The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression.
We can remember the order using PEMDAS :
Important Notes :
1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.
2. Multiplication does not always come before division. We have to do one by one in the order from left to right.
3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right.
Examples :
16 ÷ 4 x 3 = 4 x 3 = 12
18 - 3 + 6 = 15 + 6 = 21
In the above simplification, we have both division and multiplication. From left to right, we have division first and multiplication next.
So we do division first and multiplication next.
Problem 1 :
Evaluate the given expression for x = 7.
4(x - 4)
Solution :
Substitute 7 for x.
= 4(7 - 4)
Subtract inside the parentheses.
= 4(3)
Multiply.
= 12
Problem 2 :
Evaluate the given expression for x = 7.
4x - 4
Solution :
Substitute 7 for x.
= 4(7) - 4
Multiply.
= 28 - 4
Subtract.
= 24
Problem 3 :
Evaluate the given expression for x = 3 and y = 5.
3x + 2y
Solution :
Substitute 3 for x and 5 for y.
= 3(3) + 2(5)
Multiply.
= 9 + 10
Add.
= 19
Problem 4 :
Evaluate the given expression for x = 9.
x^{2} - x
Solution :
Substitute 9 for each x.
= 9^{2} - 9
Evaluate the exponent.
= 81 - 9
Subtract.
= 72
Problem 5 :
Evaluate the given expression for m = 5 and n = 2.
m^{2} + 2mn^{2}
Solution :
Substitute 5 for m and 2 for n.
= 5^{2} + 2(5)(2)^{2}
Evaluate the exponents.
= 25 + 2(5)(4)
Multiply 2, 5 and 4.
= 25 + 40
Add.
= 65
Problem 6 :
Evaluate the given expression for m = 3.
(2m^{2} + 5m - 7)/2
Solution :
Substitute 3 for m.
= [2(3)^{2} + 5(3) - 7]/2
Evaluate the exponent.
= [2(9) + 5(3) - 7]/2
Multiply.
= [18 + 15 - 7]/2
Add 18 and 15.
= [33 - 7]/2
Subtract 7 from 33.
= 26/2
Divide.
= 13
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