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2 1/2 plus 4 2/3

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6 Answers

Kaylee,

I am from AZ too.

If you collect integer parts and fractional parts separately, you can get it done simpler.

2 1/2 + 4 2/3 = (2+4) + (1/2 + 2/3) = 6 + (3/6 + 4/6) = 7 1/6 <==Answer

 

2 1/2 plus 4 2/3

The complication here is remembering that addition requires putting together things that are alike.  Halves and thirds of the same whole thing are not alike. They represent different amounts of the whole. The fractions here need to be represented by equivalent fractions that have a common denominator so that the size of the pieces being added will be the same.

1/2 has the same value as 2/4 (if you cut the halves into 2 smaller but equal pieces,) and the same value as 3/6 (if you cut the halves into 3 smaller but equal pieces.) 

2/3 has the same value as 4/6 (if you cut each of the thirds into 2 smaller but equal pieces.)

So, using sixths - you can represent BOTH the 1/2 and the 2/3.  1/2 = 3/6 and 2/3 = 4/6. 6 can be our common denominator so that we can add these values together.  The rest is just a matter of putting together these values.

2 1/2 + 4 2/3 is the same as 2 3/6 + 4 4/6 which is equal to 6 and 7/6 or 6 7/6

Because 7/6 is greater than 1 whole (6/6 or 6 out of 6 is the same as 1 whole thing,) we have 1 more step. 7/6 has the same value as 1 1/6.  Therefore the answer can be shown as 6 and 1 1/6. We can now combine the whole values of 6 and 1 for a final answer of 7 1/6.

If you'd like to see more on fractions, my blog has a similar example using area models to better visualize what is happening when we add fractions together.

2 1/2 + 4 2/3

1. Change the mixed numbers to improper fractions

2. Find the common denominators

3. Add the numerators, and keep the denominator

4. Reduce

5/2  + 14/3                (Find the least common multiple)  6

Multiply each denominator by the number that makes them 6

Multiply each numerator by the same number that you used to multiply its denominator, so  2x3 =6 and

5 x 3 = 15  then 3 x2 =6, and 14 x 2 =28

Now add 15/6 + 28/6  (Remember to add only the numerators, not the denominators) 

15 + 28 = 43  

  place 43/6 and reduce

  43 divided by 6 = 7 with a remainder of 1

the answer is  7 1/6        

Check your answer by converting the mixed number to to the fraction that you reduced.

6x7=42 +1 = 43

You could also reduce your answer to a decimal or

 43/6 =  7.166 ( rounded because  the 6 is repeated)

               

 

    

Ok, we want to add 2 and 1/2, therefore we need the same denominator:

2 = 4/2

therefore: 4/2 + 1/2 = 5/2

And we want to add 4 and 2/3, therefore we need the same denominator:

4 = 12/3

therefore: 12/3 + 2/3 = 14/3

Now we want to add those 2 new numbers:

5/2 + 14/3, therefore we need the same denominator: in this case lets time both denominators to find a common denominator: 2 x 3 = 6.

5/2 = 5 x 3 / 2 x 3 = 5 x 3 / 6 = 15 / 6

And 14/3 = 14 x 2 / 3 x 2 = 14 x 2 / 6 = 28 / 6

Add now those numbers: 15 / 6 + 28 / 6 = 43 / 6.

No you have to simplify:

By what number can you time 6 to be as close as possible of 43 without to be over 43 ?

get your math table: the closest is 6 x 7 = 42: therefore your number is 7. Which means that 42 / 6 = 7.

but we have the number 43, therefore there is still 1 point we didn't divide and which still has 6 as denominator. we then have 7 plus 1/6 = 7 1/6

 

Find the common denominator of 2 and 3. In this case, you can just multiply 2 and 3 to find the common denominator, which is 6. So for 2, you need to multiply by 3 to get 6. Also multiply by 3 to the top. For 3, you need to multiply by 2 to get 6. Also multiply by 2 to the top.

Make sure you did not touch the number before the fraction because that can be added.

2+4 = 6

1/2 = 3/6

2/3 = 4/6

3/6+4/6=1 1/6

6+  1 1/6 = 7 1/6

Hope that helps.

In order to add the two you must convert both to a common denominator in this case 6 (2*3=6)

To convert 2 and 1/2:

2= 12/6 and 1/2= 3/6 so 2 1/2= 12/6+3/6= 15/6

To convert 4 2/3:

4= 24/6 and 2/3= 4/6 so 4 2/3= 28/6

Once converted all you have to do is add then up!

15/6 + 28/6= 43/6. which is 7 1/7 because 7*6 = 42. (43-42=1)