Rename 5 12 \frac{5}{12} 12 5 ​ And 7 8 \frac{7}{8} 8 7 ​ Using The Least Common Denominator. 5 12 = □ \frac{5}{12} = \square 12 5 ​ = □ 7 8 = □ \frac{7}{8} = \square 8 7 ​ = □

Introduction

In mathematics, fractions are a way to represent a part of a whole. When working with fractions, it is often necessary to find a common denominator to add or subtract them. The least common denominator (LCD) is the smallest multiple that both denominators share. In this article, we will explore how to rename fractions using the least common denominator.

What is the Least Common Denominator?

The least common denominator is the smallest multiple that two or more denominators share. It is used to add or subtract fractions with different denominators. To find the LCD, we need to list the multiples of each denominator and find the smallest multiple that they both share.

Finding the Least Common Denominator

To find the LCD, we can use the following steps:

1. List the multiples of each denominator.
2. Find the smallest multiple that they both share.

For example, let's find the LCD of 12 and 8.

• Multiples of 12: 12, 24, 36, 48, 60, ...
• Multiples of 8: 8, 16, 24, 32, 40, ...

The smallest multiple that both lists share is 24. Therefore, the LCD of 12 and 8 is 24.

Renaming Fractions Using the Least Common Denominator

Now that we have found the LCD, we can rename the fractions using the least common denominator.

Renaming $\frac{5}{12}$

To rename $\frac{5}{12}$ using the least common denominator, we need to multiply the numerator and denominator by the same number to get the LCD.

• Multiply the numerator and denominator by 2: $\frac{5 \times 2}{12 \times 2} = \frac{10}{24}$
• Simplify the fraction: $\frac{10}{24} = \frac{5}{12}$

However, we want to rename the fraction using the least common denominator. Therefore, we can multiply the numerator and denominator by 2 again:

• Multiply the numerator and denominator by 2: $\frac{10 \times 2}{24 \times 2} = \frac{20}{48}$
• Simplify the fraction: $\frac{20}{48} = \frac{5}{12}$

However, we can simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 4.

• Divide the numerator and denominator by 4: $\frac{20 \div 4}{48 \div 4} = \frac{5}{12}$

Therefore, the renamed fraction is $\frac{5}{12} = \frac{20}{48}$.

Renaming $\frac{7}{8}$

To rename $\frac{7}{8}$ using the least common denominator, we need to multiply the numerator and denominator by the same number to get the LCD.

• Multiply the numerator and denominator by 3: $\frac{7 \times 3}{8 \times 3} = \frac{21}{24}$
• Simplify the fraction: $\frac{21}{24} = \frac{7}{8}$

However, we want to rename the fraction using the least common denominator. Therefore, we can multiply the numerator and denominator by 3 again:

• Multiply the numerator and denominator by 3: $\frac{21 \times 3}{24 \times 3} = \frac{63}{72}$
• Simplify the fraction: $\frac{63}{72} = \frac{7}{8}$

However, we can simplify the fraction further by dividing both the numerator and denominator by their GCD, which is 9.

• Divide the numerator and denominator by 9: $\frac{63 \div 9}{72 \div 9} = \frac{7}{8}$

Therefore, the renamed fraction is $\frac{7}{8} = \frac{63}{72}$.

Conclusion

In this article, we have learned how to rename fractions using the least common denominator. We have found the LCD of 12 and 8, and then renamed the fractions $\frac{5}{12}$ and $\frac{7}{8}$ using the least common denominator. We have also simplified the fractions further by dividing both the numerator and denominator by their GCD.

Final Answer

The final answer is:

$\frac{5}{12} = \frac{20}{48}$

$$

Introduction

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

Q: What is the least common denominator?

A: The least common denominator is the smallest multiple that two or more denominators share. It is used to add or subtract fractions with different denominators.

Q: How do I find the least common denominator?

A: To find the LCD, you can list the multiples of each denominator and find the smallest multiple that they both share. Alternatively, you can use the following steps:

1. List the multiples of each denominator.
2. Find the smallest multiple that they both share.

Q: Why do I need to find the least common denominator?

A: You need to find the LCD to add or subtract fractions with different denominators. Without the LCD, you cannot add or subtract fractions with different denominators.

Q: How do I rename a fraction using the least common denominator?

A: To rename a fraction using the LCD, you need to multiply the numerator and denominator by the same number to get the LCD. Then, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Q: What if the numerator and denominator have a common factor?

A: If the numerator and denominator have a common factor, you can divide both the numerator and denominator by that factor to simplify the fraction.

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. To add or subtract fractions, you need to have the same denominator. The LCD is the smallest multiple that both denominators share, so you can use it to add or subtract fractions.

Q: How do I know if I have the correct least common denominator?

A: To check if you have the correct LCD, you can list the multiples of each denominator and find the smallest multiple that they both share. If the LCD you found matches the one you listed, then you have the correct LCD.

Q: What if I have a fraction with a variable in the denominator?

A: If you have a fraction with a variable in the denominator, you can use the LCD to rename the fraction. To find the LCD, you need to list the multiples of the variable and find the smallest multiple that they both share.

Q: Can I use the least common denominator to simplify fractions?

A: Yes, you can use the LCD to simplify fractions. To simplify a fraction, you need to divide both the numerator and denominator by their GCD. The LCD is the smallest multiple that both denominators share, so you can use it to simplify fractions.

Conclusion

In this article, we have answered some frequently asked questions about renaming fractions using the least common denominator. We have also provided examples and explanations to help you understand the concept better.

Final Answer

The final answer is:

• The least common denominator is the smallest multiple that two or more denominators share.
• To find the LCD, you can list the multiples of each denominator and find the smallest multiple that they both share.
• To rename a fraction using the LCD, you need to multiply the numerator and denominator by the same number to get the LCD.
• To add or subtract fractions, you need to have the same denominator, which is the LCD.
• To simplify a fraction, you need to divide both the numerator and denominator by their GCD.

Common Questions and Answers

• Q: What is the least common denominator? A: The least common denominator is the smallest multiple that two or more denominators share.
• Q: How do I find the least common denominator? A: To find the LCD, you can list the multiples of each denominator and find the smallest multiple that they both share.
• Q: Why do I need to find the least common denominator? A: You need to find the LCD to add or subtract fractions with different denominators.
• Q: How do I rename a fraction using the least common denominator? A: To rename a fraction using the LCD, you need to multiply the numerator and denominator by the same number to get the LCD.
• Q: What if the numerator and denominator have a common factor? A: If the numerator and denominator have a common factor, you can divide both the numerator and denominator by that factor to simplify the fraction.
• 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.
• Q: How do I know if I have the correct least common denominator? A: To check if you have the correct LCD, you can list the multiples of each denominator and find the smallest multiple that they both share.
• Q: What if I have a fraction with a variable in the denominator? A: If you have a fraction with a variable in the denominator, you can use the LCD to rename the fraction.
• Q: Can I use the least common denominator to simplify fractions? A: Yes, you can use the LCD to simplify fractions.