SIMPLIFY NUMERICAL EXPRESSIONS WORKSHEET

Simplify, follow the order of operations.

Problem 1 :

(6 + 3) × 4

Solution

Problem 2 :

(7 - 5) × 6

Solution

Problem 3 :

(15 + 3) ÷ 6

Solution

Problem 4 :

8 + (5 × 3)

Solution

Problem 5 :

9 - (21 ÷ 7)

Solution

Problem 6 :

3 × (12 - 8)

Solution

Problem 7 :

7 + (6 × 3) - 10

Solution

Problem 8 :

30 - (3 × 3) + 4

Solution

Problem 9 :

(18 - 3) ÷ 5

Solution

Problem 10 :

6 + 5 × 4 - 7

Solution

Problem 11 :

18 + 9 × 7 - 13

Solution

Problem 12 :

5 × (6 + 3) × 2

Solution

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

Problem 14 :

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

Solution

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

Problem 16 :

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

Solution

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

Problem 18 :

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

i) a + b

ii) −b + c

iii)  ∣ a + b + c ∣

Solution

Problem 1 :

5 + [6 + (7 × 2)] ÷ 5

Solution

Problem 2 :

4 × [(4 × 3) ÷ 2] × 7

Solution

Problem 3 :

[(2 × 3) + (11 – 5)] ÷ 3

Solution

Problem 4 :

19 – [{3 × 7} – {9 ÷ 3}] + 14

Solution

Problem 5 :

30 ÷ 3 ÷ 5

Solution

Problem 6 :

18 ÷ 3 + 11 × 2

Solution

Problem 7 :

7 × 4 – 3 × 5

Solution

Problem 8 :

8 + 6 ÷ 3 × 4

Solution

Problem 9 :

3 × 4 + 5²

Solution

Problem 10 :

4 × 3² – (3 + 2)²

Solution

Problem 11 :

(5 - 2)² – 2²

Solution

Problem 12 :

(15 – 3²) ÷ 3

Solution

Problem 13 :

5 × (2² + 2) + 6

Solution

Problem 14 :

35 – 3 × 2³ + 7

Solution

Problem 15 :

(3 × 7 – 5)/2

Solution

Problem 16 :

[3 × (7 – 5)]/2

Solution

Problem 17 :

(56 ÷ 8 – 7)/(56 ÷ (8 – 7)

Solution

Problem 18 :

[25 – (16 – 11)]/[(12 ÷ 4 + 2)]

Solution

Problem 19 :

Evaluate the expression −8x + 5 − 2x − 4 + 5x when x = 2 before and after simplifying. Which method do you prefer? Explain

Solution

Problem 20 :

Find the value of 2x − 1 when x + 6 = 2.

Solution

Problem 21 :

A class of 144 students voted for a class president. Three-fourths of the students voted for you. Of the students who voted for you, 5/9 are female. How many female students voted for you?

a) 50      b)  60     c) 80      d) 108

Solution

Evaluate the following numerical expression.

Problem 1 :

6 x 8 - 18 ÷ (2 + 4)

Solution

Problem 2 :

10 ÷ 5 + 20 ÷ (4 + 1)

Solution

Problem 3 :

5 + (2 x 10 - 5) - 6

Solution

Problem 4 :

18 - (15 ÷ 3 + 4) + 1

Solution

Problem 5 :

(2 x 3 - 4) + (33 ÷ 11 + 5)

Solution

Problem 6 :

(18 ÷ 3 + 3) ÷ (4 x 4 - 7)

Solution

Problem 7 :

(50 ÷ 5 + 6) - (8 x 2 - 4)

Solution

Problem 8 :

(10x3-20) + 3(9÷3+2)

Solution

Problem 9 :

(7-3x2) ÷ (8÷4-1)

Solution

Problem 10 :

(5 + 3) x 2+10 ÷ (8 - 3)

Solution

Problem 11 :

Carbon-14 dating is used by scientists to determine the age of a sample.

a. The amount C (in grams) of a 100-gram sample of carbon-14 remaining after t years is represented by the equation C = 100(0.99988)^t. Use a calculator to find the amount of carbon-14 remaining after 4 years.

b. What percent of the carbon-14 remains after 4 years?

Solution

Problem 12 :

The frequency (in vibrations per second) of a note on a piano is represented by the equation F = 440(1.0595)ⁿ, where n is the number of notes above A-440. Each black or white key represents one note.

a. How many notes do you take to travel from A-440 to A?

b. What is the frequency of A?

c. Describe the relationship between the number of notes between A-440 and A and the frequency of the notes

Solution

Problem 13 :

The expression 15a + 12c is the cost (in dollars) of admission at an amusement park for a adults and c children. Find the total cost for 5 adults and 10 children.

Solution

Problem 14 :

The expression p − 15 is the amount you pay after using the coupon on a purchase of p dollars. How much do you pay for a purchase of $83?

Solution