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

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

$5\times1=5$

Now we multiply:

$8\times5=40$

According to the order of operations, we first place the multiplication operation inside parenthesis:

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

Then, we perform this operation:

$7\times1=7$

Finally, we are left with the answer:

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

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

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

$2\times1=2$

This simple rule is the order of operations which states that multiplication precedes addition and subtraction, and division precedes all of them,

In the given example, a multiplication occurs between two sets of parentheses, thus we simplify the expressions within each pair of parentheses separately,

We start with simplifying the expression within the parentheses on the left, this is done in accordance with the order of operations mentioned above, meaning that multiplication comes before subtraction, we perform the multiplications in this expression first and then proceed with the subtraction operations within it, in reverse we simplify the expression within the parentheses on the right and perform the subtraction operation within them:

What remains for us is to perform the last multiplication that was deferred, it is the multiplication that occurred between the expressions within the parentheses in the original expression, we perform it while remembering that multiplying any number by 0 will result in 0:

Therefore, the correct answer is answer d.

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

$12+(3\cdot0)=$

$3\times0=0$

$12+0=12$

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

$2+(0:3)=$

$0:3=0$

$2+0=2$

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:

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

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

$0:7=0$

$0+1=1$

According to the order of operations, the exercise is solved from left to right as it only involves an addition operation:

$12+1=13$

$13+0=13$

According to the order of operations, the exercise is solved from left to right as it contains only an addition operation:

$0+0.2=0.2$

$0.2+0.6=0.8$

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

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

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

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

$9-0=9$

$9+0.5=9.5$

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

$19+1=20$

$20-0=20$

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

$0:3=0$

$2+0=2$

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

$3\times0=0$

$12+0=12$