The Rule for Divisibility by 7

Oct 13, 2025 by miodeya.com 113 views

Understanding Divisibility by 7

To determine which of the given numbers is divisible by 7, we need to understand the concept of divisibility by 7. Divisibility by 7 is a fundamental concept in mathematics that deals with the ability of a number to be divided by 7 without leaving a remainder. In other words, a number is divisible by 7 if it can be expressed as a product of 7 and an integer.

The Rule for Divisibility by 7

There are several rules and techniques to determine if a number is divisible by 7. One of the most commonly used methods is the "Double the Dividend and Subtract the Divisor" method. This method involves doubling the dividend (the number being divided) and subtracting the divisor (the number by which we are dividing). If the result is divisible by 7, then the original number is also divisible by 7.

Applying the Rule to the Given Numbers

Let's apply the rule to the given numbers:

Option A: 300

To determine if 300 is divisible by 7, we can use the "Double the Dividend and Subtract the Divisor" method.

Double the dividend: 300 × 2 = 600
Subtract the divisor: 600 - 7 = 593
Check if the result is divisible by 7: 593 is not divisible by 7

Since 593 is not divisible by 7, we can conclude that 300 is not divisible by 7.

Option B: 1,423

To determine if 1,423 is divisible by 7, we can use the "Double the Dividend and Subtract the Divisor" method.

Double the dividend: 1,423 × 2 = 2,846
Subtract the divisor: 2,846 - 7 = 2,839
Check if the result is divisible by 7: 2,839 is not divisible by 7

Since 2,839 is not divisible by 7, we can conclude that 1,423 is not divisible by 7.

Option C: 168

To determine if 168 is divisible by 7, we can use the "Double the Dividend and Subtract the Divisor" method.

Double the dividend: 168 × 2 = 336
Subtract the divisor: 336 - 7 = 329
Check if the result is divisible by 7: 329 is not divisible by 7

However, we can also check if 168 is divisible by 7 by simply dividing it by 7.

168 ÷ 7 = 24

Since 168 can be expressed as a product of 7 and an integer (24), we can conclude that 168 is divisible by 7.

Option D: 451

To determine if 451 is divisible by 7, we can use the "Double the Dividend and Subtract the Divisor" method.

Double the dividend: 451 × 2 = 902
Subtract the divisor: 902 - 7 = 895
Check if the result is divisible by 7: 895 is not divisible by 7

Since 895 is not divisible by 7, we can conclude that 451 is not divisible by 7.

Conclusion

Based on the analysis, we can conclude that the number that is divisible by 7 is Option C: 168.

Q: What is the rule for divisibility by 7?

A: The rule for divisibility by 7 is to double the dividend and subtract the divisor. If the result is divisible by 7, then the original number is also divisible by 7.

Q: How do I determine if a number is divisible by 7?

A: There are several methods to determine if a number is divisible by 7, including:

Using the "Double the Dividend and Subtract the Divisor" method
Dividing the number by 7 and checking if the result is an integer
Using a divisibility test, such as the "Alternating Sum" method

Q: What is the "Alternating Sum" method for divisibility by 7?

A: The "Alternating Sum" method involves adding and subtracting the digits of the number in an alternating pattern. If the result is divisible by 7, then the original number is also divisible by 7.

Q: Can you give an example of the "Alternating Sum" method?

A: Yes, let's consider the number 168. To determine if it is divisible by 7 using the "Alternating Sum" method, we can follow these steps:

Add the first and last digits: 1 + 8 = 9
Subtract the second digit: 9 - 6 = 3
Add the third digit: 3 + 8 = 11
Check if the result is divisible by 7: 11 is not divisible by 7

However, we can also check if 168 is divisible by 7 by simply dividing it by 7.

168 ÷ 7 = 24

Since 168 can be expressed as a product of 7 and an integer (24), we can conclude that 168 is divisible by 7.

Q: What are some common mistakes to avoid when determining divisibility by 7?

A: Some common mistakes to avoid when determining divisibility by 7 include:

Not using the correct method for divisibility by 7
Not checking if the result is an integer
Not considering the possibility of a remainder

Q: Can you give an example of a number that is not divisible by 7?

A: Yes, let's consider the number 300. To determine if it is divisible by 7, we can use the "Double the Dividend and Subtract the Divisor" method.

Double the dividend: 300 × 2 = 600
Subtract the divisor: 600 - 7 = 593
Check if the result is divisible by 7: 593 is not divisible by 7

Since 593 is not divisible by 7, we can conclude that 300 is not divisible by 7.

Q: How do I practice divisibility by 7?

A: There are several ways to practice divisibility by 7, including:

Using online resources, such as divisibility tests and quizzes
Practicing with real-world examples, such as calculating change or determining the number of items in a package
Using flashcards or other study aids to help memorize the rules for divisibility by 7

Q: What are some real-world applications of divisibility by 7?

A: Divisibility by 7 has several real-world applications, including:

Calculating change and determining the number of items in a package
Determining the number of days in a week or month
Calculating the number of hours in a day or week

Q: Can you give an example of a real-world application of divisibility by 7?

A: Yes, let's consider a scenario where you are calculating change for a purchase. If the total cost of the purchase is $168 and you pay with a $100 bill, you would need to calculate the change.

168 ÷ 7 = 24
24 × 7 = 168
Change: 168 - 100 = 68

Since 168 is divisible by 7, we can conclude that the change is $68.