solve 2 1/2 + 4 2/3

First you will want to convert this to an improper fraction. This can be done by multiplying the whole number by the denominator (bottom of the fraction) and adding the result to the numerator (top of the fraction): 2 and 1/2 = (2*2+1) / 2 = 5/2 .... 4 and 2/3 = (4*3 +2) / 3 = 14/3 .... Then you will want to find a common denominator for these two fractions. 2 and 3 both go into 6 evenly, so this will work as a common denominator. In order to make a common denominator you should multiply the numerator and denominator by the number that will make the denominator 6: Multiply top and bottom of 5/2 by 3 to get 15/6 .... Multiply top and bottom of 14/3 by 2 to get 28/6 .... Then we need to add these two fractions. When adding fractions, you add only the numerator and the answer keeps the same common denominator as the fractions we just got above: 15/6 + 28/6 = (15+28) / 6 = 43/6. If having an improper fraction is okay, you're done. If this must be written as a mixed number, figure out how many whole times 6 goes into 43 and find the remainder. It turns out that 6 goes into 43 seven times with a remainder of one (6*7 = 42). Therefore the mixed number will be 7 and 1/6

The key to this is taking complex fractions (whole number plus a simple fraction) and turning them into simple fractions.
Original complex fraction: 2 1/2
Add the product of the denominator and whole number to the numerator: 2x2+1=5
This becomes your new numerator: 5/2

You do the same steps for the second number.
Original complex fraction: 4 2/3
Add the product of the denominator and whole number to the numerator: 4x3+2=14
This becomes your new numerator: 14/3

Now you're have this equation: 5/2 + 14/3. You cannot add two fractions that have different denominators, so you will need to find a common multiple and use that to transform both fractions.
equation: 5/2 + 14/3 =
multiply denominators to find common multiple: 2 x 3 = 6
transform first number by multiplying numerator and denominator by 3: (5x3)/(2x3) = 15/6
transform second number by multiplying numerator and denominator by 2: (14x2)/(3x2) = 28/6

Now that we've transformed both fractions so they have the same denominator, it's pretty simple; just add the numerators and leave the denominator alone.
Add: 15/6 + 28/6 = 43/6 or   7  1/6

21/2+42/3 is same as 2 3/6+4 4/6 is same as 6 7/6 is same as 7 1/6.....keep it simple and reduce to simplest answer to understand!!

WOWSA----TM / Keller, Texas 

 Photo to follow, I'm a probie.

Nicole,

The key to using fractions is to keep it simple.  So, you have two and a half of something...lets say a pizza...school is almost out and we need something to eat for the year end party...and your friend brings four and two-thirds amount of pizza...so...how much pizza do we have for the party?  well...we know we have 2 full pizzas and 4 full pizzas....so 6 full pizzas and some partials....1/2 and 2/3....so the root of the question is how to add 1/2 + 2/3...Find the LCD and Adjust ....LCD is 6...Adjust  1/2 = 3/6 and 2/3 = 4/6....Add.....3/6 + 4/6 = 7/6...which is 1 full pizza and one slice of 1/6....so you teacher and classmates are very excited to learn that you and your friend brought 7 full pizzas (6+1) and 1/6 or 7 1/6.......

I hope this helps you....it just makes me hungry.