Praxis Core Math Number Properties Quiz

1. Which of the following is a prime number?

51

57

61

65

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Among the given options, 61 is the only number that meets this criterion, as it cannot be divided evenly by any other numbers besides 1 and 61.

Explanation

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Among the given options, 61 is the only number that meets this criterion, as it cannot be divided evenly by any other numbers besides 1 and 61.

2. What is the greatest common factor (GCF) of 48 and 64?

8

12

16

32

To find the greatest common factor (GCF) of 48 and 64, we can list the factors of each number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, while the factors of 64 are 1, 2, 4, 8, 16, 32, 64. The largest factor they share is 16.

Explanation

To find the greatest common factor (GCF) of 48 and 64, we can list the factors of each number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, while the factors of 64 are 1, 2, 4, 8, 16, 32, 64. The largest factor they share is 16.

3. Which number is divisible by both 3 and 4?

26

36

42

50

To determine divisibility by both 3 and 4, a number must meet the criteria for each. For 3, the sum of the digits must be divisible by 3, and for 4, the last two digits must form a number divisible by 4. The number 36 meets both conditions, as 3 + 6 = 9 (divisible by 3) and 36 is divisible by 4.

Explanation

To determine divisibility by both 3 and 4, a number must meet the criteria for each. For 3, the sum of the digits must be divisible by 3, and for 4, the last two digits must form a number divisible by 4. The number 36 meets both conditions, as 3 + 6 = 9 (divisible by 3) and 36 is divisible by 4.

4. Simplify: 3/4 + 5/8 = ____

To add the fractions 3/4 and 5/8, first convert 3/4 to a fraction with a denominator of 8, which is 6/8. Then, add 6/8 and 5/8 to get 11/8. This fraction can be expressed as a mixed number, but 11/8 is the simplified result.

Explanation

To add the fractions 3/4 and 5/8, first convert 3/4 to a fraction with a denominator of 8, which is 6/8. Then, add 6/8 and 5/8 to get 11/8. This fraction can be expressed as a mixed number, but 11/8 is the simplified result.

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5. What is the least common multiple (LCM) of 6 and 9?

18

27

36

54

To find the least common multiple (LCM) of 6 and 9, identify the smallest multiple that both numbers share. The multiples of 6 are 6, 12, 18, 24, etc., and the multiples of 9 are 9, 18, 27, etc. The smallest common multiple is 18, making it the LCM.

Explanation

To find the least common multiple (LCM) of 6 and 9, identify the smallest multiple that both numbers share. The multiples of 6 are 6, 12, 18, 24, etc., and the multiples of 9 are 9, 18, 27, etc. The smallest common multiple is 18, making it the LCM.

6. The sum of two even numbers is always ____

The sum of two even numbers is always even because even numbers can be expressed as 2n, where n is an integer. When you add two even numbers (2n + 2m), the result is 2(n + m), which is also divisible by 2, confirming that the sum remains even.

Explanation

The sum of two even numbers is always even because even numbers can be expressed as 2n, where n is an integer. When you add two even numbers (2n + 2m), the result is 2(n + m), which is also divisible by 2, confirming that the sum remains even.

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7. Which expression equals 2⁵?

10

25

32

52

2⁵ represents 2 raised to the power of 5, which means multiplying 2 by itself five times: 2 × 2 × 2 × 2 × 2. This calculation equals 32, making it the correct expression that matches the value of 2 raised to the fifth power.

Explanation

2⁵ represents 2 raised to the power of 5, which means multiplying 2 by itself five times: 2 × 2 × 2 × 2 × 2. This calculation equals 32, making it the correct expression that matches the value of 2 raised to the fifth power.

8. What is the absolute value of −7?

-7

0

7

14

The absolute value of a number is its distance from zero on the number line, regardless of direction. For −7, this distance is 7 units away from zero, making its absolute value 7. Thus, the absolute value of −7 is 7.

Explanation

The absolute value of a number is its distance from zero on the number line, regardless of direction. For −7, this distance is 7 units away from zero, making its absolute value 7. Thus, the absolute value of −7 is 7.

9. Evaluate: 12 ÷ (−3) = ____

Dividing 12 by -3 results in -4 because dividing a positive number by a negative number yields a negative result. In this case, 12 divided by 3 is 4, and since one of the numbers is negative, the final answer becomes -4.

Explanation

Dividing 12 by -3 results in -4 because dividing a positive number by a negative number yields a negative result. In this case, 12 divided by 3 is 4, and since one of the numbers is negative, the final answer becomes -4.

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10. Which of the following is a rational number?

√2

π

3/5

√5

A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. The fraction 3/5 meets this criterion, as both 3 and 5 are integers. In contrast, √2 and √5 are irrational numbers, and π is also irrational.

Explanation

A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. The fraction 3/5 meets this criterion, as both 3 and 5 are integers. In contrast, √2 and √5 are irrational numbers, and π is also irrational.

11. A number that divides evenly into another number is called a ____

A factor is a number that can be multiplied by another whole number to produce a given number. For example, in the equation 6 = 2 × 3, both 2 and 3 are factors of 6 because they divide it evenly without leaving a remainder.

Explanation

A factor is a number that can be multiplied by another whole number to produce a given number. For example, in the equation 6 = 2 × 3, both 2 and 3 are factors of 6 because they divide it evenly without leaving a remainder.

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12. True or False: Zero is considered a positive integer.

True

False

Zero is not considered a positive integer because positive integers are defined as the set of whole numbers greater than zero. The set of positive integers includes numbers like 1, 2, 3, and so forth, while zero is neither positive nor negative, placing it outside this classification.

Explanation

Zero is not considered a positive integer because positive integers are defined as the set of whole numbers greater than zero. The set of positive integers includes numbers like 1, 2, 3, and so forth, while zero is neither positive nor negative, placing it outside this classification.