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# how to add fractions?

i have this fraction problem and i thought i understood it but now im not sure

.......1

2...-----

.......2

.......2

1...-----

........3

........1

2..-----

......4

.......5

3--------

.....6

thats 2 1/2 + 1 2/3 + 2 1/4 +3 5/6=

### 4 Answers

- Marley KLv 79 years agoFavorite Answer
add the whole numbers first:

2+1+2+3 = 8

to add the fractions:

1/2 + 2/3 + 1/4 + 5/6

multiply numerator and denominator by the same number to get a common denominator:

1/2 = (1/2)(6/6) = 6/12

2/3 = (2/3)(4/4) = 8/12

1/4 = (1/4)(3/3) = 3/12

5/6 = (5/6)(2/2) = 10/12

add the new numerators:

6+8+3+10 = 27

keep the common denominator so that the sum of your fractions is: 27/12

now change 27/12 to a reduced mixed number:

27/12 = 2 3/12 = 2 1/4

Whole numbers + fractions =

8 + 2 1/4 = 10 1/4

There you go! All those beautiful mixed numbers sum to:

10¼

that's it! ;)

- MathBioMajorLv 79 years ago
Before attempting to add the fractions, convert them all to improper fractions first:

5/2 + 5/3 + 9/4 + 23/6.

Now add them by giving them all a common denominator first. By inspection, we can see that 12 is the lowest common denominator (LCD) of all the fractions. To convert each fraction, we multiply its denominator by an appropriate factor to make its new denominator the LCD of all of them. But, in order not to change the value of the fraction, we must also multiply its numerator by the same factor. This has the effect of multiplying the fraction by 1, i.e. 6/6 = 1, 4/4 = 1, and so forth. Consequently, it changes each fractions form, but not its value.

So we get this when we add the given fractions:

5/2 (6/6) + 5/3 (4/4) + 9/4 (3/3) + 23/6 (2/2) =

30/12 + 20/12 + 27/12 + 46/12 =

(30 + 20 + 27 + 46)/12 =

123/12 =

10 3/12 =

10 ¼

- Anonymous9 years ago
The answer is 10 1/4.

1) Find the least common denominator which is 12

2) Add up all the fractions(not the whole numbers) which will give you an improper fraction, 27/12

3) Simplify the fraction by dividing 27 by 12 which will give you 2 1/4

4) Add all the whole numbers(dont forget the two) which will equal 10. Then add the fraction.

5) The answer is 10 1/4

- 9 years ago
You have to make it so they all have the same denominator (bottom number) you do that by multiplying until they all go into the same number which in your case is 12 since 6 goes into it twice you multiply the numerator by 2 and the 4 goes in 3 times so multiply that by 3 and so on (I struggled with fractions for a little bit too)