Order or Hierarchy of Operations with Fractions - Examples, Exercises and Solutions

$8\times(5\times1)=$

According to the order of operations, we first solve the expression in parentheses:

$5\times1=5$

Now we multiply:

$8\times5=40$

40

$7\times1+\frac{1}{2}=$

According to the order of operations rules, we first insert the multiplication exercise into parentheses:

$(7\times1)+\frac{1}{2}=$

Let's solve the exercise inside the parentheses:

$7\times1=7$

And now we get the exercise:

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

$7\frac{1}{2}$

$\frac{6}{3}\times1=$

According to the order of operations rules, we will solve the exercise from left to right, since there are only multiplication and division operations:

$\frac{6}{3}=2$

$2\times1=2$

$2$

Solve:

$3-4+2+1$

We will use the substitution property to arrange the exercise a bit more comfortably, we will add parentheses to the addition operation:
$(3+2+1)-4=$
We first solve the addition, from left to right:
$3+2=5$

$5+1=6$
And finally, we subtract:

$6-4=2$

2

Solve:

$9-3+4-2$

According to the rules of the order of operations, we will solve the exercise from left to right since it only has addition and subtraction operations:

$9-3=6$

$6+4=10$

$10-2=8$

8

Solve:

$-5+4+1-3$

According to the order of operations, addition and subtraction are on the same level and, therefore, must be resolved from left to right.

However, in the exercise we can use the substitution property to make solving simpler.

-5+4+1-3

4+1-5-3

5-5-3

0-3

-3

$-3$

$9+3-1=$

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

9+3=11

11-1=10

And this is the solution!

$11$

Solve the following exercise:

$12+3\cdot0=$

According to the order of operations, we first multiply and then add:

$12+(3\cdot0)=$

$3\times0=0$

$12+0=12$

$12$

Solve the following exercise:

$2+0:3=$

According to the order of operations rules, we first divide and then add:

$2+(0:3)=$

$0:3=0$

$2+0=2$

$2$

$10-3+7-5=$

Due to the fact that the exercise only involves addition and subtraction operations, we will solve it from left to right:

$10-3=7$

$7+7=14$

$14-5=9$

$9$

$\frac{25+25}{10}=$

Let's begin by multiplying the numerator:

$25+25=50$

We obtain the following fraction:

$\frac{50}{10}$

Finally let's reduce the numerator and denominator by 10 and we are left with the following result:

$\frac{5}{1}=5$

$5$

$0:7+1=$

According to the order of operations rules, we first divide and then add:

$0:7=0$

$0+1=1$

$1$

$12+1+0=$

According to the order of operations rules, since the exercise only involves addition operations, we will solve the problem from left to right:

$12+1=13$

$13+0=13$

13

$0+0.2+0.6=$

According to the order of operations rules, since the exercise only involves addition operations, we will solve the problem from left to right:

$0+0.2=0.2$

$0.2+0.6=0.8$

0.8

$\frac{1}{2}+0+\frac{1}{2}=$

According to the order of operations, since the exercise only involves addition operations, we will solve the problem from left to right:

$\frac{1}{2}+0=\frac{1}{2}$

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

$1$