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How do you add 6/5 + 1/4? Thank you

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4 Answers

When adding/subtracting fractions, the fractions must have a common denominator. 

For this problem:     6/5 + 1/4 ,  

         the least common denominator is the least common multiple of the denominators in the fractions you are adding. Here, the two denominators are 4 and 5. Let's make a list of the multiples of 4 and the multiples of 5 and find the least common multiple of the two:

Multiples of 4:   4, 8, 12, 16, 20, 24, 28, 32, .....

Multiples of 5:   5, 10, 15, 20, 25, 30, 35, ..... 

We find that the least common multiple of 4 and 5 is 20. So we change the two fractions in the problem above to generate two fractions with a common denominator of 20.

      6/5 + 1/4          multiply the first fraction by 4/4 and the second fraction by 5/5 

    (6/5)*(4/4) + (1/4)*(5/5) = (6*4)/(5*4) + (1*5)/(4*5)

                                          = 24/20 + 5/20

                                          = (24 + 5)/20

                                          = 29/20

   29/20 = 20/20 + 9/20 = 1+ 9/20 = 1 9/20

Thus,    6/5 + 1/4 = 24/20 + 5/20 = 29/20  OR  1 9/20      

The key is to find the "least common denominator."  This is done by multiplying the denominators (5 and 4) together, this number (20 in this situation) the denominator.  

Now that we know 20 is to be our denominator (from now and in the answer!!) we can move onward to adjust the top number individually by the same manner as follows:

6x4=24.....leading to 24/20

1x5=5......leading to 5/20

See what I meant by 20 being the bottom number ("least common denominator") for BOTH. Good!

Now add the top numbers (numerators) together:

24+5= 29

Answer=29/20 

Multiply bottom numbers to get the "lease common denominator".....use is for both fractions!

remember 29 is Numerator

and 

remember 20 is the denominator (it dominates the bottom!!),   that makes it a little cooler, no?

Dear Luis and daughter:

I agree with both of the other contributors.  However, an easier way to come up with the same answer below.  It involves multiplication and adding.

6/5 + 1/4 = N

Multiply the numerator of the first number (6) times the denominator of the second number (4) and get 24.

Multiply the numerator of the second number(1) times the denominator of the first number (5) and get 5

Add the 24+5 and get 29.

Finally, multiply the two denominators (5 times 4) and get 20.   The denominators remain denominators and form the new denominator of 20.

Place the results of the first equation 29 over 20 for 29/20.  This could be read as 29 over 20 or 29 divided by 20.  Thus, 29/20 (or 1 and 9/20) = N.  

This is much easier and saves you the steps of looking for the common denominator and multiplying inverses, because by multiplying the denominators you create a "common denominator" for both numbers. Then, if it is possible to reduce the denominator further, that process will be simpler.

Let me know how this works for you!  Test it by doing it this way: 7/6 + 2/5 and let me know what you get!

To add fractions with different denominators, the first step is to write them as fractions with a common denominator.  This is done by multiplying both top and bottom of each fraction by 4 and 5, respectively.

6/5 + 1/4 = (6*4)/(5*4) + (1*5)/(4*5) = 24/20 + 5/20.

Now that both fractions have the same denominator, the result is calculated by adding the numerators and placing this over the common denominator, 20.

24/20 + 5/20 = (24+5)/20 = 29/20.

In summary,

6/5 + 1/4 = 24/20 + 5/20 = 29/20.

Hope this helps.