What are the different types of numbers in the number system?

The number system consists of several types of numbers, including natural numbers (1, 2, 3, ...), whole numbers (0, 1, 2, 3, ...), integers (..., -2, -1, 0, 1, 2, ...), rational numbers (fractions like 1/2, 3/4), and irrational numbers (numbers that cannot be expressed as fractions, such as √2 or π).

How do you determine if a number is rational?

A number is rational if it can be expressed as the quotient of two integers, where the denominator is not zero. For example, 0.75 is rational because it can be written as 3/4.

What is the least common multiple (LCM) of 12 and 15?

To find the least common multiple of 12 and 15, first find the prime factorization: 12 = 2² * 3 and 15 = 3 * 5. The LCM is found by taking the highest power of each prime: LCM = 2² * 3¹ * 5¹ = 60.

If x is an integer such that 2x + 3 is even, what can you conclude about x?

Since 2 times any integer is even, adding 3 to it always gives an odd number.  In other words:

• 2x is even for every integer x.

• Even + 3 = odd.

Therefore 2x + 3 can never be even for any integer x.  There is no integer solution.

What is the difference between prime and composite numbers?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself (e.g., 2, 3, 5, 7). A composite number is a natural number greater than 1 that is not prime, meaning it has divisors other than 1 and itself (e.g., 4, 6, 8, 9).

What is the greatest common divisor (GCD) of 24 and 36?

To find the GCD of 24 and 36, first find the prime factorization: 24 = 2³ * 3 and 36 = 2² * 3². The GCD is found by taking the lowest power of each common prime: GCD = 2² * 3¹ = 12.

How can you tell if a number is even or odd?

A number is even if it is divisible by 2 (i.e., n mod 2 = 0) and odd if it is not divisible by 2 (i.e., n mod 2 = 1).

What is the decimal representation of 1/8?

The decimal representation of 1/8 is 0.125.

If a number is divisible by both 2 and 3, what else must it be divisible by?

If a number is divisible by both 2 and 3, it must also be divisible by 6, which is the least common multiple of 2 and 3.

What is the square of 7?

The square of 7 is 7² = 49.

If x is a positive integer, what is the value of x if 3x = 12?

To solve for x, divide both sides by 3: x = 12/3 = 4.

What are the first five prime numbers?

The first five prime numbers are 2, 3, 5, 7, and 11.

Which of the following is an irrational number? A) 0.5 B) √4 C) π D) 3/7

C) π is an irrational number because it cannot be expressed as a fraction of two integers.

If a number ends in 0 or 5, what can you conclude about its divisibility?

If a number ends in 0 or 5, it is divisible by 5.

How do you convert a fraction to a decimal?

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.