How do we add a mixed number to two fractions? Like 2 2/3 + 3/8 + 4/6?

2 2/3 + 3/8 + 4/6

First make all of them proper fractions
2 2/3 = (3*2 + 2)/3
8/3 + 3/8 + 4/6

Then find LCM of denominators, LCM of 3,8,6 is 24
8*8 + 3*3 + 4*4
---------------------
24

= (64 + 9 + 16)/24 = 89/24

To convert this into mixed faction 89/24 = 3 is divisor and 89 - 24*3 = 17 is the remainder
so the number is 3 17/24

post a few examples

Steps:
1. Change them to similar fractions---
---> 2 2/3 + 3/8 + 4/6 = 2 16/ 24 + 9/24 + 16/24

2. Add them---
---> 2 16/24 + 9/24 + 16/24= 2 41/24

3. Change the answer to simpliest form---
---> 2 41/24 = 3 17/24

Answer: 3 17/24

2 2/3 + 3/8 + 4/6
= 8/3 + 3/8 + 4/6
= 64/24 + 9/24 + 16/24
= 73/24 + 16/24
= 89/24
= 3 17/24

2 2/3 + 3/8 + 4/6?
First convert to improper fractions

8/3 + 3/8 + 4/6

Bring the denominators (bottom number) to the same value by multiplying them together.
3 x 8 x 6 = 144
Then factorise = 24
Take each fraction in turn
and multiply both top and bottom by a factor that will bring the nummber to 24 on the bottom.

8/3 = 64/24 (x 8)
3/8 = 9/24 (x 3)
4/6 = 16/24 ( x 4)

64/24 + 9/24 + 16/24 =
{64 + 9 + 16} / 24 =
89 / 24 = convert back to an mixed number by dividing through by 24. The answer is the whole number, and the remainder is the fraction.
3 17/24 = (If possible reduce the fraction to its simplest terms, which cannot be done is this case because 17 is a prime number).
3 17/24. !!!!!

Solution: In order to solve this complex fractions, use the Law of Addition of Fractions, such as

a/b + c/b = (a + c)/b ------------------->> (1)

and

a/b + c/d = (ad + bc)/bd ------------>>> (2)

From the equation, 2 2/3 + 3/8 + 4/6;

the 2 2/3 can be written as 2 + 2/3 (or 2/1 + 2/3)

Use (2) to simplify this
2 + 2/3 = [2(3) + (2)]/(3)(1)
= (6 + 2)/3 = 8/3

and

4/6 can be reduced to 2/3

thus, the resulting equation is

= 8/3 + 3/8 + 2/3 ------>>> resulting equation

You can combine terms with similar denominator first, such as

= 8/3 + 2/3

so that you can use (1)

= (8 + 2)/3

= 10/3

The resulting terms now are;

= 3/8 + 10/3

You can now use (2) again,

= [9 + 8(10)]/8(3)
= 89/24 ---------------------->>> Ans

If you want, you can still reduce this fraction into its lowest term by performing the division operation; of which, the quotient is 3 and remainder is 17/24.

= 3 + 17/24

or

= 3 17/24 ----------------------->>> Ans

convert 2 2/3 to improper fraction by multiplying the demoninator with the whole number and add the numerator.
3*2+2 = 8
and retain the demoninator.
get the lcd and add..
ans. 3 17/24

2 2/3 = 8/3

8/3 + 3/8 + 4/6 =
find common dominiator (3, 8 and 6 goes into 24)
= (8*8 (3 goes 8 times into 24) + 3*3 (8 goes 3 times into 24) + 4 * 4 (6 goes 4 times into 24)) / 24
= (64+9+16)/24
=89/24