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Lesson

Simplifying numerical expressions

The order of operations are as follows:

  1. First perform all operations inside brackets, starting with the innermost brackets first.
  2. Then evaluate expressions with exponents.
  3. Then do the operations of multiplication and division from left to right.
  4. Then do the operations of addition and subtraction from left to right.
Example 1

Evaluate without a calculator: 3(8 - 3)2 + (-9) ¸ (-3) - 23

Solution

Example 2

Evaluate without a calculator: 250 - 3[2(-32 +2) - 5]

Solution

Example 3

Evaluate:  

Solution

Simplifying algebraic  expressions

The same rules for order of operations that apply to numerical expressions also apply to algebraic expressions. They are:

  1. First perform all operations inside brackets, starting with the innermost brackets first.
  2. Then evaluate expressions with exponents.
  3. Then do the operations of multiplication and division from left to right.
  4. Then do the operations of addition and subtraction from left to right.
Example 1

Simplify:  

Solution

Example 2

Simplify:      

Solution

Example 3

Evaluate     for x =   and y =

Solution (Method 1)

Solution (Method 2)

Activity

Print off a copy of this page and add it to your Math 3103 binder. Then answer the questions in your binder.

A. Simplify the following. Do as many as possible mentally and do not use a calculator:

  1.  4 + 3 x 7 - 2                  2. (2 + 3) x (8 - 3)              3.  6 ¸ 3 x 4 - 1

  4.                       5.                      6.

  7.  3.4 - 5.2 x 0.6 + 1.8      8.  -2.12 + 1.22                   9. (4.8 - 6.7) x 0.8

10.  3[2x - 3(4 - x)]             11. 5 - [(x - 2)(x + 3) + 2x]

12.  -(2x - 1)2                      13.

14.                          15.

B. Evaluate -3x2y(x2 - 2xy + y2)  for:

    1.  x = -2 and y = -1

    2.  x = and y =

    3.  x = -0.3  and y = 0.2

Answers

Test Yourself

A. Simplify the following. Do as many as possible mentally and do not use a calculator:

(1)   -24 ¸ 6 - 2            (2) -24 ¸ (6 - 2)                (3)  -24 - 6 ¸ 2 

(4)  3(4 - 2)2                (5)  3(4 - 22)                     (6) 

(7)                 (8)              (9)  5x - (6 - 3x)

(10)   -4x - 3(x + 1)2                        (11)  (2x - 1)(x + 2)

(12)  3 - (3x - 1)2                             (13)   5[2x - 4(2x - 1)]   

(14)   5x - [(4x + 6) - (x - 2)]           (15)   2 - [3(x - 1)2 - (2 - x)2]

B. Evaluate the following expressions for x =    and y =

(16) -2x - y2            (17)

Answers