Understanding the Concept of Doubling

Oct 13, 2025 by talynt.org 67 views

Introduction

In mathematics, understanding the concept of doubling a quantity is a fundamental skill that can be applied to various real-world scenarios. In this article, we will explore the concept of doubling the original amount in a savings account, using the variable ${$ s $}$ to represent the original amount. We will also examine how to represent the new balance in Fiona's savings account when the original amount is ${$ s = 160 $}$.

Understanding the Concept of Doubling

Doubling a quantity means multiplying it by 2. In mathematical terms, if we have a quantity ${$ s $}$, doubling it can be represented as ${$ 2s $}$. This is because when we multiply ${$ s $}$ by 2, we are essentially adding ${$ s $}$ to itself, resulting in a new quantity that is twice the original amount.

Representing the New Balance

To represent the new balance in Fiona's savings account, we need to use the expression ${$ 2s $}$. This expression indicates that the new balance is twice the original amount, which is represented by the variable ${$ s $}$.

Substituting the Original Amount

Now that we have the expression ${$ 2s $}$ to represent the new balance, we can substitute the original amount ${$ s = 160 $}$ into the expression. This will give us the new balance in Fiona's savings account.

Calculating the New Balance

To calculate the new balance, we simply need to substitute ${$ s = 160 $}$ into the expression ${$ 2s $}$. This gives us:

${$ 2s $}$ = ${$ 2(160) $}$

Using the distributive property of multiplication, we can simplify the expression as follows:

${$ 2(160) $}$ = ${$ 320 $}$

Therefore, the new balance in Fiona's savings account is ${$ 320 $}$.

Conclusion

In conclusion, the expression ${$ 2s $}$ represents the new balance in Fiona's savings account when the original amount is doubled. By substituting the original amount ${$ s = 160 $}$ into the expression, we can calculate the new balance as ${$ 320 $}$. This demonstrates the importance of understanding the concept of doubling a quantity in mathematics and its application to real-world scenarios.

Key Takeaways

Doubling a quantity means multiplying it by 2.
The expression ${$ 2s $}$ represents the new balance in Fiona's savings account when the original amount is doubled.
To calculate the new balance, substitute the original amount into the expression ${$ 2s $}$.
The new balance in Fiona's savings account is ${$ 320 $}$ when the original amount is ${$ s = 160 $}$.

Real-World Applications

Understanding the concept of doubling a quantity has numerous real-world applications. For example:

In finance, doubling a investment can result in significant returns.
In science, doubling a quantity can be used to model population growth or chemical reactions.
In everyday life, doubling a recipe can be used to feed a larger group of people.

Common Misconceptions

Some people may think that doubling a quantity means adding it to itself, rather than multiplying it by 2.
Others may think that doubling a quantity is the same as tripling it, which is not the case.

Conclusion

Q&A: Doubling the Original Amount in Fiona's Savings Account

Q: What does it mean to double a quantity?

A: Doubling a quantity means multiplying it by 2. In mathematical terms, if we have a quantity ${$ s $}$, doubling it can be represented as ${$ 2s $}$.

Q: How do I represent the new balance in Fiona's savings account?

A: To represent the new balance in Fiona's savings account, we need to use the expression ${$ 2s $}$. This expression indicates that the new balance is twice the original amount, which is represented by the variable ${$ s $}$.

Q: What if the original amount is ${$ s = 160 $}$? How do I calculate the new balance?

A: To calculate the new balance, we simply need to substitute ${$ s = 160 $}$ into the expression ${$ 2s $}$. This gives us:

${$ 2s $}$ = ${$ 2(160) $}$

Using the distributive property of multiplication, we can simplify the expression as follows:

${$ 2(160) $}$ = ${$ 320 $}$

Therefore, the new balance in Fiona's savings account is ${$ 320 $}$.

Q: What if I want to double a quantity that is not a multiple of 10? How do I do it?

A: To double a quantity that is not a multiple of 10, you can simply multiply it by 2. For example, if you have a quantity of 25, doubling it would be:

${$ 2(25) $}$ = ${$ 50 $}$

Q: Can I use the concept of doubling to solve real-world problems?

A: Yes, the concept of doubling can be applied to various real-world scenarios. For example, in finance, doubling an investment can result in significant returns. In science, doubling a quantity can be used to model population growth or chemical reactions. In everyday life, doubling a recipe can be used to feed a larger group of people.

Q: What are some common misconceptions about doubling a quantity?

A: Some common misconceptions about doubling a quantity include:

Thinking that doubling a quantity means adding it to itself, rather than multiplying it by 2.
Thinking that doubling a quantity is the same as tripling it, which is not the case.

Q: How can I apply the concept of doubling to my everyday life?

A: You can apply the concept of doubling to your everyday life in various ways, such as:

Doubling a recipe to feed a larger group of people.
Doubling an investment to increase your returns.
Doubling a quantity to model population growth or chemical reactions.

Conclusion

In conclusion, the concept of doubling a quantity is a fundamental skill in mathematics that has numerous real-world applications. By understanding how to represent the new balance in Fiona's savings account, we can apply this concept to various scenarios and make informed decisions.