The Commutative property: Addition only

To make solving the exercise easier, we try to add numbers that give us a result of 10.

Let's keep in mind that:

$7+3=10$

$6+4=10$

Hence we obtain a more manageable exercise to solve:

$10+10=20$

In order to simplify our calculations, we try to add numbers that give us a round result.

Keep in mind that:

$19+21=40$

$34+6=40$

Now, we get a more manageable exercise to solve:

$40+40+10=80+10=90$

In order to simplify the resolution process we try to add numbers that give us a round result.

Keep in mind that:

$4+4=8$

Now we get the exercise:

$74+36+6+8=$

Keep in mind that:

$74+6=80$

$32+8=40$

Now, we get a more manageable exercise to solve:

$80+40=120$

In order to simplify our calculations we try to add numbers that give us a round result.

Let's keep in mind that:

$113+57=170$

$59+71=130$

Now we have a more manageable exercise to solve:

$170+130=300$

Given that this is an exercise with only addition operation, we can change the order of the numbers.

We organize the exercise in a way that we can obtain a pair that gives us an integer.

Keep in mind that there is a pair of fractions that if we add them we will obtain an integer:

$4\frac{2}{3}+3\frac{1}{3}+2\frac{2}{7}+1\frac{3}{7}=$

We solve the exercise from left to right:

$4\frac{2}{3}+3\frac{1}{3}=$

$4+3=7$

$\frac{2}{3}+\frac{1}{3}=\frac{3}{3}=1$

$7+1=8$

Now we obtain the exercise:

$8+2\frac{2}{7}+1\frac{3}{7}=$

We leave the 8 aside and add the rest of the exercise:

$2\frac{2}{7}+1\frac{3}{7}=$

$2+1=3$

$\frac{2}{7}+\frac{3}{7}=\frac{5}{7}$

Now we obtain the exercise:

$8+3+\frac{5}{7}=11\frac{5}{7}$