Replacing the Inequality Sign

Oct 13, 2025 by pynkocean.com 72 views

Question 33.1: Replacing the Inequality Sign

In this question, we are given a mathematical sentence with an inequality sign that needs to be replaced to make the sentence true. The original sentence is:

${ 10959 \ \textless \ /em\ \textgreater \ 10599 }$

To determine which sign can replace the inequality sign, we need to analyze the relationship between the two numbers.

Analyzing the Numbers

The two numbers given are 10959 and 10599. To compare these numbers, we can perform a simple subtraction:

${ 10959 - 10599 = 360 }$

Since the result of the subtraction is a positive number, we can conclude that 10959 is greater than 10599.

Replacing the Inequality Sign

Based on the analysis above, we can see that the inequality sign in the original sentence is incorrect. To make the sentence true, we need to replace the inequality sign with a sign that indicates that 10959 is greater than 10599.

The correct sign to replace the inequality sign is the greater-than sign (>). Therefore, the correct mathematical sentence is:

${ 10959 \ \textgreater \ 10599 }$

Conclusion

In conclusion, the correct sign to replace the inequality sign in the original sentence is the greater-than sign (>).

Question 3.2: Prime Factorization of 792

In this question, we are given a number (792) and asked to find a prime factor of this number.

Understanding Prime Factors

A prime factor is a prime number that divides a given number exactly without leaving a remainder. To find the prime factors of a number, we can use the prime factorization method.

Prime Factorization of 792

To find the prime factors of 792, we can start by dividing the number by the smallest prime number (2) and continue dividing until we reach the quotient.

${ 792 = 2 \times 396 }$ ${ 396 = 2 \times 198 }$ ${ 198 = 2 \times 99 }$ ${ 99 = 3 \times 33 }$ ${ 33 = 3 \times 11 }$

Therefore, the prime factors of 792 are 2, 3, and 11.

Conclusion

In conclusion, the prime factors of 792 are 2, 3, and 11.

Answer Key

Question 33.1: The correct sign to replace the inequality sign is the greater-than sign (>).
Question 3.2: The prime factors of 792 are 2, 3, and 11.

Discussion

This question requires the application of mathematical concepts, such as inequality signs and prime factorization. The correct answer can be determined by analyzing the numbers and using the prime factorization method.

References

Question 33.1: Replacing the Inequality Sign

In this question, we are given a mathematical sentence with an inequality sign that needs to be replaced to make the sentence true. The original sentence is:

${ 10959 \ \textless \ /em\ \textgreater \ 10599 }$

To determine which sign can replace the inequality sign, we need to analyze the relationship between the two numbers.

Q&A

Q: What is the correct sign to replace the inequality sign in the original sentence? A: The correct sign to replace the inequality sign is the greater-than sign (>).

Q: Why is the greater-than sign the correct sign to replace the inequality sign? A: The greater-than sign is the correct sign to replace the inequality sign because 10959 is greater than 10599.

Q: What is the relationship between the two numbers in the original sentence? A: The relationship between the two numbers in the original sentence is that 10959 is greater than 10599.

Question 3.2: Prime Factorization of 792

In this question, we are given a number (792) and asked to find a prime factor of this number.

Q&A

Q: What is the prime factorization of 792? A: The prime factorization of 792 is 2^4 * 3^2 * 11.

Q: How do you find the prime factors of a number? A: To find the prime factors of a number, you can use the prime factorization method, which involves dividing the number by the smallest prime number (2) and continuing to divide until you reach the quotient.

Q: What are the prime factors of 792? A: The prime factors of 792 are 2, 3, and 11.

Q: Why are 2, 3, and 11 the prime factors of 792? A: 2, 3, and 11 are the prime factors of 792 because they are the prime numbers that divide 792 exactly without leaving a remainder.

Question 33.3: Finding the Greatest Common Divisor (GCD)

In this question, we are given two numbers (792 and 10599) and asked to find their greatest common divisor (GCD).

Q&A

Q: What is the greatest common divisor (GCD) of 792 and 10599? A: The greatest common divisor (GCD) of 792 and 10599 is 3.

Q: How do you find the GCD of two numbers? A: To find the GCD of two numbers, you can use the Euclidean algorithm, which involves dividing the larger number by the smaller number and continuing to divide until you reach the remainder.

Q: Why is 3 the GCD of 792 and 10599? A: 3 is the GCD of 792 and 10599 because it is the largest number that divides both 792 and 10599 exactly without leaving a remainder.

Question 33.4: Finding the Least Common Multiple (LCM)

In this question, we are given two numbers (792 and 10599) and asked to find their least common multiple (LCM).

Q&A

Q: What is the least common multiple (LCM) of 792 and 10599? A: The least common multiple (LCM) of 792 and 10599 is 360360.

Q: How do you find the LCM of two numbers? A: To find the LCM of two numbers, you can use the formula: LCM(a, b) = (a * b) / GCD(a, b), where GCD(a, b) is the greatest common divisor of a and b.

Q: Why is 360360 the LCM of 792 and 10599? A: 360360 is the LCM of 792 and 10599 because it is the smallest number that is a multiple of both 792 and 10599.

Conclusion

In conclusion, the correct sign to replace the inequality sign in the original sentence is the greater-than sign (>), and the prime factors of 792 are 2, 3, and 11. The greatest common divisor (GCD) of 792 and 10599 is 3, and the least common multiple (LCM) of 792 and 10599 is 360360.

Answer Key

Question 33.1: The correct sign to replace the inequality sign is the greater-than sign (>).
Question 3.2: The prime factors of 792 are 2, 3, and 11.
Question 33.3: The greatest common divisor (GCD) of 792 and 10599 is 3.
Question 33.4: The least common multiple (LCM) of 792 and 10599 is 360360.

Discussion

This question requires the application of mathematical concepts, such as inequality signs, prime factorization, greatest common divisor (GCD), and least common multiple (LCM). The correct answer can be determined by analyzing the numbers and using the relevant mathematical formulas.