Rename $\frac{1}{6}$ And $\frac{1}{24}$ Using The Least Common Denominator.$ 1 6 = \frac{1}{6} = 6 1 ​ = [/tex]

Introduction

In mathematics, fractions are a way to represent a part of a whole. When working with fractions, it's often necessary to find a common denominator to add or subtract them. In this article, we will explore how to rename fractions using the least common denominator (LCD). We will focus on renaming the fractions $\frac{1}{6}$ and $\frac{1}{24}$.

What is the Least Common Denominator?

The least common denominator (LCD) is the smallest multiple that two or more denominators have in common. It's an essential concept in mathematics, especially when working with fractions. The LCD is used to add or subtract fractions with different denominators.

Finding the Least Common Denominator

To find the LCD of two fractions, we need to list the multiples of each denominator. The first step is to find the multiples of each denominator.

Multiples of 6

• 6, 12, 18, 24, 30, ...

Multiples of 24

• 24, 48, 72, 96, 120, ...

Now, we need to find the smallest multiple that appears in both lists. In this case, the smallest multiple is 24.

Renaming Fractions with the Least Common Denominator

Now that we have found the LCD, we can rename the fractions $\frac{1}{6}$ and $\frac{1}{24}$.

Renaming $\frac{1}{6}$

To rename $\frac{1}{6}$, we need to multiply the numerator and denominator by the LCD, which is 24.

$$\frac{1}{6} = \frac{1 \times 24}{6 \times 24} = \frac{24}{144}$$

Renaming $\frac{1}{24}$

To rename $\frac{1}{24}$, we don't need to multiply the numerator and denominator by the LCD, because the denominator is already the LCD.

$$\frac{1}{24} = \frac{1}{24}$$

Simplifying the Fractions

Now that we have renamed the fractions, we can simplify them by dividing the numerator and denominator by their greatest common divisor (GCD).

Simplifying $\frac{24}{144}$

To simplify $\frac{24}{144}$, we need to find the GCD of 24 and 144.

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

The GCD of 24 and 144 is 24.

$$\frac{24}{144} = \frac{24 \div 24}{144 \div 24} = \frac{1}{6}$$

Conclusion

In this article, we learned how to rename fractions using the least common denominator. We focused on renaming the fractions $\frac{1}{6}$ and $\frac{1}{24}$. We found the LCD of 6 and 24, which is 24. We then renamed the fractions and simplified them by dividing the numerator and denominator by their GCD.

Real-World Applications

Renaming fractions with the least common denominator is an essential concept in mathematics, especially in real-world applications. For example, in cooking, we often need to convert between different units of measurement, such as cups and tablespoons. Renaming fractions with the least common denominator can help us make accurate conversions.

Practice Problems

1. Rename the fraction $\frac{1}{8}$ using the least common denominator.
2. Rename the fraction $\frac{1}{12}$ using the least common denominator.
3. Simplify the fraction $\frac{18}{36}$.

Answer Key

1. $\frac{1}{8} = \frac{1 \times 12}{8 \times 12} = \frac{12}{96}$
2. $\frac{1}{12} = \frac{1 \times 24}{12 \times 24} = \frac{24}{288}$
3. $\frac{18}{36} = \frac{18 \div 18}{36 \div 18} = \frac{1}{2}$
   Q&A: Renaming Fractions with the Least Common Denominator =====================================================

Introduction

In our previous article, we explored how to rename fractions using the least common denominator (LCD). In this article, we will answer some frequently asked questions about renaming fractions with the LCD.

Q: What is the least common denominator (LCD)?

A: The least common denominator (LCD) is the smallest multiple that two or more denominators have in common. It's an essential concept in mathematics, especially when working with fractions.

Q: How do I find the least common denominator?

A: To find the LCD, you need to list the multiples of each denominator and find the smallest multiple that appears in both lists.

Q: What if the denominators have different prime factors?

A: If the denominators have different prime factors, you need to find the product of the highest power of each prime factor that appears in either denominator.

Q: Can I use a calculator to find the least common denominator?

A: Yes, you can use a calculator to find the LCD. However, it's essential to understand the concept behind it to apply it correctly.

Q: How do I rename a fraction with a variable denominator?

A: To rename a fraction with a variable denominator, you need to find the LCD of the variable denominator and the other denominator. Then, you can multiply the numerator and denominator by the LCD.

Q: Can I simplify a fraction after renaming it with the least common denominator?

A: Yes, you can simplify a fraction after renaming it with the LCD. However, you need to make sure that the numerator and denominator are both divisible by the greatest common divisor (GCD).

Q: What if I have a fraction with a negative denominator?

A: If you have a fraction with a negative denominator, you need to multiply the numerator and denominator by -1 to make the denominator positive.

Q: Can I use the least common denominator to add or subtract fractions?

A: Yes, you can use the LCD to add or subtract fractions. However, you need to make sure that the fractions have the same denominator.

Q: What if I have a fraction with a decimal denominator?

A: If you have a fraction with a decimal denominator, you need to convert the decimal to a fraction and then find the LCD.

Q: Can I use the least common denominator to convert between different units of measurement?

A: Yes, you can use the LCD to convert between different units of measurement. For example, you can use it to convert between cups and tablespoons.

Conclusion

In this article, we answered some frequently asked questions about renaming fractions with the least common denominator. We hope that this article has helped you understand the concept of renaming fractions with the LCD and how to apply it in different situations.

Practice Problems

1. Rename the fraction $\frac{1}{9}$ using the least common denominator.
2. Rename the fraction $\frac{1}{15}$ using the least common denominator.
3. Simplify the fraction $\frac{24}{48}$.

Answer Key

1. $\frac{1}{9} = \frac{1 \times 20}{9 \times 20} = \frac{20}{180}$
2. $\frac{1}{15} = \frac{1 \times 24}{15 \times 24} = \frac{24}{360}$
3. $\frac{24}{48} = \frac{24 \div 24}{48 \div 24} = \frac{1}{2}$