)/(2 x 2 x 2)
We can cross off one 2 since it exists in both numerator and denominators and we get.
(2)/(2 x 2 x 2) > 1/(2 x 2) > 1 and 1/4 (I took out 1 temporary because adding it to the fraction while I was simplifying might have confused you)
So Mr. McFattenMeup has 1 and 1/4 of cakes altogether
Hope this helped and your curiosity has rewarded you with a +1 vote :D
P.S Would your Hopper care to cuddle with my Hopper?
Mr. McFattenMeUp has 4/8 of a chocolate cake in his refrigerator. Later his friend Mr. MeFillMyTummy gave him 3/4 of a vanilla cake. How many cakes does Mr. McFattenMeUp has all together?
(0)(0)(0)(0)( )( )( )( ) 4/8
( 0 )( 0 )( 0 )( ) 3/4
I got this diagram ready. now if I were to add them both without converting them you would get 7/12 and the answer would look like this
[][][][][][][]00000 7/12
And this would be false since if you combine my previous diagram you would get this
[(0)(0)(0)(0)( 0 )( 0 )] ( 0 ) 1 and 1/4
The reason why we change the denominator is because the pieces of chocolate and vanilla cake have different size. So to get the correct answer, we change the denominator to make the pieces of chocolate and vanilla cake have same size. I showed you the answer but lets do the math anyways.
(0)(0)(0)(0)( )( )( )( ) + ( 0 )( 0 )( 0 )( )
4/8 3/4
( 0 )( 0 )( 0 )( ) > (0)(0)(0)(0)(0)(0)( )( )
3/4 times 2 on both sides is 6/8 and 2 x 4 is 8 so the slice changes from ( 0 ) to (0)
So...
(0)(0)(0)(0)( )( )( )( ) + (0)(0)(0)(0)(0)(0)( )( )
4/8 6/8
And we add them up which we get:
[(0)(0)(0)(0)(0)(0)(0)(0)] (0)(0) 10/8 which is 1 2/8
Now we must simplify them.
2/8 factor> (2)/(2 x 2 x 2)
We can cross off one 2 since it exists in both numerator and denominators and we get.
(2)/(2 x 2 x 2) > 1/(2 x 2) > 1 and 1/4 (I took out 1 temporary because adding it to the fraction while I was simplifying might have confused you)
So Mr. McFattenMeup has 1 and 1/4 of cakes altogether
Hope this helped and your curiosity has rewarded you with a +1 vote :D
P.S Would your Hopper care to cuddle with my Hopper?
I want you to name my children
Why can't you just add the numbers
Here are some practice problems.
9/10 times 3/10
5/15 time 17/45
9/10 times 3/10
5/15 time 17/45
Not sure if you want me to solve them but I welcome your question.
9/10 x 3/10 = 27/100
5/15 x 17/45 = 85/675 factor>
(5 x 17)/(5 x 5 x 3 x 3 x 3) cross off>
17/(5 x 3 x 3 x 3)
17/135
You should have posted this on multiplying fraction but that's alright. I appreciated your problems and will give you +1 vote.
9/10 x 3/10 = 27/100
5/15 x 17/45 = 85/675 factor>
(5 x 17)/(5 x 5 x 3 x 3 x 3) cross off>
17/(5 x 3 x 3 x 3)
17/135
You should have posted this on multiplying fraction but that's alright. I appreciated your problems and will give you +1 vote.
thats confusing
at the end do you have to divide the numbers
Hi there, no you do not have to divide the number because 1 and 13/36 cannot be divided any further. However if the answer was 1 and 12/36, it would be divisible.
12/36 (2 x 2 x 3)/(2 x 2 x 3 x 3)
I factored them
Now I cross off the numbers that exist in both numerator and the denominator.
(2 x 2 x 3)/(2 x 2 x 3 x 3) > 1/3 since there are 2 of 2 and 1 of 3 that exist in both sides. I placed 1 in the numerator on the top because all of the number in there has been crossed off. So the answer is 1 and 1/3
But in the problem that Sal gave us, 1 and 13/36 cannot be divisible any further.
Hope this helped and +1 vote for your curiosity :D
12/36 (2 x 2 x 3)/(2 x 2 x 3 x 3)
I factored them
Now I cross off the numbers that exist in both numerator and the denominator.
(2 x 2 x 3)/(2 x 2 x 3 x 3) > 1/3 since there are 2 of 2 and 1 of 3 that exist in both sides. I placed 1 in the numerator on the top because all of the number in there has been crossed off. So the answer is 1 and 1/3
But in the problem that Sal gave us, 1 and 13/36 cannot be divisible any further.
Hope this helped and +1 vote for your curiosity :D
I don't get this it is hard can anybody help me?
it is quite simple if you ask me all you have do is this Whenever you add fractions with unlike denominators, you must make the denominators of the same value. In this example, the easiest approach is to multiply 8 x 3 to get 24. Here, you multiply by 3 to get . Then you multiply the second equation by 8 to get . Note that both addends have 24 as a denominator. Add in the same manner as with the unit Adding fractions with like denominators.
For adding fractions with unlike denominators, you would need to change the numbers below the bar (denominators) by finding the least common factor/multiple.
Example:
3/4 + 3/16
Convert 3/4 to sixteenths.
4 (4) is 16
3 (4) is 12
Both numerators have to be multiplied by the same numbers.
12/16 + 3/16 = 15/16
Hope this helps!
Example:
3/4 + 3/16
Convert 3/4 to sixteenths.
4 (4) is 16
3 (4) is 12
Both numerators have to be multiplied by the same numbers.
