Parentheses in advanced 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.

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,

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

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

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.

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 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:

$18-(3+3)= \\ 18-6= \\ 12$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 solve the expression $(2+1\times2)^2$ 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 $(2+1\times2)$:

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

Now the expression simplifies to $4^2$.

Second, handle the exponent:

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

Thus, the final answer is $16$.

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:

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

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

$5\times1=5$

Now we multiply:

$8\times5=40$

Let's solve exercise A:

$8\times8=64$

Let's solve exercise B:

$10\times6=60$

Let's solve exercise C:

$12\times5=60$

Let's solve exercise D:

$15\times4=60$

According to the order of operations, we'll first solve the exercises in parentheses:

$(16-6)=10$

$(7-3)=4$

We should obtain the following exercise:

$10\times9+4$

We'll place the multiplication exercise in parentheses to avoid confusion in the rest of the solution:

$(10\times9)+4=$

According to the order of operations, we'll solve the multiplication exercise and then add:

$90+4=94$

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.

The problem to be solved is $0.6\times(1+2)=$. Let's go through the solution step by step, following the order of operations.

Step 1: Evaluate the expression inside the parentheses.
Inside the parentheses, we have $1+2$. According to the order of operations, we first solve expressions in parentheses. Thus, we have:

$1 + 2 = 3$

So, the expression simplifies to $0.6\times3$.

Step 2: Perform the multiplication.
With the parentheses removed, we now carry out the multiplication:

$0.6 \times 3 = 1.8$

Thus, the final answer is $1.8$.

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:

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