Andrew Eats \[$\frac{1}{2}\$\] Of A Cupcake On Monday And \[$\frac{2}{6}\$\] Of Another Cupcake On Tuesday. How Much Cake Did He Eat Altogether Over These Two Days?

Introduction

In this article, we will delve into the world of fractions and explore how they can be used to calculate the total amount of cake consumed by Andrew over two days. We will examine the fractions representing the amount of cake eaten on each day and then combine them to find the total amount of cake consumed.

The Fractions

On Monday, Andrew eats $\frac{1}{2}$ of a cupcake. This fraction represents half of a whole cupcake. To understand this fraction, we can think of it as a part of a whole. In this case, the whole is a cupcake, and Andrew eats half of it.

On Tuesday, Andrew eats $\frac{2}{6}$ of another cupcake. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Simplifying the fraction, we get $\frac{1}{3}$. This means that Andrew eats one-third of a cupcake on Tuesday.

Adding Fractions with Different Denominators

To find the total amount of cake consumed by Andrew over the two days, we need to add the fractions representing the amount of cake eaten on each day. However, the fractions have different denominators, which makes it difficult to add them directly. To add fractions with different denominators, we need to find a common denominator.

Finding a Common Denominator

The least common multiple (LCM) of 2 and 3 is 6. Therefore, we can use 6 as the common denominator for both fractions. To convert the fractions to have a common denominator, we need to multiply the numerator and the denominator of each fraction by the necessary factor.

For the first fraction, $\frac{1}{2}$, we need to multiply the numerator and the denominator by 3 to get $\frac{3}{6}$.

For the second fraction, $\frac{1}{3}$, we need to multiply the numerator and the denominator by 2 to get $\frac{2}{6}$.

Adding the Fractions

Now that the fractions have a common denominator, we can add them directly. Adding $\frac{3}{6}$ and $\frac{2}{6}$, we get $\frac{5}{6}$.

Conclusion

In conclusion, Andrew eats $\frac{5}{6}$ of a cupcake altogether over the two days. This means that he eats five-sixths of a cupcake, which is equivalent to 5/6 of a whole cupcake.

Real-World Applications

Understanding fractions and how to add them is an essential skill in mathematics. It has numerous real-world applications, such as calculating the total cost of items, measuring ingredients for recipes, and determining the probability of events.

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.

Common Denominators

A common denominator is a number that both fractions can divide into evenly. It's essential to find a common denominator when adding fractions with different denominators.

Least Common Multiple (LCM)

The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly. It's used to find a common denominator when adding fractions with different denominators.

Conclusion

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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. It's used to find a common denominator when adding 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) of two numbers?

A: The greatest common divisor (GCD) of two numbers is the largest number that both numbers can divide into evenly. It's used to simplify fractions and find the LCM of two numbers.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator. You can do this by finding the LCM of the denominators and converting each fraction to have the common denominator. Then, you can add the fractions directly.

Q: What is the rule for adding fractions with different denominators?

A: The rule for adding fractions with different denominators is:

1. Find the LCM of the denominators.
2. Convert each fraction to have the common denominator.
3. Add the fractions directly.

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 is not always the most efficient or accurate way to add fractions.

Q: What is the difference between adding fractions and adding mixed numbers?

A: Adding fractions and adding mixed numbers are two different operations. Adding fractions involves adding the numerators and keeping the same denominator, while adding mixed numbers involves adding the whole numbers and adding the fractions separately.

Q: Can I add fractions with negative numbers?

A: Yes, you can add fractions with negative numbers. When adding fractions with negative numbers, you need to follow the same rules as adding fractions with positive numbers, but you also need to consider the signs of the fractions.

Q: What is the rule for adding fractions with negative numbers?

A: The rule for adding fractions with negative numbers is:

1. Follow the same rules as adding fractions with positive numbers.
2. Consider the signs of the fractions and add or subtract accordingly.

Q: Can I add fractions with variables?

A: Yes, you can add fractions with variables. When adding fractions with variables, you need to follow the same rules as adding fractions with numbers, but you also need to consider the variables and their exponents.

Q: What is the rule for adding fractions with variables?

A: The rule for adding fractions with variables is:

1. Follow the same rules as adding fractions with numbers.
2. Consider the variables and their exponents and add or subtract accordingly.

Conclusion

In this article, we answered some frequently asked questions about adding fractions. We covered topics such as the least common multiple (LCM), greatest common divisor (GCD), and adding fractions with different denominators. We also discussed adding fractions with negative numbers and variables. By following the rules and guidelines outlined in this article, you should be able to add fractions with confidence and accuracy.