Why can't we add denominators when we add fractions?

Question

why dont we add the denominators when we are adding fractions? why cant we do this ---> (2/5)+(1/5)=(2+1)/(5+5)

Answer 1

Because the denominator is what defines how much is there. (2/5) +(1/5) would equal 3/5, and if you added the denom., then it woud be 3/10. A fraction half the size of the actual product.

Answer 2

This is a tricky question to answer. You cannot add the tops and bottoms of the fractions together because they are only parts of a a whole number.

Think of a pie divided into five equal pieces. Each piece is just 1/5th  of the whole pie. So if you add one piece and two more, then you would have 3 pieces of the pie which is 3/5ths of one whole pie. There are still 2/5ths for someone else. If you draw it you will understand better. I am sorry that I do not know enough about computers to do it for you.

Just remember that those 5s on the bottom are not numbers; they are just parts of a whole number. They are fractions because you get only a fraction of the pie. When you draw the pie you will see that you have only 3/5 ths because that's what you are adding.

It might be clearer with money. Try working it out with $10.

1/5 of $10=$2    

2/5 of $10=$4  

So 3/5 of $10 =$6

You have asked a logical question and I sympathise with you as I know that many teachers do not explain fractions clearly. They just teach the operations and hope for the best. Wrestle with it till you "get it". it will be a big " Ah-ha " moment.

Answer 3

If you add the denominator, you are subtracting instead of adding.

The numerator tells how many units of the denominator exist (two fifths, one fifth, etc.) The larger the denominator, the more units an entity, a "thing," is divided into and therefore the smaller each unit is.

To illustrate, suppose you are depositing dimes into your bank account. There are 10 dimes to a dollar (each one is 1/10th of a dollar). If you go up to the deposit window and give the teller two dimes and then a moment later one more one dime--(2/10) + (1/10), you should be credited for 3/10th of a dollar, or thirty cents. If the teller adds the denominators when he or she tallies your deposit, you'd be credited with 3/20ths of a dollar, or 15 cents--half what you should have. Would you want to bank there?

Answer 4

Well I'll use this example just to explain it.

If take a biscuit and cut it in half then if you followed your rule 1/2 + 1/2 = (1+1)/(2+2) = 2/4 = 1/2 So according to your rule if you cut a biscuit in two then half of a biscuit disappears!

2/5 = 4/10 1/5 = 2/10 so if you add 2/10 and 4/10 instead of getting 6/10 you get 3/10 so that means if you ADD your fractions it is the same as SUBTRACTING 1/10 from the 4/10 what's wrong with that. Hmm....

Answer 5

The number "1" as a fraction is any number on top and on bottom (numerator and denominator both same number) i.e. 1/1 = 1 and 4/4 = 1 and 8/8 = 1 and Y/Y = 1 and 2million/2million = 1.  Because basically, we are dividing the top number into the bottom number 5/5 MEANS "five divided by five"

So, when adding fractions, we are finding out how much of a "1" do we have and therefore need to have the bottom number be the same so we have a constant to start us.   Once we have that constant, the upper numbers will fit into place for adding, subtracting, etc.

If we added the bottom numbers, we would be s******g up the whole system of "1".  1/4 + 1/5 can not equal 2/9  because as a deciman 1/4 of "1" = .25 and 1/5 of "1" = .20  and   {.20 + .25 = .45}

1/4 = 5/20 {or.20)  1/5 = 4/20 added together we get 9/20  9 divided by 20 = .45  

You would not be able to do the same thing if you added as 2/9 because 2 divided by 9 (the wrong way) = .222222...  

As you can see - it doesn't match up with the true decimal equivilents.

Does this make sense????