SIMPLIFY NUMERICAL EXPRESSIONS

Simplify, follow the order of operations.

Problem 1 :

(6 + 3) × 4

Solution :

Expression          Evaluation          Operation

(6 + 3) × 4           = (6 + 3) × 4        Parentheses

                             = 9 × 4                Multiplication

                             = 36                     Result.

Problem 2 :

(7 - 5) × 6

Solution :

Expression          Evaluation          Operation

(7 - 5) × 6            = (7 - 5) × 6        Parentheses

                             = 2 × 6                Multiplication

                             = 12                     Result

Problem 3 :

(15 + 3) ÷ 6

Solution :

Expression          Evaluation          Operation

(15 + 3) ÷ 6         = (15 + 3) ÷ 6      Parentheses

                             = 18 ÷ 6              Divide

                             = 3                       Result

Problem 4 :

8 + (5 × 3)

Solution :

Expression          Evaluation          Operation

8 + (5 × 3)         = 8 + (5 × 3)         Parentheses

                       = 8 + 15                Add

                           = 23                     Result

Problem 5 :

9 - (21 ÷ 7)

Solution :

Expression          Evaluation          Operation

9 - (21 ÷ 7)         = 9 - (21 ÷ 7)         Parentheses

                             = 9 - 3                  Subtract

                             = 6                        Result

Problem 6 :

3 × (12 - 8)

Solution :

Expression          Evaluation          Operation

3 × (12 - 8)         = 3 × (12 - 8)         Parentheses

                             = 3 × 4                 Multiplication

                     = 12                      Result

Problem 7 :

7 + (6 × 3) - 10

Solution :

Expression              Evaluation                  Operation

7 + (6 × 3) - 10        = 7 + (6 × 3) - 10         Parentheses

                         = 7 + 18 - 10                 Add

                                = 25 - 10                     Subtract 

                              = 15                              Result

Problem 8 :

30 - (3 × 3) + 4

Solution :

Expression              Evaluation                  Operation

30 - (3 × 3) + 4        = 30 - (3 × 3) + 4         Parentheses

                         = 30 - 9 + 4                 Add

                           = 30 - 13                  Subtract

                           = 17                         Result

Problem 9 :

(18 - 3) ÷ 5

Solution :

Expression          Evaluation          Operation

(18 - 3) ÷ 5         = (18 - 3) ÷ 5        Parentheses

                             = 15 ÷ 5              Divide

                             = 3                       Result

Problem 10 :

6 + 5 × 4 - 7

Solution :

Expression              Evaluation                  Operation

6 + 5 × 4 - 7             = 6 + 5 × 4 - 7           Multiplication

                                 = 6 + 20 - 7                 Add

                                 = 26 - 7                      Subtract

                                = 19                              Result

Problem 11 :

18 + 9 × 7 - 13

Solution :

Expression                  Evaluation                  Operation

18 + 9 × 7 - 13          = 18 + 9 × 7 - 13        Multiplication

                                 = 18 + 63 - 13             Add

                                  = 81 - 13                      Subtract

                                    = 68                            Result

Problem 12 :

5 × (6 + 3) × 2

Solution :

Expression              Evaluation                  Operation

5 × (6 + 3) × 2         = 5 × (6 + 3) × 2         Parentheses

                                 = 5 × 9 × 2                 Multiplication

                                 = 45 × 2                    Multiplication

                                = 90                              Result

Problem 13 :

The summit elevation of a volcano is the elevation of the top of the volcano relative to sea level. The summit elevation of the volcano Kilauea in Hawaii is 1277 meters. The summit elevation of the underwater volcano Loihi in the Pacific Ocean is −969 meters. Which summit is closer to sea level?

Solution :

Above the sea level, the height = +1277 meters

= |1277|

= 1277 meters

Underwater the height = -969 meters

= |-969|

= 969 meters

Comparing these two heights, underwater volcano Loihi in the Pacific Ocean is closer to the sea level.

Problem 14 :

The list shows four bank account transactions in July. Find the change C in the account balance.

Solution :

By finding the sum of transaction, we get

= -40 + 50 + 75 - 50

= -90 + 125

= 35

Because C = 35, the account balance increased $35 in July.

Problem 15 :

The temperature is −3°F at 7:00 a.m. During the next 4 hours, the temperature increases 21°F. What is the temperature at 11:00 a.m.?

Solution :

Temperature at 7 am = -3°F

At 11 am, the temperature increases =  21°F

= -3 + 21

= 18°F

So, the temperature at 11 am is 18°F.

Problem 16 :

Your bank account has a balance of −$12. You deposit $60. What is your new balance?

Solution :

Old balance = -$12

Amount depositing = $60

New balance = -12 + 60

= 48

So, the required new balance is $48.

Problem 17 :

A lithium atom has positively charged protons and negatively charged electrons. The sum of the charges represents the charge of the lithium atom. Find the charge of the atom.

Solution :

Positively charged protons = +1 + 1 + 1

= +3

Negatively charged protons = -1 - 1 - 1

= -3

Charge of atom = +3 + (-3)

= 0

Problem 18 :

Evaluate the expression when a = 4, b = −5, and c = −8.

i) a + b

ii) −b + c

iii)  ∣ a + b + c ∣

Solution :

i) a + b

= 4 + (-5)

= -1

ii) −b + c

= -(-5) + (-8)

= 5 - 8

= -3

iii)  ∣ a + b + c ∣

= |4 + (-5) + (-8)|

= |4 - 5 - 8|

= |4 - 13|

= | -11|

= 11