Addition and Subtraction of Mixed Numbers: Using fractions

According to the order of operations, we will solve the exercise from left to right.

Let's note that in the first addition exercise, we have an addition between two halves that will give us a whole number, so:

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

Now we will get the exercise:

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

Let's note that we can simplify the mixed fraction:

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

Now the exercise we get is:

$4+4\frac{1}{2}=8\frac{1}{2}$

According to the rules of the order of operations in arithmetic, we solve the exercise from left to right.

Let's note that:

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

We should obtain the following exercise:

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

Let's solve the exercise from left to right.

We will combine the left expression in the following way:

$\frac{6+8}{7}x=\frac{14}{7}x=2x$

Now we get:

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

Note that the right-hand side of the addition exercise between the fractions gives a result of a whole number, so we'll start with that:

$6\frac{2}{3}+\frac{1}{3}=7$

Giving us:

$7\frac{5}{6}+7=14\frac{5}{6}$