Arithmetic Simulator

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Test your knowledge of Arithmetic with 40 multiple-choice questions. The simulator covers numbers and operations, rational numbers and proportionality, percentages, powers, divisibility, scientific notation, and numerical sequences.

Read each question carefully, select one answer, and check your score at the end. You can then review the correct answers and the procedure for each exercise.

Instructions

• Select only one answer for each question.
• Work through the calculations before choosing your answer.
• Try to complete the simulator without using a calculator.
• When you finish, click the button to see your result.
• Then review the answers and procedures to identify the topics you need to reinforce.

Block 1. Numbers and Operations

1. Which of the following numbers belongs to the set of natural numbers?

A) −5 B) 0 C) 3 D) −2

2. What is the result of −7 + 12?

A) −19 B) −5 C) 5 D) 19

3. What is the result of (−6)(−4)?

A) −24 B) 10 C) −10 D) 24

4. What is the result of 18 ÷ (−3)?

A) −6 B) 6 C) −15 D) 15

5. Which property is illustrated by 7 + 4 = 4 + 7?

A) Associative B) Commutative C) Distributive D) Identity element

6. Where is −4 located on the number line in relation to −1?

A) To the right B) At the same position C) To the left D) They cannot be compared

7. What is the result of |−15|?

A) −15 B) 0 C) 15 D) −1

Block 2. Rational Numbers and Proportionality

8. Which of the following fractions is equivalent to 3/4?

A) 6/12 B) 9/12 C) 8/12 D) 12/20

9. What is the result of 1/2 + 1/4?

A) 2/6 B) 1/6 C) 3/4 D) 2/4

10. What is the result of 3/5 × 10?

A) 3 B) 6 C) 15 D) 30

11. Which decimal number represents the fraction 7/10?

A) 0.07 B) 0.7 C) 7.0 D) 0.17

12. Which number is greater?

A) 0.45 B) 0.405 C) 0.054 D) 0.045

13. If 3 notebooks cost $45, how much do 5 notebooks cost at the same unit price?

A) $60 B) $65 C) $75 D) $90

14. If 4 liters of paint cover 28 m², how many square meters can 7 liters cover at the same rate?

A) 35 m² B) 42 m² C) 49 m² D) 56 m²

Block 3. Proportionality and Percentages

15. If 6 people complete a job in 8 days, how many days would 12 people need, working at the same rate?

A) 2 days B) 4 days C) 8 days D) 16 days

16. What is 20% of 250?

A) 20 B) 40 C) 50 D) 75

17. A product costs $800 and has a 15% discount. What is the price after the discount?

A) $680 B) $700 C) $720 D) $785

18. An item costs $500 and increases by 12%. What is its new price?

A) $512 B) $550 C) $560 D) $612

19. If 8 workers complete a task in 6 days, how many days would 4 workers need, working at the same rate?

A) 3 days B) 6 days C) 12 days D) 24 days

20. In a proportion, if 5/8 = x/40, what is the value of x?

A) 20 B) 25 C) 30 D) 32

Block 4. Powers, Roots, and Operations

21. What is the result of 2⁵?

A) 10 B) 16 C) 25 D) 32

22. What is the result of 3² × 3³?

A) 27 B) 81 C) 243 D) 729

23. What is the value of √144?

A) 10 B) 11 C) 12 D) 14

24. What is the result of 5 + 3 × 4?

A) 32 B) 20 C) 17 D) 12

25. What is the result of (18 − 6) ÷ 3 + 4?

A) 6 B) 8 C) 10 D) 12

26. What is the result of 2³ + 4²?

A) 20 B) 24 C) 26 D) 32

27. What is the result of 36 ÷ 6 + 2 × 5?

A) 16 B) 20 C) 40 D) 50

Block 5. Divisibility

28. Which of the following numbers is divisible by 3?

A) 124 B) 135 C) 142 D) 151

29. Which of the following numbers is prime?

A) 21 B) 27 C) 29 D) 33

30. What is the prime factorization of 60?

A) 2² × 3 × 5 B) 2 × 3² × 5 C) 2² × 3² × 5 D) 2 × 3 × 5

31. What is the LCM of 6 and 8?

A) 12 B) 18 C) 24 D) 48

32. What is the GCF of 24 and 36?

A) 6 B) 8 C) 12 D) 18

33. Which of the following numbers is divisible by 5?

A) 124 B) 237 C) 340 D) 418

Block 6. Representation and Patterns

34. Which of the following expressions is correctly written in scientific notation?

A) 45 × 10⁴ B) 4.5 × 10⁵ C) 0.45 × 10⁶ D) 450 × 10³

35. How is 0.00072 written in scientific notation?

A) 7.2 × 10⁻⁴ B) 7.2 × 10⁻³ C) 72 × 10⁻⁵ D) 0.72 × 10⁻³

36. What is the result of 3.5 × 10⁴?

A) 350 B) 3,500 C) 35,000 D) 350,000

37. What is the next term in the sequence 4, 7, 10, 13, ...?

A) 15 B) 16 C) 17 D) 18

38. What is the next term in the sequence 2, 6, 18, 54, ...?

A) 108 B) 126 C) 162 D) 216

39. What is the next term in the sequence 1, 4, 9, 16, 25, ...?

A) 30 B) 32 C) 36 D) 49

40. What is the next term in the sequence 2, 5, 10, 17, 26, ...?

A) 35 B) 36 C) 37 D) 38

Answers and Procedures

This second section allows you to check each answer and review the procedure. If you completed the simulator first, use this section to identify the topics you need to reinforce.

