NYSTCE ATAS Mathematical Concepts and Operations 2 — Questions and Answers
Question 1: A student is simplifying the fraction 18/24. What is the greatest common factor (GCF) of 18 and 24?
- 3
- 6 (Correct answer)
- 9
- 12
Correct answer: 6
The GCF of 18 and 24 is 6, since 6 is the largest number that divides evenly into both.
Question 2: Which of the following best describes a prime number?
- A number divisible by 2
- A number with exactly two factors: 1 and itself (Correct answer)
- A number that is always odd
- A number divisible only by even numbers
Correct answer: A number with exactly two factors: 1 and itself
A prime number has exactly two distinct factors: 1 and itself.
Question 3: A teaching assistant needs to help a student convert 0.75 to a fraction. What is the correct simplified form?
- 75/10
- 3/4 (Correct answer)
- 7/5
- 15/20
Correct answer: 3/4
0.75 = 75/100, which simplifies to 3/4 by dividing numerator and denominator by 25.
Question 4: A student counts 12 red cubes and 8 blue cubes. What is the ratio of red to blue cubes in simplest form?
- 12:8
- 3:2 (Correct answer)
- 2:3
- 4:3
Correct answer: 3:2
12:8 simplifies to 3:2 by dividing both values by the GCF of 4.
Question 5: Which number sentence illustrates the commutative property of addition?
- (3 + 4) + 5 = 3 + (4 + 5)
- 3 + 4 = 4 + 3 (Correct answer)
- 3 × (4 + 5) = 3×4 + 3×5
- 3 + 0 = 3
Correct answer: 3 + 4 = 4 + 3
The commutative property states that the order of addends does not change the sum: a + b = b + a.
Question 6: A student earns $7.50 per hour babysitting. How much does she earn after working 4 hours?
- $28.00
- $30.00 (Correct answer)
- $11.50
- $32.50
Correct answer: $30.00
7.50 × 4 = $30.00.
Question 7: Which of the following is an example of an improper fraction?
- 3/7
- 1/2
- 9/4 (Correct answer)
- 2/5
Correct answer: 9/4
An improper fraction has a numerator greater than or equal to its denominator; 9/4 qualifies because 9 > 4.
NYSTCE ATAS Mathematical Concepts and Operations 2
A student is simplifying the fraction 18/24.
What is the greatest common factor (GCF) of 18 and 24?