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

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

$5\times1=5$

Now we multiply:

$8\times5=40$

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:

$0\times4=0$

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:

$6\times4=24$

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

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

$(7+3)=10$

Now let's solve the multiplication problem:

$15\times10=150$

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

$(16-6)=10$

$(7-3)=4$

Now we'll get the exercise:

$10\times9+4$

We'll put 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:

$90+4=94$

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.

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 rules, we must first solve the expression within the parentheses:

$85+5=90$

We should obtain the following expression:

$90:10=9$

We solve the exercise in parentheses:$3\cdot3+5:1=$

We place in parentheses the multiplication and division exercises:

$(3\cdot3)+(5:1)=$

We solve the exercises in parentheses:

$9+5=14$

First, we solve the exercise within the parentheses:

$4\cdot2-3:4=$

We place multiplication and division exercises within parentheses:

$(4\cdot2)-(3:4)=$

We solve the exercises within the parentheses:

$8-\frac{3}{4}=7\frac{1}{4}$

We solve the exercise in parentheses:

$3:9\cdot9-6=$

$\frac{3}{9}\cdot9-6=$

We simplify and subtract:

$3-6=-3$

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

$30+6=36$

Now we solve the exercise

$36:4\times3=$

Since the exercise only involves multiplication and division operations, we solve from left to right:

$36:4=9$

$9\times3=27$

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:

$9-6:(4\cdot3)-1= \\ 9-6:12-1= \\ 9-0.5-1= \\ 7.5$

Therefore, the correct answer is option C.

According to the order of operations, we will first solve the multiplication exercises in parentheses:

$(13\times2)=26$

$(12\times1.5)=18$

Now we will subtract:

$26-18=8$

We begin by simplifying the given expression paying attention to the order of arithmetic operations which states that powers precede multiplication, division precedes addition and subtraction and that parentheses precede all of the above.

Let's keep in mind that in the given expression there are no parentheses or powers. However there are multiplication and division operations, so we will use them as our starting point. After which we will perform the addition and subtraction operations:

$27:3-9\cdot2+5+3= \\ 9-18+5+3=\\ -1$Therefore, the correct answer is option B.