Parentheses in simple Order of Operations - Examples, Exercises and Solutions

Let's begin by simplifying the expression following the order of operations.

P- PARENTHESES

E-EXPONENTS

D-DIVISION

A-ADDITION

S-SUBTRACTION

$18-(3+3)= \\ 18-6= \\ 12$

Therefore the correct answer is answer D.

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

$5\times1=5$

Now we multiply:

$8\times5=40$

Let's start with the part inside the parentheses. 

$2+2=4$
Then we will solve the exercise from left to right 

$8:2=4$
$4 × (4)=16$

The answer: $16$

First, we solve the exercise in the parentheses

$(1+9:9)=$

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

$1+1=2$

Now we obtain the exercise:

$20-2=18$

According to the order of operations rules, we must first solve the expressions inside of the parentheses:

$15-9=6$

$7-3=4$

We obtain the following expression:

$6\times4=24$

Apply the distributive property and proceed to multiply each term inside of the parentheses by 187:

$187\times8-187\times5=$

Solve the first multiplication problem vertically, making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )

$187\\\times8$

We should obtain the following result: 1496

Proceed to solve the second multiplication problem vertically, once again making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )

$187\\\times5$

We should obtain the following result: 935

Now to tackle the next problem:

$1496-935=$

We should once again solve this vertically. Make sure to align the digits properly, ones under ones, tens under tens, etc.:

$1496\\-935$

Subtract ones from ones, tens from tens, etc., to obtain the final result: $561$

Let's simplify this expression while maintaining the order of operations.

Let's start by solving what's in the parentheses:

$29-4=25$

Now we get the expression:

$25:5=$

In the next step, to make the division easier, we'll break down 25 into two smaller factors that are divisible by 5:

$(20+5):5=$

Let's divide each factor in the parentheses by 5:

$(20:5)+(5:5)=$

We'll solve each expression in the parentheses and obtain:

$4+1=5$

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of them,

We will therefore start by simplifying the expression inside the parentheses and calculate the result of the addition within them, then - we will first perform the division operation:

$(85+5):10= \\ 90:10= \\ 9$

$$Therefore, the correct answer is answer A.

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of them,

We will start by simplifying the expression inside the parentheses and calculate the result of the subtraction within them, then - since division comes before subtraction, we will first perform the division operation and then perform the subtraction operation:

$10-(10-4):2= \\ 10-6:2= \\ 10-3= \\ 7$

$$Therefore, the correct answer is answer B.

Let's simplify this expression while adhering to the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses take priority over all.

In our expression, there is a term in parentheses that needs to be multiplied. We'll start by simplifying this expression, remembering that division comes before addition, so we'll first perform the division operation within the parentheses and then the addition operation in this expression:

$4+(6+6:3)\cdot2= \\ 4+(6+2)\cdot2= \\ 4+8\cdot2=$

Let's continue simplifying the expression we that we got in the last step. Since multiplication comes before addition, we'll first calculate the multiplication in the expression and then perform the addition operation:

$4+8\cdot2= \\ 4+16= \\ 20$

To summarise:

$4+(6+6:3)\cdot2= \\ 4+8\cdot2= \\ 20$

Therefore the correct answer is answer C.

In the order of operations, parentheses come before everything else.

We start by solving the inner parentheses in the subtraction operation:

$((3):3-1)\times4=$ We continue with the inner parentheses in the division operation and then subtraction:

$(1-1)\times4=$

We continue solving the subtraction exercise within parentheses and then multiply:

$0\times4=0$

First, we perform the operation inside the parentheses:

$12:3(2)$

When there is no mathematical operation between parentheses and a number, we assume it is a multiplication.

Therefore, we can also write the exercise like this:

$12:3\times2$

Here we solve from left to right:

$12:3\times2=4\times2=8$

According to the rules of the order of operations, we first solve the exercise within parentheses:

$4+5=9$

Now we obtain the exercise:

$2\times3-9:2=$

We place in parentheses the multiplication and division exercises:

$(2\times3)-(9:2)=$

We solve the exercises within parentheses:

$2\times3=6$

$9:2=4.5$

Now we obtain the exercise:

$6-4.5=1.5$

According to the rules of the order of operations, we first solve the exercise within parentheses from left to right:

$8:4=2$

$2:2=1$

Now we get the exercise:

$1-3-1=$

We solve the exercise from left to right:

$1-3=-2$

$-2-1=-3$

First, we solve the exercise in the parentheses

$(20-4\times5)=$

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

$20-20=0$

Now we obtain the exercise:

$19\times0=0$