What is a rational number?

A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. For example, 1/2, 3, and -4.75 are rational numbers.

What is the difference between a prime number and a composite number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A composite number is a natural number greater than 1 that has more than two positive divisors. For example, 2 is prime, while 4 is composite.

What is the rule for the divisibility of a number by 3?

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, for the number 123, the sum of the digits is 1 + 2 + 3 = 6, which is divisible by 3, so 123 is also divisible by 3.

If the product of two consecutive integers is 240, what are the integers?

Let the integers be n and n + 1. Then n(n + 1) = 240. This simplifies to n² + n - 240 = 0. Factoring gives (n - 15)(n + 16) = 0. Therefore, n = 15 (the positive solution), so the integers are 15 and 16.

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

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

What is the greatest common divisor (GCD) of 48 and 180?

To find the GCD, we can use prime factorization: 48 = 2⁴ * 3¹ and 180 = 2² * 3² * 5¹. The GCD is found by taking the lowest power of each prime: GCD = 2² * 3¹ = 12.

What is the decimal representation of 1/8?

To convert 1/8 into decimal, divide 1 by 8. The decimal representation is 0.125.

How many prime numbers are there between 1 and 50?

The prime numbers between 1 and 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. There are a total of 15 prime numbers.

What is the sum of the first 10 natural numbers?

The sum of the first n natural numbers is given by the formula n(n + 1)/2. For n = 10, the sum is 10(10 + 1)/2 = 10 * 11/2 = 55.

What is the definition of an irrational number?

An irrational number is a number that cannot be expressed as a fraction of two integers. Its decimal representation is non-repeating and non-terminating. Examples include √2 and π.

What is the rule for divisibility by 9?

A number is divisible by 9 if the sum of its digits is divisible by 9. For example, the number 729 has digits that sum to 7 + 2 + 9 = 18, which is divisible by 9, so 729 is also divisible by 9.