Parentheses in simple Order of Operations: Addition, subtraction, multiplication and division

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:

$20-2=18$

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 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:

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

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:

$19\times0=0$

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 place the multiplication and division exercise within parentheses:

$(9:3)-(1.5\times2)=$

Now we solve the exercises within parentheses:

$9:3=3$

$1.5\times2=3$

And we obtain the exercise:

$3-3=0$

Given that, according to the rules of the order of operations, parentheses come first, we will first solve the exercise that appears within the parentheses.

$4\times2-\frac{9}{3}=$

We solve the multiplication exercise:

$4\times2=8$

We divide the fraction (numerator by denominator)$\frac{9}{3}=3$

And now the exercise obtained within the parentheses is$8-3=5$

Finally, we divide:$12:5=\frac{12}{5}$

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 expressions in parentheses first:
$4:2\cdot(5+4+6)= \\ 4:2\cdot15$Note that between multiplication and division operations there is no defined precedence for either operation, so we'll calculate the result of the expression obtained in the last stage step by step from left to right (which is the regular order in arithmetic operations), meaning we'll first perform the division operation, as it appears first from the left, and then we'll perform the multiplication operation that comes after it:

$4:2\cdot15 =\\ 2\cdot15 =\\ 30$Therefore the correct answer is answer B.

Let's simplify this expression whilst following the order of operations. Exponents precede multiplication and division, which in turn precede addition and subtraction, and parentheses precede all of the above.

Therefore, we'll start by simplifying the expressions in parentheses first:
$(8-3-1)\cdot4\cdot3= \\ 4\cdot4\cdot3$

We'll continue to calculate the result of the expression obtained in the last step, step by step from left to right (which is the regular order of arithmetic calculations):

$4\cdot4\cdot3 =\\ 16\cdot3 =\\ 48$

Note that since the commutative property applies to multiplication, and in the expression we simplified above there is multiplication between all terms, the order of operations in this calculation doesn't matter (it's not necessary to perform the left multiplication first etc. as we did), however, it is recommended to practice performing operations from left to right since this is the natural order of arithmetic calculations (in the absence of parentheses, or other preceding arithmetic operations according to the order of operations mentioned at the beginning of the solution)

Therefore, the correct answer is answer B.

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

Thus, let's begin by simplifying the expressions within the parentheses, and following this, the multiplication between them.

$(12+2)\cdot(3+5)= \\ 14\cdot8=\\ 112$

Therefore, the correct answer is option C.

Simplify this expression paying attention to the order of arithmetic operations. Exponentiation precedes multiplication whilst division precedes addition and subtraction. Parentheses precede all of the above.

Therefore, let's first start by simplifying the expressions within the parentheses. Then we can proceed to perform the multiplication between them:

$(3+20)\cdot(12+4)=\\ 23\cdot16=\\ 368$

Therefore, the correct answer is option A.

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.

First, we solve the exercise within the parentheses:

$3:4\cdot6+3=$

$\frac{3}{4}\times6+3=$

We multiply:

$\frac{18}{4}+3=$

$4\frac{1}{2}+3=7\frac{1}{2}$

Let's simplify this expression whilst following the order of operations. Exponents precede multiplication and division, which in turn precede addition and subtraction, and parentheses precede all of the above,

Therefore, we'll start by simplifying the expressions inside of the parentheses first:
$(9+7+3)(4+5+3)(7-3-4)= \\ 19\cdot12\cdot0$

Now we'll calculate the multiplication result step by step from left to right, remembering also that multiplying any number by 0 gives a result of 0:

$19\cdot12\cdot0 =\\ 228\cdot0 =\\ 0$

Since the commutative property of multiplication applies, and in the expression we simplified above there is multiplication between all terms, the order of operations in this calculation doesn't matter (it's not necessary to perform the leftmost multiplication first etc. as we did), however, it is recommended to practice performing operations from left to right as this is the natural order of arithmetic operations (in the absence of parentheses, or other preceding arithmetic operations according to the order of operations mentioned at the beginning of this solution)

Therefore, the correct answer is answer B.

Let's simplify this expression whilst following the order of operations. Exponents precede multiplication and division, which in turn precede addition and subtraction, and that parentheses precede all of the above:

Therefore, we'll start by simplifying the expressions inside of the parentheses first:
$(7-4-3)(15-6-2)+3\cdot5\cdot2= \\ 0\cdot7+3\cdot5\cdot2=$

We'll continue to perform the multiplications in the two terms we obtained in the expression in the last stage, this is because multiplication comes before addition. In each term we'll perform the multiplications step by step from left to right, also remember that multiplying any number by 0 gives a result of 0:

$0\cdot7+3\cdot5\cdot2= \\ 0+15\cdot2= \\ 30$

Note that since the commutative property of multiplication applies, and in the second term from the left in the expression we simplified above there is multiplication between all terms, the order of operations in this calculation doesn't matter (it's not necessary to perform the left multiplication first etc. as we did), however it is recommended to practice performing operations from left to right as this is the natural order of arithmetic operations (in the absence of parentheses, or other preceding arithmetic operations according to the known order of operations mentioned at the beginning of this solution)

Therefore the correct answer is answer D.

Let's simplify this expression whilst making sure to follow the order of operations. Exponents precede multiplication and division, which in turn precede addition and subtraction, and that parentheses precede all of the above.

Therefore, we'll start by simplifying the expressions inside of the parentheses first:
$(4+7+3):2:3= \\ 14:2:3$

We'll continue and calculate the result of the expression obtained in the last stage, step by step from left to right (which is the regular order of arithmetic operations):

$14:2:3 =\\ 7:3 =\\ \frac{7}{3}=\\ 2\frac{1}{3}$

In the second stage where we performed the last division operation, we wrote the result as an improper fraction (a fraction where the numerator is greater than the denominator) given that this operation's result is not a whole number. Later, we converted it to a mixed number by finding the whole numbers and adding the remainder divided by the divisor (3),

Therefore, the correct answer is answer A.

We simplify this expression by observing the order of arithmetic operations which states that exponentiation precedes multiplication, division precedes addition and subtraction, and that parentheses precede everything else.

Therefore, we first start by simplifying the expression within the parentheses. We then multiply the result of the expression within the parentheses by the term that multiplies it:

$(40+70+35-7)\cdot9= \\ 138\cdot9=\\ 1242$Therefore, the correct answer is option C.