How to find order of operations
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SAT Math › How to find order of operations
Explanation
When there's multiplication and division, they have the same priority. We will work from left to right.
Solve:
Explanation
In PEMDAS, division and multiplication comes before addition and subtraction. Therefore,
Explanation
In PEMDAS, we have parantheses so those come first.
(11)(4 – 3)2 – (22 + 6) = ?
–53
1
2
111
24
Explanation
The answer is 1.
The correct order of operations is parenthesis, exponents, multiplication and division, then addition and subraction.
(11) * (4 – 3)2 – (22 + 6)
(11) * (1)2 – (4 + 6)
(11) * (1) – (10)
(11) – (10) = 1
For all positive integers, let a ★b be defined by a ★b = a b 2. Which of the following is equal to 8★2?
2★4
4★2
6★3
3★6
1★32
Explanation
To solve this problem, we first evaluate 8★2 and then see which of the answer choices is equal to the resulting number. Using the definition of ★, we see that 8★2 = 8(22) = 8(4) = 32. The only answer choice that is equivalent to 32 is 2★4, which evaluates to 2(42) = 32.
(Tip: If we quickly scan the answer choices by squaring the number on the right of the symbol, we immediately see that 3★6 and 1★32 are too big to be 32, even before being multiplied by any of the integers on the left of the symbol.)
Evaluate (√4 + √4)2
4
8
16
6
40
Explanation
The square root of 4 is 2. 2 + 2 = 4. Four squared is 16.
Solve:
Explanation
In PEMDAS, we will apply the parentheses from left to right. Then we apply the exponent and addition inside the parentheses. Finally, we do division.
Therefore,
Consider the function:
What is the value of 
–17
17
–49
–33
It is impossible to square a negative number.
Explanation
Explanation
In PEMDAS, the paranthesis comes first followed by the exponent. We have subtraction so the difference is 
Consider the expression
If the values of all of the variables are known, which operation is carried out third?
Multiplication
Division
Squaring
Addition
Subtraction
Explanation
The order of operations dictates that any operations within grouping symbols, such as parentheses, be carried out first; in this expression. There are two expressions - an exponentiation (squaring) and an addition - that fall between the parentheses; by the order of operations, the squaring is carried out, then the addition.
This leaves a multiplication, a division, and a subtraction. Multiplication and division have precedence over subtraction; since the multiplication appears first in left-to-right order, the multiplication is carried out next. This makes multiplication the correct response.