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

Right then!

Lets solve this together!

First of all, we will need to turn all of the Mixed Fractions into improper fraction for ease of understanding.

To turn an Mixed Number or Mixed Fraction into an improper fraction the steps are quite simple. First look at the denominator. Lets use an Mixed Number in the equation.

2 1/3.

The denominator is 3 correct? Now we need to look at the Whole number. That is 2. Now we just multiply then together.

$${\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}}$$

What does that equal? 6.

Now we just add the 6 to the numerator. So we get a fraction of:

$${\frac{{\mathtt{7}}}{{\mathtt{3}}}}$$

Now we do that for all the mixed numbers.

So we should end up with:

$${\frac{{\mathtt{7}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{8}}}{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{19}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{11}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{22}}}{{\mathtt{5}}}}$$

Now we reach the hardest part of solving this equation.

What is the LCM of all of these numbers?

LCM is Lowest Common Multiple.

So what is the lowest number that all 5 of these numbers go into. 

Let me guide you through this step.

Lets start with any number.

20?

Okay. Does 3 Go into 20?

Sadly no. So this does not qualify as the Lowest Common Multiple.

60?

Does 3 Go into 60? Yes!

Does 5 Go into 60? Yes!

Does 4 Go into 60? Yes!

Does 6 Go into 60? Yes!

We skip the other one, because there are two 5's, making writing it again useless.

How then we found a number, we will need to calculate the amount of the number goes to the other number.

So.. How many 3's go into 60?

20.

5 to 60?

12.

4 to 60?

15.

6 to 60?

10. 

Now lets utilise this!

Back to the Equation.

$${\frac{{\mathtt{7}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{8}}}{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{19}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{11}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{22}}}{{\mathtt{5}}}}$$

We want to the the demoninator the LCM. Or in this equation 60.

Go do that, we must multiply what we do to the demoninator also to the Numerator.

So. For Example:

$${\frac{{\mathtt{7}}}{{\mathtt{3}}}}$$

What do we need to do with the Demoninator to get it to 60?

Multiply by 20!

So we multiply both the top and the bottom with 20.

$${\frac{\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{20}}\right)}{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{20}}\right)}}$$

We get:

$${\frac{{\mathtt{140}}}{{\mathtt{60}}}}$$

Now do the same to all the other fractions so we will get:

$${\frac{{\mathtt{140}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{96}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{190}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{165}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{264}}}{{\mathtt{60}}}}$$

Now add them all together.

$${\frac{{\mathtt{140}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{96}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{190}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{165}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{264}}}{{\mathtt{60}}}} = {\frac{{\mathtt{57}}}{{\mathtt{4}}}} = {\mathtt{14.25}}$$

There we are! The Answer.

14.25

Nice explanation, Takahiro....Thumbs Up !!!

It is a good explanation Takahiro,

Thumbs up from me too

but it would have been better and easier if you had just added all the whole numbers first.

So you would have

$$2+1+3+2+4+\frac{1}{3}+\frac{3}{5}+\frac{1}{6}+\frac{3}{4}+\frac{2}{5}\\\\
\mbox{as you worked out the LCD (Lowest Common Denominator is 60)}\\\\
12+\frac{20}{60}+\frac{36}{60}+\frac{10}{60}+\frac{45}{60}+\frac{24}{60}\\\\
etc$$

I hope you don't mind me pointing this out - I am a compulsive teacher.  

Nah, I understand. However, generally when they ask a question like this, they are looking for a detailed answer. So they don't ask again, they can do it themselves

Sorry but no:   You haven't understood me.

THE DETAIL OF YOUR ANSWER IS FABULOUS!

But when you add mixed numerals you do not change them to improper fractions.

##  THAT IS TOTALLY UNNECESSARY

FIRST you add up the whole numbers

THEN you find the LCD for the fraction part.

THEN you change each fraction part so that it has a common denominator.

THEN you add up the fraction parts 

THEN if the fraction part is an improper fraction you convert it to a mixed numeral.

THEN you add the whole number part to the sum of the fractions part.

THEN you are finished.