1. Correct answer: C) 3

Natural numbers are numbers used for counting. The number 3 belongs to this set.

2. Correct answer: C) 5

−7 + 12 = 5

3. Correct answer: D) 24

The product of two negative numbers is positive: (−6)(−4) = 24.

4. Correct answer: A) −6

18 ÷ (−3) = −6.

5. Correct answer: B) Commutative

The commutative property allows the order of the addends to be changed without changing the result: 7 + 4 = 4 + 7.

6. Correct answer: C) To the left

On the number line, −4 is to the left of −1 because −4 < −1.

7. Correct answer: C) 15

Absolute value represents the distance of a number from zero: |−15| = 15.

8. Correct answer: B) 9/12

Multiply the numerator and denominator of 3/4 by 3: 3/4 = 9/12.

9. Correct answer: C) 3/4

1/2 = 2/4. Therefore: 2/4 + 1/4 = 3/4.

10. Correct answer: B) 6

(3/5) × 10 = 30/5 = 6.

11. Correct answer: B) 0.7

7/10 = 0.7.

12. Correct answer: A) 0.45

0.45 = 0.450. Since 0.450 > 0.405, 0.45 is the greatest number among the choices.

13. Correct answer: C) $75

Unit price: 45 ÷ 3 = 15. For 5 notebooks: 5 × 15 = 75.

14. Correct answer: C) 49 m²

Coverage per liter: 28 ÷ 4 = 7 m² per liter. For 7 liters: 7 × 7 = 49 m².

15. Correct answer: B) 4 days

This is an inverse proportion: 6 × 8 = 48. Then: 48 ÷ 12 = 4 days.

16. Correct answer: C) 50

20% of 250: 250 × 0.20 = 50.

17. Correct answer: A) $680

Discount: 800 × 0.15 = 120. Final price: 800 − 120 = 680.

18. Correct answer: C) $560

Increase: 500 × 0.12 = 60. New price: 500 + 60 = 560.

19. Correct answer: C) 12 days

Total work: 8 × 6 = 48 worker-days. With 4 workers: 48 ÷ 4 = 12 days.

20. Correct answer: B) 25

5/8 = x/40. Cross multiplication: 8x = 5 × 40. 8x = 200. x = 25.

21. Correct answer: D) 32

2⁵ = 2 × 2 × 2 × 2 × 2 = 32.

22. Correct answer: C) 243

When multiplying powers with the same base, add the exponents: 3² × 3³ = 3⁵. Then: 3⁵ = 243.

Result: 243

23. Correct answer: C) 12

12 × 12 = 144. Therefore: √144 = 12.

24. Correct answer: C) 17

First perform the multiplication: 3 × 4 = 12. Then: 5 + 12 = 17.

25. Correct answer: B) 8

First: 18 − 6 = 12. Then: 12 ÷ 3 = 4. Finally: 4 + 4 = 8.

26. Correct answer: B) 24

2³ = 8. 4² = 16. Therefore: 8 + 16 = 24.

27. Correct answer: A) 16

First perform division and multiplication: 36 ÷ 6 = 6. 2 × 5 = 10. Then: 6 + 10 = 16.

28. Correct answer: B) 135

A number is divisible by 3 if the sum of its digits is divisible by 3. 1 + 3 + 5 = 9. Since 9 is divisible by 3, 135 is also divisible by 3.

29. Correct answer: C) 29

29 has only two positive divisors: 1 and 29. Therefore, it is a prime number.

30. Correct answer: A) 2² × 3 × 5

60 = 2 × 30

60 = 2 × 2 × 15

60 = 2² × 3 × 5.

31. Correct answer: C) 24

Multiples of 6: 6, 12, 18, 24...

Multiples of 8: 8, 16, 24...

The least common positive multiple is 24.

32. Correct answer: C) 12

Common divisors of 24 and 36 include: 1, 2, 3, 4, 6, and 12. The greatest is 12.

33. Correct answer: C) 340

A number is divisible by 5 when it ends in 0 or 5. 340 ends in 0, so it is divisible by 5.

34. Correct answer: B) 4.5 × 10⁵

In scientific notation, the coefficient must be greater than or equal to 1 and less than 10. 45 × 10⁴ can be written as: 4.5 × 10⁵.

35. Correct answer: A) 7.2 × 10⁻⁴

Move the decimal point four places to the right to obtain 7.2. Because the original number is less than 1, the exponent is negative: 0.00072 = 7.2 × 10⁻⁴.

36. Correct answer: C) 35,000

3.5 × 10⁴ = 3.5 × 10,000 = 35,000.

37. Correct answer: B) 16

The differences are constant: 7 − 4 = 3

10 − 7 = 3

13 − 10 = 3

Therefore: 13 + 3 = 16.

38. Correct answer: C) 162

Each term is obtained by multiplying by 3: 2 × 3 = 6

6 × 3 = 18

18 × 3 = 54

54 × 3 = 162.

39. Correct answer: C) 36

The sequence corresponds to the squares of the natural numbers: 1², 2², 3², 4², 5²...

The next term is: 6² = 36.

40. Correct answer: C) 37

Observe the differences: 5 − 2 = 3

10 − 5 = 5

17 − 10 = 7

26 − 17 = 9

The differences increase by 2 each time. The next difference is 11.

Therefore: 26 + 11 = 37.

Result Interpretation

36–40 correct answers: solid mastery of the assessed content.

30–35 correct answers: good overall mastery; some procedures should be reinforced.

24–29 correct answers: additional practice is recommended in several areas.

0–23 correct answers: it is recommended to reinforce Arithmetic fundamentals before moving forward.