EVALUATE VARIABLE EXPRESSIONS INVOLVING INTEGERS
To evaluate a variable expression involving integers, replace the variables in the expression by the given values of the variables and simplify PEMDAS.
PEMDAS is the rule that can be used to simplify or evaluate complicated numerical expressions with more than one binary operation.
P ----> Parentheses
E ----> Exponent
M ----> Multiply
D ----> Divide
A ----> Add
S ----> Subtract
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. Division does not always come before multiplication. We have to do one by one in the order from left to right.
Example 1 :
Evaluate the expression for x = 2.
5 + x
Solution :
= 5 + x
Substitute x = 2.
= 5 + 2
= 7
Example 2 :
Evaluate the expression for x = -1.
-x + 5
Solution :
Substitute x = -1.
= -x + 5
= -(-1) + 5
= 1 + 5
= 6
Example 3 :
Evaluate the expression for p = 3.
p - 6
Solution :
= p - 6
Substitute p = 3.
= 3 - 6
= -3
Example 4 :
Evaluate the expression for r = -2.
-r + 5
Solution :
= -r + 5
Substitute r = -2.
= -(-2) + 5
= 2 + 5
= 7
Example 5 :
Evaluate the expression for m = 0.
m - 5
Solution :
= m - 5
Substitute m = 0.
= 0 - 5
= -5
Example 6 :
Evaluate the expression for t = -4.
5t - 3
Solution :
= 5t - 3
Substitute t = -4.
= 5(-4) - 3
= -20 - 3
= -23
Example 7 :
Evaluate the expression for x = 5 and y = 6.
x + y - 9
Solution :
= x + y - 9
Substitute x = 5 and y = 6.
= 5(-4) - 3
= -20 - 3
= -23
Example 8 :
Evaluate the expression for x = 2 and y = -3.
3x + 2y
Solution :
= 3x + 2y
Substitute x = 2 and y = -3.
= 3(2) + 2(-3)
= 6 - 6
= 0
Example 9 :
Evaluate the expression for m = -1 and n = -2.
-2m + 3n + 5
Solution :
= -2m + 3n + 5
Substitute m = -1 and n = -2.
= -2(-1) + 3(-2) + 5
= 2 - 5 + 5
= 2
Example 10 :
Evaluate the expression for p = 5 and q = 7.
(5/p) + (7/q)
Solution :
= (5/p) + (7/q)
Substitute p = 5 and q = 7.
= (5/5) + (7/7)
= 1 + 1
= 2
Example 11 :
Evaluate the expression for x = 5, y = 8 and z = 6.
(y2 + z) ÷ x
Solution :
= (y2 + x) ÷ x
Substitute x = 5, y = 8 and z = 6.
= (82 + 6) ÷ 5
= (64 + 6) ÷ 5
= 70 ÷ 5
= 14
Example 12 :
Evaluate the expression for p = 6, q = 5 and r = 4.
(pq - 28)2 ÷ r
Solution :
(pq - 28)2 ÷ r
Substitute p = 6, q = 5 and r = 4.
= [(6)(5) - 28]2 ÷ 4
= (30 - 28)2 ÷ 4
= 22 ÷ 4
= 4 ÷ 4
= 1
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