Math Number Sense and Operations — Questions and Answers

Question 1: Evaluate: 3 + 4 × 2 − 1

10 (Correct answer)
13
5
14

Correct answer: 10

Following order of operations (PEMDAS), multiplication is performed first: 4 × 2 = 8, then left to right: 3 + 8 − 1 = 10.

Question 2: Which property is illustrated by: 5 × (3 + 4) = 5 × 3 + 5 × 4?

Commutative Property
Associative Property
Distributive Property (Correct answer)
Identity Property

Correct answer: Distributive Property

The Distributive Property states that a(b + c) = ab + ac, which is exactly what is shown here.

Question 3: What is the absolute value of −17?

−17
17 (Correct answer)
1/17
0

Correct answer: 17

Absolute value represents the distance from zero on the number line, so |−17| = 17.

Question 4: Which of the following is a prime number?

1
51
57
53 (Correct answer)

Correct answer: 53

53 is prime because it has no divisors other than 1 and itself; 51 = 3 × 17, 57 = 3 × 19, and 1 is not prime by definition.

Question 5: What is the least common multiple (LCM) of 6 and 8?

14
24 (Correct answer)
2
48

Correct answer: 24

Since 6 = 2 × 3 and 8 = 2³, the LCM = 2³ × 3 = 24.

Question 6: Evaluate: (−3) × (−4) + (−2)

−14
10 (Correct answer)
14
−10

Correct answer: 10

Two negatives multiplied give a positive: (−3) × (−4) = 12, then 12 + (−2) = 10.

Question 7: What is 2⁵?

10
25
32 (Correct answer)
64

Correct answer: 32

2⁵ means 2 multiplied by itself 5 times: 2 × 2 × 2 × 2 × 2 = 32.

Question 8: Which number is written in correct scientific notation?

23.5 × 10³
2.35 × 10⁴ (Correct answer)
0.235 × 10⁵
235 × 10²

Correct answer: 2.35 × 10⁴

Scientific notation requires the coefficient to be at least 1 and less than 10; 2.35 × 10⁴ = 23,500 and satisfies this condition.

Question 9: Which of the following numbers is divisible by 9?

245
432 (Correct answer)
361
127

Correct answer: 432

A number is divisible by 9 if the sum of its digits is divisible by 9; for 432: 4 + 3 + 2 = 9.

Question 10: What is the greatest common factor (GCF) of 36 and 48?

6
12 (Correct answer)
18
144

Correct answer: 12

36 = 2² × 3² and 48 = 2⁴ × 3, so GCF = 2² × 3 = 12.

Question 11: What is √144?

11
12 (Correct answer)
13
14

Correct answer: 12

12 × 12 = 144, so the square root of 144 is 12.

Question 12: Which of the following is an irrational number?

0.333…
√16
√5 (Correct answer)
7/3

Correct answer: √5

√5 ≈ 2.2360679… is a non-terminating, non-repeating decimal and cannot be expressed as a fraction, making it irrational.

Question 13: Which list correctly orders −3, 0.5, −1.2, and 2 from least to greatest?

−3, −1.2, 0.5, 2 (Correct answer)
−1.2, −3, 0.5, 2
2, 0.5, −1.2, −3
0.5, −1.2, 2, −3

Correct answer: −3, −1.2, 0.5, 2

On the number line, −3 < −1.2 < 0.5 < 2, so the correct order is −3, −1.2, 0.5, 2.

Question 14: Round 3,847 to the nearest hundred.

3,800 (Correct answer)
3,850
3,900
4,000

Correct answer: 3,800

The tens digit is 4 (less than 5), so the hundreds digit stays at 8 and the number rounds down to 3,800.

Question 15: What is 3/4 + 5/6?

8/10
19/12 (Correct answer)
8/24
4/5

Correct answer: 19/12

Converting to a common denominator of 12: 3/4 = 9/12 and 5/6 = 10/12, so 9/12 + 10/12 = 19/12.

Question 16: What is 15% of 80?

10
12 (Correct answer)
14
15

Correct answer: 12

15% of 80 = 0.15 × 80 = 12.

Question 17: The ratio of boys to girls in a class is 3:5. If there are 24 boys, how many girls are there?

32
40 (Correct answer)
8
15

Correct answer: 40

Since 24 boys corresponds to 3 parts, one part = 8; 5 parts (girls) = 5 × 8 = 40.

Question 18: In the number 5,847,392, what is the place value of the digit 4?

Thousands
Ten-thousands (Correct answer)
Hundred-thousands
Hundreds

Correct answer: Ten-thousands

Reading from right to left: ones, tens, hundreds, thousands, ten-thousands — the digit 4 sits in the ten-thousands place.

Question 19: Evaluate: −8 + 15 − 3

4 (Correct answer)
−4
20
10

Correct answer: 4

−8 + 15 = 7, then 7 − 3 = 4.

Question 20: Which fraction is equivalent to 0.625?

3/4
5/8 (Correct answer)
2/3
7/10

Correct answer: 5/8

0.625 = 625/1000; simplifying by dividing numerator and denominator by 125 gives 5/8.

Question 21: Which of the following is NOT an integer?

−5
0
3/1
1/3 (Correct answer)

Correct answer: 1/3

1/3 = 0.333… is a repeating decimal and cannot be expressed as a whole number, so it is not an integer.

Math Number Sense and Operations

Evaluate: 3 + 4 × 2 − 1

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