2. Circle A Set Of Expressions Below That, When Added Together, Could Be Used To Find The Quotient Of $805 \div 35$.$\[ \begin{tabular}{|c|c|c|} \hline $350 \div 10$ & $350 \div 35$ & $70 \div 35$ \\ \hline $35 \div 35$ & $700 \div 35$ &

Finding the Quotient of 805 Divided by 35: A Set of Expressions to Consider

When dealing with division problems, it's essential to understand the concept of partial quotients and how they can be used to find the quotient of a given division problem. In this article, we will explore a set of expressions that, when added together, could be used to find the quotient of 805 divided by 35.

Understanding Partial Quotients

Partial quotients are a way of breaking down a division problem into smaller, more manageable parts. By finding the quotient of each part, we can then add these quotients together to find the overall quotient of the original division problem. This concept is particularly useful when dealing with large numbers or when the divisor is not a factor of the dividend.

The Given Division Problem

The given division problem is 805 divided by 35. To find the quotient of this problem, we can use the set of expressions provided below.

A Set of Expressions to Consider

The following expressions are given:

• $350 \div 10$
• $350 \div 35$
• $70 \div 35$
• $35 \div 35$
• $700 \div 35$

Evaluating Each Expression

Let's evaluate each expression to see if it can be used to find the quotient of 805 divided by 35.

$350 \div 10$

To evaluate this expression, we simply divide 350 by 10.

$350 \div 10 = 35$

This expression can be used to find the quotient of 805 divided by 35.

$350 \div 35$

To evaluate this expression, we simply divide 350 by 35.

$350 \div 35 = 10$

This expression can also be used to find the quotient of 805 divided by 35.

$70 \div 35$

To evaluate this expression, we simply divide 70 by 35.

$70 \div 35 = 2$

This expression can also be used to find the quotient of 805 divided by 35.

$35 \div 35$

To evaluate this expression, we simply divide 35 by 35.

$35 \div 35 = 1$

This expression can also be used to find the quotient of 805 divided by 35.

$700 \div 35$

To evaluate this expression, we simply divide 700 by 35.

$700 \div 35 = 20$

This expression can also be used to find the quotient of 805 divided by 35.

Adding the Quotients Together

Now that we have evaluated each expression, we can add the quotients together to find the overall quotient of 805 divided by 35.

$35 + 10 + 2 + 1 + 20 = 68$

However, this is not the correct quotient. We need to consider the fact that 805 is the sum of 350 and 455, and that 35 is a factor of both 350 and 455.

Revising the Quotients

Let's revise the quotients by considering the fact that 35 is a factor of both 350 and 455.

• $350 \div 35 = 10$
• $455 \div 35 = 13$

Now, let's add the revised quotients together.

$10 + 13 = 23$

This is the correct quotient of 805 divided by 35.

Conclusion

In this article, we explored a set of expressions that, when added together, could be used to find the quotient of 805 divided by 35. We evaluated each expression and added the quotients together to find the overall quotient. However, we needed to revise the quotients by considering the fact that 35 is a factor of both 350 and 455. The correct quotient of 805 divided by 35 is 23.

Key Takeaways

• Partial quotients are a way of breaking down a division problem into smaller, more manageable parts.
• The set of expressions provided can be used to find the quotient of 805 divided by 35.
• The correct quotient of 805 divided by 35 is 23.

Further Exploration

• Consider other division problems that can be broken down into smaller parts using partial quotients.
• Explore other sets of expressions that can be used to find the quotient of a given division problem.
  Frequently Asked Questions: Finding the Quotient of 805 Divided by 35

In our previous article, we explored a set of expressions that, when added together, could be used to find the quotient of 805 divided by 35. We also discussed the concept of partial quotients and how they can be used to break down a division problem into smaller, more manageable parts. In this article, we will answer some frequently asked questions related to finding the quotient of 805 divided by 35.

Q: What is the concept of partial quotients?

A: Partial quotients are a way of breaking down a division problem into smaller, more manageable parts. By finding the quotient of each part, we can then add these quotients together to find the overall quotient of the original division problem.

Q: How do I use partial quotients to find the quotient of 805 divided by 35?

A: To use partial quotients to find the quotient of 805 divided by 35, you need to break down the division problem into smaller parts. In this case, we can break down 805 into 350 and 455, and then find the quotient of each part. We can then add the quotients together to find the overall quotient.

Q: What are the steps to find the quotient of 805 divided by 35 using partial quotients?

A: The steps to find the quotient of 805 divided by 35 using partial quotients are as follows:

1. Break down the division problem into smaller parts.
2. Find the quotient of each part.
3. Add the quotients together to find the overall quotient.

Q: Why do I need to revise the quotients when using partial quotients?

A: When using partial quotients, you need to revise the quotients by considering the fact that the divisor is a factor of both the dividend and the quotient. In this case, 35 is a factor of both 350 and 455, so we need to revise the quotients accordingly.

Q: What is the correct quotient of 805 divided by 35?

A: The correct quotient of 805 divided by 35 is 23.

Q: Can I use partial quotients to find the quotient of other division problems?

A: Yes, you can use partial quotients to find the quotient of other division problems. The concept of partial quotients can be applied to any division problem, as long as you can break down the problem into smaller parts.

Q: What are some common mistakes to avoid when using partial quotients?

A: Some common mistakes to avoid when using partial quotients include:

• Not breaking down the division problem into smaller parts.
• Not revising the quotients when the divisor is a factor of both the dividend and the quotient.
• Not adding the quotients together to find the overall quotient.

Q: How can I practice using partial quotients to find the quotient of division problems?

A: You can practice using partial quotients to find the quotient of division problems by working through a series of examples. Start with simple division problems and gradually move on to more complex problems. You can also use online resources or worksheets to practice using partial quotients.

Conclusion

In this article, we answered some frequently asked questions related to finding the quotient of 805 divided by 35 using partial quotients. We discussed the concept of partial quotients, the steps to find the quotient of a division problem using partial quotients, and some common mistakes to avoid. We also provided some tips on how to practice using partial quotients to find the quotient of division problems.