Comparing Fractions to Represent the Total Amount of Cheese Bought by Amy and Alex

Oct 13, 2025 by wbrum.org 27 views

Comparing Fractions to Represent the Total Amount of Cheese Bought by Amy and Alex

When it comes to comparing fractions, it's essential to understand the concept of equivalent ratios. In this scenario, we have two individuals, Amy and Alex, who purchase different amounts of cheese. To determine the total amount of cheese they buy altogether, we need to find a common denominator and add the fractions.

Understanding the Fractions

Amy buys $$\frac{3}{10}$$ of a pound of cheese, while Alex buys $$\frac{70}{100}$$ of a pound of cheese. To compare these fractions, we need to find a common denominator. The least common multiple (LCM) of 10 and 100 is 100.

Converting the Fractions to Have a Common Denominator

To convert Amy's fraction to have a denominator of 100, we multiply the numerator and denominator by 10:

\frac{3}{10} \times \frac{10}{10} = \frac{30}{100}

Now that both fractions have a common denominator, we can add them together to find the total amount of cheese bought by Amy and Alex.

Adding the Fractions

To add the fractions, we add the numerators while keeping the denominator the same:

\frac{30}{100} + \frac{70}{100} = \frac{100}{100}

Simplifying the fraction, we get:

\frac{100}{100} = 1

Modeling the Total Amount of Cheese Bought

The total amount of cheese bought by Amy and Alex is represented by the fraction $$\frac{100}{100}$$, which simplifies to 1. This means that together, they buy 1 pound of cheese.

Conclusion

In conclusion, to find the total amount of cheese bought by Amy and Alex, we need to compare their fractions and find a common denominator. By adding the fractions, we can determine the total amount of cheese they buy altogether.

Answer

The correct model that represents the amount of cheese that Amy and Alex buy altogether is:

\frac{100}{100}

This simplifies to 1, indicating that together, they buy 1 pound of cheese.

Key Takeaways

To compare fractions, we need to find a common denominator.
The least common multiple (LCM) of 10 and 100 is 100.
To add fractions, we add the numerators while keeping the denominator the same.
The total amount of cheese bought by Amy and Alex is represented by the fraction $$\frac{100}{100}$$, which simplifies to 1.

Additional Practice

Try the following problems to practice comparing and adding fractions:

Sarah buys $$\frac{2}{5}$$ of a pound of cheese. Tom buys $$\frac{40}{50}$$ of a pound of cheese. What is the total amount of cheese they buy altogether?
Emily buys $$\frac{3}{8}$$ of a pound of cheese. Michael buys $$\frac{60}{80}$$ of a pound of cheese. What is the total amount of cheese they buy altogether?

Answer Key

Sarah and Tom buy $$\frac{40}{50}$$ of a pound of cheese altogether.
Emily and Michael buy $$\frac{60}{80}$$ of a pound of cheese altogether.

References

[1] Khan Academy. (n.d.). Adding and Subtracting Fractions. Retrieved from https://www.khanacademy.org/math/fractions-and-decimals/fractions-and-decimals-article
[2] Math Open Reference. (n.d.). Fractions. Retrieved from https://www.mathopenref.com/fractions.html
Frequently Asked Questions: Comparing and Adding Fractions

In this article, we will address some common questions and concerns related to comparing and adding fractions.

Q: What is the least common multiple (LCM) and why is it important?

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. In the context of comparing fractions, the LCM is used to find a common denominator. This is important because it allows us to add or subtract fractions with different denominators.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists. Alternatively, you can use the following formula:

LCM(a, b) = (a × b) / GCD(a, b)

where GCD(a, b) is the greatest common divisor of a and b.

Q: What is the greatest common divisor (GCD) and why is it important?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. In the context of comparing fractions, the GCD is used to find the LCM.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator. This can be done by finding the LCM of the two denominators. Once you have a common denominator, you can add the fractions by adding the numerators while keeping the denominator the same.

Q: Can I subtract fractions with different denominators?

A: Yes, you can subtract fractions with different denominators. The process is similar to adding fractions. You need to find a common denominator, and then subtract the numerators while keeping the denominator the same.

Q: What is the difference between adding and subtracting fractions?

A: The main difference between adding and subtracting fractions is the operation you perform on the numerators. When adding fractions, you add the numerators, while when subtracting fractions, you subtract the numerators.

Q: Can I multiply or divide fractions with different denominators?

A: Yes, you can multiply or divide fractions with different denominators. However, you need to follow the rules of fraction multiplication and division. When multiplying fractions, you multiply the numerators and denominators separately. When dividing fractions, you invert the second fraction and multiply.

Q: What are some common mistakes to avoid when comparing and adding fractions?

A: Some common mistakes to avoid when comparing and adding fractions include:

Not finding a common denominator before adding or subtracting fractions
Not simplifying fractions after adding or subtracting
Not following the rules of fraction multiplication and division
Not using the correct operation (addition or subtraction) when comparing fractions

Q: How can I practice comparing and adding fractions?

A: You can practice comparing and adding fractions by working through examples and exercises. You can also use online resources, such as Khan Academy or Math Open Reference, to practice and review the concepts.

Q: What are some real-world applications of comparing and adding fractions?

A: Comparing and adding fractions has many real-world applications, including:

Cooking and baking: When a recipe calls for a certain amount of an ingredient, you may need to compare and add fractions to determine the total amount needed.
Science and engineering: When working with measurements and conversions, you may need to compare and add fractions to determine the total amount or quantity.
Finance and economics: When working with percentages and ratios, you may need to compare and add fractions to determine the total amount or value.

Conclusion

Comparing and adding fractions is an essential skill in mathematics, with many real-world applications. By understanding the concepts and following the rules, you can confidently compare and add fractions to solve problems and make informed decisions.