Mixed Fractions - Examples, Exercises and Solutions

$7\frac{5}{6}+6\frac{2}{3}+\frac{1}{3}=$

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

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

Now we get:

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

$14\frac{5}{6}$

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

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:

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

$8\frac{1}{2}$

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

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

Let's note that:

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

Now we'll get the exercise:

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

$3\frac{3}{4}$

$\frac{6}{7}x+\frac{8}{7}x+3\frac{2}{3}x=$

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:

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

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

$2\times\frac{5}{7}=$

$1\frac{3}{7}$

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

$1\frac{1}{2}$

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

$1\frac{1}{2}$

$4\times\frac{2}{3}=$

$2\frac{2}{3}$

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

$4$

$6\times\frac{3}{4}=$

$4\frac{1}{2}$

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

$6$

$7\times\frac{2}{5}=$

$2\frac{4}{5}$

$3\times\frac{6}{7}=$

$2\frac{4}{7}$

Solve:

$7\times\frac{3}{8}=$

$2\frac{5}{8}$

$1:\frac{3}{4}=$

$1\frac{1}{3}$