Calculate the Sum: 4⅔ + 2⅖ + 3⅓ + 1⅗ Mixed Number Addition

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

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:

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