Which Of These Division Problems Have The Same Quotient As 12.3 Divided By 0.4? Check All That Apply.- $123 \div 4$- $1.23 \div 0.4$- $1.230 \div 40$- $123 \div 0.04$

Division Problems with the Same Quotient as 12.3 Divided by 0.4

When it comes to division problems, understanding the concept of equivalent ratios is crucial. In this article, we will explore which division problems have the same quotient as 12.3 divided by 0.4. We will examine each option carefully and determine which ones meet the criteria.

Understanding Equivalent Ratios

To begin with, let's understand what equivalent ratios are. Equivalent ratios are ratios that have the same value, but are expressed in different forms. For example, 12.3 divided by 0.4 is an equivalent ratio to 123 divided by 4, as both ratios have the same value.

Option 1: $123 \div 4$

Let's start by examining the first option: $123 \div 4$. To determine if this option has the same quotient as 12.3 divided by 0.4, we need to calculate the quotient of $123 \div 4$.

$123 \div 4 = 30.75$

As we can see, the quotient of $123 \div 4$ is 30.75, which is not equal to 12.3 divided by 0.4. Therefore, this option does not have the same quotient as 12.3 divided by 0.4.

Option 2: $1.23 \div 0.4$

Next, let's examine the second option: $1.23 \div 0.4$. To determine if this option has the same quotient as 12.3 divided by 0.4, we need to calculate the quotient of $1.23 \div 0.4$.

$1.23 \div 0.4 = 3.075$

As we can see, the quotient of $1.23 \div 0.4$ is 3.075, which is not equal to 12.3 divided by 0.4. Therefore, this option does not have the same quotient as 12.3 divided by 0.4.

Option 3: $1.230 \div 40$

Now, let's examine the third option: $1.230 \div 40$. To determine if this option has the same quotient as 12.3 divided by 0.4, we need to calculate the quotient of $1.230 \div 40$.

$1.230 \div 40 = 0.03075$

As we can see, the quotient of $1.230 \div 40$ is 0.03075, which is not equal to 12.3 divided by 0.4. Therefore, this option does not have the same quotient as 12.3 divided by 0.4.

Option 4: $123 \div 0.04$

Finally, let's examine the fourth option: $123 \div 0.04$. To determine if this option has the same quotient as 12.3 divided by 0.4, we need to calculate the quotient of $123 \div 0.04$.

$123 \div 0.04 = 3075$

As we can see, the quotient of $123 \div 0.04$ is 3075, which is equal to 12.3 divided by 0.4. Therefore, this option has the same quotient as 12.3 divided by 0.4.

Conclusion

In conclusion, only one of the division problems has the same quotient as 12.3 divided by 0.4, which is $123 \div 0.04$. This option meets the criteria of having the same quotient as 12.3 divided by 0.4.

Key Takeaways

• Equivalent ratios are ratios that have the same value, but are expressed in different forms.
• To determine if a division problem has the same quotient as 12.3 divided by 0.4, we need to calculate the quotient of the division problem.
• Only one of the division problems has the same quotient as 12.3 divided by 0.4, which is $123 \div 0.04$.

Final Answer

The final answer is: $123 \div 0.04$
Frequently Asked Questions: Division Problems with the Same Quotient as 12.3 Divided by 0.4

In our previous article, we explored which division problems have the same quotient as 12.3 divided by 0.4. We examined each option carefully and determined which ones meet the criteria. In this article, we will answer some frequently asked questions related to division problems with the same quotient as 12.3 divided by 0.4.

Q: What is the concept of equivalent ratios?

A: Equivalent ratios are ratios that have the same value, but are expressed in different forms. For example, 12.3 divided by 0.4 is an equivalent ratio to 123 divided by 4, as both ratios have the same value.

Q: How do I determine if a division problem has the same quotient as 12.3 divided by 0.4?

A: To determine if a division problem has the same quotient as 12.3 divided by 0.4, you need to calculate the quotient of the division problem. If the quotient is equal to 12.3 divided by 0.4, then the division problem has the same quotient.

Q: What is the quotient of $123 \div 4$?

A: The quotient of $123 \div 4$ is 30.75.

Q: What is the quotient of $1.23 \div 0.4$?

A: The quotient of $1.23 \div 0.4$ is 3.075.

Q: What is the quotient of $1.230 \div 40$?

A: The quotient of $1.230 \div 40$ is 0.03075.

Q: What is the quotient of $123 \div 0.04$?

A: The quotient of $123 \div 0.04$ is 3075.

Q: Which division problem has the same quotient as 12.3 divided by 0.4?

A: Only one of the division problems has the same quotient as 12.3 divided by 0.4, which is $123 \div 0.04$.

Q: Why is it important to understand equivalent ratios?

A: Understanding equivalent ratios is important because it helps you to determine if a division problem has the same quotient as another division problem. This is useful in various mathematical applications, such as solving equations and inequalities.

Q: Can you provide more examples of division problems with the same quotient?

A: Yes, here are a few more examples:

• $123.45 \div 4.5 = 27.3$
• $123.45 \div 0.45 = 2745$
• $123.45 \div 45 = 2.745$

Conclusion

In conclusion, understanding equivalent ratios is crucial in determining if a division problem has the same quotient as another division problem. By calculating the quotient of a division problem, you can determine if it has the same quotient as 12.3 divided by 0.4. We hope this article has provided you with a better understanding of division problems with the same quotient.

Key Takeaways

• Equivalent ratios are ratios that have the same value, but are expressed in different forms.
• To determine if a division problem has the same quotient as 12.3 divided by 0.4, you need to calculate the quotient of the division problem.
• Only one of the division problems has the same quotient as 12.3 divided by 0.4, which is $123 \div 0.04$.

Final Answer

The final answer is: $123 \div 0.04$