ORDER OF OPERATIONS WITH POSITIVE AND NEGATIVE NUMBERS

To evaluate expressions that involve more than one operation, we will use a set of rules called the order of operations.

PEMDAS is the rule that can be used to simplify or evaluate complicated numerical expressions with more than one  operation.

Note :

In some expressions, if there is multiplication and division, we have to do the operations one by one in the order from left to right.

Problem 1 :

((-8) × 7) ÷ ((-2)² + 5 - 10)³

Solution :

Evaluate within parentheses.

= (-56 ÷ (4 + 5 - 10))³

= (-56 ÷ (9 - 10)³)

= (-56 ÷ (-1)³)

= (-56 ÷ (-1))

= 56

Problem 2 :

((-10)² - 10²) ÷ (5 + (-3)) × 3

Solution :

Evaluate within parentheses.

= (100 - 100) ÷ (5 - 3) × 3 

Simplifying the terms inside the bracket.

= 0 ÷ (-2) × 3

Doing division, 

= 0 × 3

= 0

Problem 3 :

(3 + (-3)) × ((-4) - 6) ÷ ((-5)² + (-6))

Solution :

Evaluate within parentheses.

= (3 - 3) × (-4 - 6) ÷ (25 - 6)

= 0 × (-10) ÷ (19)

= 0  ÷ 19

= 0

Problem 4 :

(8 + (-7) - 6)  ÷ ((4 × (-9)) ÷ (-6)²)

Solution :

Evaluate within parentheses.

= (8 - 7 - 6) ÷ (-36 ÷ 36)

= (8 - 13) ÷ (-1)

= -5 ÷ (-1)

= 5

Problem 5 :

((-8) × (-5)) ÷ ((-2)³ - (-3) + 7)³

Solution :

Evaluate within parentheses.

= 40 ÷ (-8 + 3 + 7)³

= 40 ÷ (-5 + 7)³

= 40 ÷ (2)³

= 40 ÷ 8

= 5

Problem 6 :

(-9) - (-5)² + (-7) × (((-8) ÷ 8) × 6

Solution :

Evaluate within parentheses.

= -9 - 25 - 7 × -1 × 6

= -34 + 7 × 6

= -34 + 42

= 8

Problem 7 :

3 + -7 × 2

Solution:

Problem 8 :

-2 - 3 × - 4

Solution:

Problem 9 :

-4 - 18 ÷ 3

Solution:

Problem 10 :

(5 - 10) × (3 - 5)

Solution:

Problem 11 :

-10 + 2 × -4

Solution:

Problem 12 :

3 × -4 + -5 × -2

Solution:

Problem 13 :

(8 - 12) × 3 - 7

Solution:

Problem 14 :

8 - 12 × (3 - 7)

Solution:

Problem 15 :

8 - 12 × 3 - 7

Solution:

Problem 16 :

7 - 2 × -3 + 4 × -5

Solution: