Alexis Used 3 4 \frac{3}{4} 4 3 Cup Of Brown Sugar And 2 3 \frac{2}{3} 3 2 Cup Of White Sugar To Bake Desserts For The Bake Sale. What Is The Total Amount Of Sugar Alexis Used?

Mar 10, 2025 by ADMIN 181 views

**Finding the Total Amount of Sugar Used by Alexis**

Introduction

In this problem, we are given the amounts of brown sugar and white sugar used by Alexis to bake desserts for the bake sale. We need to find the total amount of sugar used by Alexis. This problem involves adding fractions with different denominators, which requires us to find a common denominator and then add the fractions.

Understanding the Problem

Alexis used $\frac{3}{4}$ cup of brown sugar and $\frac{2}{3}$ cup of white sugar. To find the total amount of sugar used, we need to add these two fractions together.

Finding a Common Denominator

To add fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of 4 and 3 is 12. We can convert both fractions to have a denominator of 12.

$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$

Adding the Fractions

Now that we have both fractions with a common denominator of 12, we can add them together.

$\frac{9}{12} + \frac{8}{12} = \frac{17}{12}$

Simplifying the Fraction

The fraction $\frac{17}{12}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1. Therefore, the simplified fraction is still $\frac{17}{12}$ .

Conclusion

In conclusion, Alexis used a total of $\frac{17}{12}$ cup of sugar to bake desserts for the bake sale. This problem required us to find a common denominator and then add the fractions together.

Real-World Applications

This problem has real-world applications in cooking and baking. When measuring ingredients, it's essential to have accurate measurements to ensure that the final product turns out correctly. This problem demonstrates the importance of adding fractions with different denominators in real-world scenarios.

Tips and Tricks

When adding fractions with different denominators, it's essential to find a common denominator. The least common multiple (LCM) of the denominators is the smallest number that both denominators can divide into evenly. In this problem, the LCM of 4 and 3 is 12.

Common Mistakes

One common mistake when adding fractions with different denominators is to add the numerators directly without finding a common denominator. This can lead to incorrect answers. It's essential to find a common denominator and then add the fractions together.

Practice Problems

Here are some practice problems to help you understand how to add fractions with different denominators:

Add $\frac{5}{6}$ and $\frac{3}{8}$ .
Add $\frac{2}{3}$ and $\frac{5}{9}$ .
Add $\frac{7}{10}$ and $\frac{3}{5}$ .

Answer Key

$\frac{31}{24}$
$\frac{29}{27}$
$\frac{23}{25}$

Conclusion

Introduction

In our previous article, we discussed how to add fractions with different denominators. In this article, we will answer some frequently asked questions about adding fractions with different denominators.

Q: What is the least common multiple (LCM) of two numbers?

A: The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly. For example, the LCM of 4 and 3 is 12.

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) of two numbers?

A: The greatest common divisor (GCD) of two numbers is the largest number that both numbers can divide into evenly. For example, the GCD of 12 and 18 is 6.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator and then add the fractions together. Here's a step-by-step guide:

Find the LCM of the denominators.
Convert both fractions to have the LCM as the denominator.
Add the fractions together.

Q: What if the denominators are not multiples of each other?

A: If the denominators are not multiples of each other, you can find the LCM of the denominators and then convert both fractions to have the LCM as the denominator.

Q: Can I add fractions with different denominators by converting them to decimals?

A: Yes, you can add fractions with different denominators by converting them to decimals. However, this method may not be as accurate as finding a common denominator and adding the fractions together.

Q: What are some common mistakes to avoid when adding fractions with different denominators?

A: Some common mistakes to avoid when adding fractions with different denominators include:

Adding the numerators directly without finding a common denominator.
Not converting both fractions to have the same denominator.
Not simplifying the fraction after adding.

Q: How can I practice adding fractions with different denominators?

A: You can practice adding fractions with different denominators by using online resources, such as math worksheets or online calculators. You can also practice by working through examples and exercises in a math textbook.

Q: What are some real-world applications of adding fractions with different denominators?

A: Adding fractions with different denominators has many real-world applications, including:

Cooking and baking: When measuring ingredients, it's essential to have accurate measurements to ensure that the final product turns out correctly.
Science: When measuring quantities, such as volume or weight, it's essential to have accurate measurements to ensure that the results are accurate.
Finance: When calculating interest rates or investment returns, it's essential to have accurate measurements to ensure that the results are accurate.

Conclusion

In conclusion, adding fractions with different denominators requires finding a common denominator and then adding the fractions together. By following the steps outlined in this article, you can become proficient in adding fractions with different denominators. Remember to avoid common mistakes and practice regularly to build your skills.