Applying the Division Algorithm to 679 and 4

Oct 13, 2025 by miodeya.com 81 views

Understanding the Problem

When we divide a number by another number, we are essentially finding out how many times the divisor fits into the dividend. In this case, we need to divide 679 by 4. To do this, we will use the division algorithm, which involves finding the quotient (result of division) and the remainder (leftover amount).

The Division Algorithm

The division algorithm states that for any two integers a and b, with b > 0, there exist unique integers q and r such that:

a = bq + r

where q is the quotient and r is the remainder.

Applying the Division Algorithm to 679 and 4

To divide 679 by 4, we can use the division algorithm as follows:

679 = 4q + r

We need to find the value of q and r.

Step 1: Divide 679 by 4

To divide 679 by 4, we can start by multiplying 4 by the largest possible integer that is less than or equal to 679. This will give us the first part of the quotient.

4 × 169 = 676

Now, we subtract 676 from 679 to get the remainder.

679 - 676 = 3

Step 2: Find the Quotient and Remainder

From the previous step, we have:

q = 169 (since 4 × 169 = 676) r = 3 (since 679 - 676 = 3)

Therefore, the quotient is 169 and the remainder is 3.

Conclusion

In conclusion, when we divide 679 by 4, we get a quotient of 169 and a remainder of 3. This can be written as:

679 ÷ 4 = 169; R3

Answer

The correct answer is:

A. 169; R3

Why is this the Correct Answer?

This is the correct answer because we have followed the division algorithm to find the quotient and remainder. We have also checked our work by multiplying the quotient by the divisor and subtracting the product from the dividend. This ensures that our answer is accurate.

Common Mistakes to Avoid

When dividing numbers, it's easy to make mistakes. Here are some common mistakes to avoid:

Not following the division algorithm
Not checking your work
Not using the correct order of operations

Tips for Dividing Numbers

Here are some tips for dividing numbers:

Use the division algorithm to find the quotient and remainder
Check your work by multiplying the quotient by the divisor and subtracting the product from the dividend
Use the correct order of operations

Conclusion

Understanding the Problem

The Division Algorithm

The division algorithm states that for any two integers a and b, with b > 0, there exist unique integers q and r such that:

a = bq + r

where q is the quotient and r is the remainder.

Applying the Division Algorithm to 679 and 4

To divide 679 by 4, we can use the division algorithm as follows:

679 = 4q + r

We need to find the value of q and r.

Step 1: Divide 679 by 4

To divide 679 by 4, we can start by multiplying 4 by the largest possible integer that is less than or equal to 679. This will give us the first part of the quotient.

4 × 169 = 676

Now, we subtract 676 from 679 to get the remainder.

679 - 676 = 3

Step 2: Find the Quotient and Remainder

From the previous step, we have:

q = 169 (since 4 × 169 = 676) r = 3 (since 679 - 676 = 3)

Therefore, the quotient is 169 and the remainder is 3.

Conclusion

In conclusion, when we divide 679 by 4, we get a quotient of 169 and a remainder of 3. This can be written as:

679 ÷ 4 = 169; R3

Answer

The correct answer is:

A. 169; R3

Why is this the Correct Answer?

Common Mistakes to Avoid

When dividing numbers, it's easy to make mistakes. Here are some common mistakes to avoid:

Not following the division algorithm
Not checking your work
Not using the correct order of operations

Tips for Dividing Numbers

Here are some tips for dividing numbers:

Use the division algorithm to find the quotient and remainder
Check your work by multiplying the quotient by the divisor and subtracting the product from the dividend
Use the correct order of operations

Q&A

Q: What is the division algorithm?

A: The division algorithm is a mathematical process that involves finding the quotient and remainder when dividing one number by another.

Q: How do I find the quotient and remainder?

A: To find the quotient and remainder, you can use the division algorithm, which states that for any two integers a and b, with b > 0, there exist unique integers q and r such that:

a = bq + r

Q: What is the remainder?

A: The remainder is the leftover amount after dividing one number by another.

Q: How do I check my work?

A: To check your work, you can multiply the quotient by the divisor and subtract the product from the dividend.

Q: What are some common mistakes to avoid when dividing numbers?

A: Some common mistakes to avoid when dividing numbers include not following the division algorithm, not checking your work, and not using the correct order of operations.

Q: What are some tips for dividing numbers?

A: Some tips for dividing numbers include using the division algorithm to find the quotient and remainder, checking your work by multiplying the quotient by the divisor and subtracting the product from the dividend, and using the correct order of operations.

Conclusion

In conclusion, dividing 679 by 4 is a simple process that involves using the division algorithm to find the quotient and remainder. By following the steps outlined in this article and using the Q&A section to clarify any questions, you can accurately divide numbers and avoid common mistakes.