a Note that the innermost parentheses should be calculated before the outermost.
B
b Follow the order of operations, start with the parentheses.
C
c Follow the order of operations, start with the exponent.
D
d Note that you should simplify the expression inside the parentheses first, then follow the order of operations.
A
a See solution.
B
b See solution.
C
c See solution.
D
d See solution.
Practice makes perfect
a When we simplify an expression, we have to consider the order of operations PEMDAS.
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P & - & Parentheses & (first)
E & - & Exponents & (second)
M & - & Multiplication & (third)
D & - & Division & (third)
A & - & Addition & (fourth)
S & - & Subtraction & (fourth)
It is important to notice that multiplication and division have the same priority, as do addition and subtraction. When two operations have the same priority, complete them in the order that they appear, moving from left to right.
The given expression contains two sets of parentheses, one outer pair and one inner pair.
2* (3 (5+2 )-1 )
We start by simplifying the addition in the innermost parentheses.
Now we can proceed with simplifying the remaining parentheses. These contain multiplication and subtraction. Again, we have to consult the order of operations. Multiplication comes before subtraction.
Having simplified the parentheses, the expression now has multiplication, addition, and subtraction. By the order of operations, we have to start with the multiplication. Then we proceed with the addition and subtraction moving from left to right.
c The next expression has an exponent, multiplication, division and addition. Following the order of operations, we begin with the exponent. Then we can proceed with multiplication and division, moving from left to right, before finishing with addition.
d This expression has many operations and might look more difficult, but we still follow the order of operations. We begin by calculating the expression within the parentheses. In these parentheses, we have two different operations. By the order of operations, we begin with the exponent.
Now that the parentheses are simplified, we can continue. There are two multiplication operations. We complete these from left to right. We can then proceed to calculate the addition and subtraction, also from left to right.
