In previous articles, we have seen what is the order of operations for addition, subtraction, multiplication, and division and also the order we must follow when there are exponents.

When the exercise we need to solve includes parentheses, we always (always!) start with the operation contained within them.

  1. Parentheses
  2. Exponents and roots
  3. Multiplications and divisions
  4. Additions and subtractions

Reminder: when an exercise presents operations that have the same precedence, that is, multiplications and divisions or additions and subtractions, we will solve the exercise from left to right.

Suggested Topics to Practice in Advance

  1. The Order of Basic Operations: Addition, Subtraction, and Multiplication
  2. Order of Operations: Exponents
  3. Order of Operations: Roots

Practice Parentheses in advanced Order of Operations

Examples with solutions for Parentheses in advanced Order of Operations

Exercise #1

Solve the following expression:

(85+5):10= (85+5):10=

Video Solution

Step-by-Step Solution

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

Therefore, the correct answer is answer A.

Answer

9 9

Exercise #2

Solve the following expression:

10(104):2= 10-(10-4):2=

Video Solution

Step-by-Step Solution

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,

Therefore we'll start by simplifying the expression inside the parentheses and perform the subtraction within them, then since division comes before subtraction, we'll first perform the division operation and then the subtraction operation

10(104):2=106:2=103=7 10-(10-4):2= \\ 10-6:2= \\ 10-3=\\ 7 Therefore the correct answer is answer D.

Answer

7 7

Exercise #3

Solve the following expression:

18(3+3)= 18-(3+3)=

Video Solution

Step-by-Step Solution

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,

Therefore we'll start by simplifying the expression in parentheses, and perform the addition operation in this expression, then we'll perform the subtraction operation that applies to the expression in parentheses:

18(3+3)=186=12 18-(3+3)= \\ 18-6= \\ 12 Therefore the correct answer is answer A.

Answer

12

Exercise #4

Solve the following equation:

(294):5= (29-4):5=

Video Solution

Step-by-Step Solution

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

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

294=25 29-4=25

Now we get the expression:

25:5= 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= (20+5):5=

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

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

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

4+1=5 4+1=5

Answer

5 5

Exercise #5

187×(85)= 187\times(8-5)=

Video Solution

Step-by-Step Solution

We'll use the distributive property and multiply each term in parentheses by 187:

187×8187×5= 187\times8-187\times5=

Let's solve the first multiplication problem vertically, making sure to solve it correctly, meaning units times units, units times tens, units times hundreds.

187×8 187\\\times8

We get the result: 1496

Let's solve the second multiplication problem vertically, making sure to solve it correctly, meaning units times units, units times tens, units times hundreds.

187×5 187\\\times5

We get the result: 935

Now we'll get the problem:

1496935= 1496-935=

We'll solve this vertically as well. We'll make sure to align the digits properly, units under units, tens under tens, etc.:

1496935 1496\\-935

We'll subtract units from units, tens from tens, etc., and get the result: 561 561

Answer

561 561

Exercise #6

(7+2)×(3+8)= (7+2)\times(3+8)=

Video Solution

Step-by-Step Solution

Simplify this expression paying attention to the order of operations. Whereby exponentiation precedes multiplication, division precedes addition and subtraction and that parentheses precede all of the above.

Therefore, let's first start by simplifying the expressions within the parentheses. After which we perform the multiplication between them:

(7+2)(3+8)=911=99 (7+2)\cdot(3+8)= \\ 9\cdot11=\\ 99 Therefore, the correct answer is option B.

Answer

99

Exercise #7

(85+5):10= (85+5):10=

Video Solution

Step-by-Step Solution

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

85+5=90 85+5=90

We should obtain the following expression:

90:10=9 90:10=9

Answer

9

Exercise #8

8×(5×1)= 8\times(5\times1)=

Video Solution

Step-by-Step Solution

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

5×1=5 5\times1=5

Now we multiply:

8×5=40 8\times5=40

Answer

40

Exercise #9

(2+1×2)2= (2+1\times2)^2=

Video Solution

Step-by-Step Solution

Let's solve the expression (2+1×2)2 (2+1\times2)^2 step-by-step, adhering to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Firstly, handle the expression inside the parentheses (2+1×2) (2+1\times2) :

  • Within the parentheses, according to PEMDAS, we first perform the multiplication 1×21\times2 which equals 22.
  • Now, the expression inside the parentheses becomes (2+2) (2+2) .
  • Next, perform the addition: 2+2=42+2=4.

Now the expression simplifies to 424^2.

Second, handle the exponent:

  • Calculate the square of 4: 42=164^2 = 16.

Thus, the final answer is 1616.

Answer

16

Exercise #10

Solve the following equation:

18(3+3)= 18-(3+3)=

Video Solution

Step-by-Step Solution

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)=186=12 18-(3+3)= \\ 18-6= \\ 12

Therefore the correct answer is answer D.

Answer

12

Exercise #11

10(104):2= 10-(10-4):2=

Video Solution

Step-by-Step Solution

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(104):2=106:2=103=7 10-(10-4):2= \\ 10-6:2= \\ 10-3= \\ 7

Therefore, the correct answer is answer B.

Answer

7

Exercise #12

96:(4×3)1= 9-6:(4\times3)-1=

Video Solution

Step-by-Step Solution

We simplify this expression paying attention to the order of operations which states that exponentiation comes before multiplication and division, and before addition and subtraction, and that parentheses precede all of them.

Therefore, we start by performing the multiplication within parentheses, then we carry out the division operation, and we finish by performing the subtraction operation:

96:(43)1=96:121=90.51=7.5 9-6:(4\cdot3)-1= \\ 9-6:12-1= \\ 9-0.5-1= \\ 7.5

Therefore, the correct answer is option C.

Answer

7.5

Exercise #13

[(52):31]×4= [(5-2):3-1]\times4=

Video Solution

Step-by-Step Solution

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

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

((3):31)×4= ((3):3-1)\times4= We continue with the inner parentheses in the division operation and then subtraction:

(11)×4= (1-1)\times4=

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

0×4=0 0\times4=0

Answer

0 0

Exercise #14

(159)×(73)= (15-9)\times(7-3)=

Video Solution

Step-by-Step Solution

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

159=6 15-9=6

73=4 7-3=4

We obtain the following expression:

6×4=24 6\times4=24

Answer

24 24

Exercise #15

(126+9)×(7+3)= (12-6+9)\times(7+3)= ?

Video Solution

Step-by-Step Solution

According to the order of operations, we will first solve the expressions in parentheses and then multiply:

(126+9)=(6+9)=15 (12-6+9)=(6+9)=15

(7+3)=10 (7+3)=10

Then solve the multiplication exercise:

15×10=150 15\times10=150

Answer

150 150