12/16 + 3/16 = 15/16
Hope this helps!
you have to multiply 8 to get 24.
Don't worry I learned this in class. The way I do it is stacking the two fractions then putting equal signs and fraction bars. Multiply the two denominators and that is your Least Common Factor. Then you add the numerators and then BOOM! Awnser is there. Only simplify if directed in math book. JUST evaluate if simplifying not needed.
I don't get your question that you asking me women please be specific but I don't give up so im going to give you the awnser any way............................................... m2;00 so yes
does it take away energy pints to vote
No. Voting is encouraged; in fact, there are badges for it.
no it doesn't khan academy gives you points for everything that you do for then so voting os very okay
Can we do another step like this:
3/8+5/9=(3*9)+(5*8)/72=27+40/72=67/72
3/8+5/9=(3*9)+(5*8)/72=27+40/72=67/72
Yes, that method works perfectly.
why does the denominater have to be greater than the top number?
Excellent question my friend. If you had two fractions like 6/5 and 7/5 you would get 13/5. That is what you would call a improper fraction. In arithmetic you wouldn't leave it like that because it's considered a improper fraction. You would need to change it into a mixed number. When you get to algebra 1 they will allow you to leave it as a improper fraction as an answer to a problem.
It's called a improper fraction and there's only 1 strategies to do the problem divide it and get your answer.
add the 7 and the 6 the answer to that will be 13 so divided the 13 and the 5 and that will be the answer.
the denominator must be bigger because the numerator has to go into the denominator.
It doesn't have to but if you are in 5th grade, you haven't learned about that yet. If it is smaller, it is a proper fraction. If the numerator is larger than the denominator, that just means it is an improper fraction and it hasn't yet been reduced into whole numbers.
How do You do tris
The formula is (HOCH^2)^3 CNH^2 , but this is math not chemistry.
3/4 + 1/2=answer in simplest terms
In order to add fractions, the denominators must be the same.
The lowest common denominator or multiple (LCD or LCM) is 4.
Whatever we multiply the denominator by, we must multiply the numerator by.
Therefore, 1/2 = 2/4.
So, 3/4 + 2/4 = 5/4 as an improper fraction or as 1 1/4 as a mixed number.
The lowest common denominator or multiple (LCD or LCM) is 4.
Whatever we multiply the denominator by, we must multiply the numerator by.
Therefore, 1/2 = 2/4.
So, 3/4 + 2/4 = 5/4 as an improper fraction or as 1 1/4 as a mixed number.
The answer is:
1 2/4 or 1 1/2
1 2/4 or 1 1/2
how would you break own 3/5 + 1/11
3/5 + 1/11 = 38/55.
why do you need to multiply the numerator when you multiply the denominator to add or subtract fractions?
Good question. The answer is that if you didn't then you would change the value of the fraction. Like 2/3. If you multiplied both of them by 2, you would have 4/6. Both equal 0.66. If you multiplied the bottom only, then it would be 2/6 which is equal to 0.33. It would change the value.
can both fractions be negativs
Right Patrick Crandon!
check the number line. can you add two negative numbers? the answer is yes.
yes they both can be negtive
yes you can by when you go on the number line and added.
Yes!Negative fractions do exist.
Not helpful pmc,I flagged you as my 2nd flag......
I didn't know you can have negitave fractions!!
JMAtlason
JMAtlason
Why does the denominator have to be the same as the other denominator?
Think of it this way:
When you are adding or subtracting two things, they must be the same in order to make it work. If you had 6 basketballs, could you subtract 3 iPhones from them? Of course not!
When working with fractions, the denominator describes the SIZE of the piece, so to do the addition or subtraction, you must make them the same size.
The numerator tells you HOW MANY of each "size" you have, so you only add or subtract the numerator, not the denominator (you aren't changing the "size" of the pieces).
Hope this helps.
When you are adding or subtracting two things, they must be the same in order to make it work. If you had 6 basketballs, could you subtract 3 iPhones from them? Of course not!
When working with fractions, the denominator describes the SIZE of the piece, so to do the addition or subtraction, you must make them the same size.
The numerator tells you HOW MANY of each "size" you have, so you only add or subtract the numerator, not the denominator (you aren't changing the "size" of the pieces).
Hope this helps.
i cant understand this, how did you get the x3 but the other x4?
If you're adding a fraction, you must have denominators that are alike. For example, if you are adding 1/4 + 1/3, you have to make both the denominators the same. So the lowest common denominator for 4 and 3 is 12, so you would multiply 1/4 by 3 and get 3/12. Then you would multiply 1/3 by 4 because you need to get the denominator to 12, and 3 times 4 is 12. So you would get 4/12. Now you would add 3/12 and 4/12 together and get 7/12.
I hope this helped and good luck!
I hope this helped and good luck!
Because it is a fraction you can multiply it by anything  it will still be the same fraction of a whole number. (1/2 * 2 is 2/4  but both are 0.5 in decimal terms)
The objective is to get the denominators the same.
The objective is to get the denominators the same.
45= 44
for know we can say * 34 3 g
for know we can say * 34 3 g
It's because the two fractions aren't connected. You can multiply one by three and the other by four and they wouldn't affect each other. As long as the numerators are also being multiplied, you can keep multiplying and switching and dividing forever. I don't usually do this because it only works with a few fractions, and then there's the decimals to worry about, but it can be fun.
Cause we took LCM of both 9 and 12 and they both are divisible by 3 and 3 times 3 = 9 and 3 times 4 = 12
and So, we get x3 and x4
and So, we get x3 and x4
I don't get it at all
i wish your videos would help me but they dont.:(
You can simplify right
you're right.
or