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

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.

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 $1.8$.

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.

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 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 these,

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

We'll continue and perform the multiplications in the two terms we got 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 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:
$(8-3-1)\cdot4\cdot3= \\ 4\cdot4\cdot3$

We'll continue and 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.

First, we solve the exercise within the parentheses:

$3:4\cdot6+3=$

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

We multiply:

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

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

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 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.

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:
$(4+7+3):2:3= \\ 14:2:3$

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) because this operation's result doesn't give 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.

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 these,

Therefore, we'll start by simplifying the expressions in 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:

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

Note that 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 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 these,

Therefore, we'll start by simplifying the expressions in parentheses first:
$(\frac{1}{4}+\frac{7}{4}-\frac{5}{4}-\frac{1}{4})\cdot10:7:5=\\ \frac{1+7-5-1}{4}\cdot10:7:5 =\\ \frac{2}{4}\cdot10:7:5 = \\ \frac{1}{2}\cdot10:7:5$

We calculated the expression inside the parentheses by adding the fractions, which we did by creating one fraction using the common denominator (4) which in this case is the denominator in all fractions, so we only added/subtracted the numerators (according to the fraction sign), then we reduced the resulting fraction,

We'll continue and note that between multiplication and division operations there is no defined precedence for either operation, therefore we'll calculate the result of the expression obtained in the last step step by step from left to right (which is the regular order in arithmetic operations), meaning we'll first perform the multiplication operation, which is the first from the left, and then we'll perform the division operation that comes after it, and so on:

$\frac{1}{2}\cdot10:7:5 =\\ \frac{1\cdot10}{2}:7:5 =\\ \frac{10}{2}:7:5 =\\ 5:7:5 =\\ \frac{5}{7}:5$

In the first step, we performed the multiplication of the fraction by the whole number, remembering that multiplying by a fraction means multiplying by the fraction's numerator, then we simplified the resulting fraction and reduced it (effectively performing the division operation that results from it), in the final step we wrote the division operation as a simple fraction, since this division operation yields a non-whole result,

We'll continue and to perform the final division operation, we'll remember that dividing by a number is the same as multiplying by its reciprocal, and therefore we'll replace the division operation with multiplication by the reciprocal:

$\frac{5}{7}:5 =\\ \frac{5}{7}\cdot\frac{1}{5}$

In this case we preferred to multiply by the reciprocal because the divisor in the expression is a fraction and it's more convenient to perform multiplication between fractions,

We will then perform the multiplication between the fractions we got in the last step, while remembering that multiplication between fractions is performed by multiplying numerator by numerator and denominator by denominator while maintaining the fraction line, then we'll simplify the resulting expression by reducing it:

$\frac{5}{7}\cdot\frac{1}{5} =\\ \frac{5\cdot1}{7\cdot5}=\\ \frac{5}{35}=\\ \frac{1}{7}$

Let's summarize the solution steps, we got that:

$(\frac{1}{4}+\frac{7}{4}-\frac{5}{4}-\frac{1}{4})\cdot10:7:5=\\ \frac{1+7-5-1}{4}\cdot10:7:5 =\\ \frac{1}{2}\cdot10:7:5 =\\ 5:7:5 =\\ \frac{5}{7}\cdot\frac{1}{5} =\\ \frac{1}{7}$

Therefore the correct answer is answer B.