Type The Correct Answer In Each Box. Use Numerals Instead Of Words. If Necessary, Use / For The Fraction Bar(s).Rename $\frac{4}{9}$ And $\frac{17}{18}$ Using The Least Common Denominator.

Feb 25, 2025 by ADMIN 195 views

**Renaming Fractions with the Least Common Denominator**

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Introduction

In mathematics, fractions are a way to represent a part of a whole. When we have two or more fractions, we often need to compare or add them together. However, fractions with different denominators can make this process more complicated. To simplify this, we can use the least common denominator (LCD) to rename fractions. In this article, we will learn how to rename the fractions $\frac{4}{9}$ and $\frac{17}{18}$ using the least common denominator.

What is the Least Common Denominator?

The least common denominator (LCD) is the smallest number that is a multiple of both denominators of the fractions. It is used to rename fractions with different denominators to have the same denominator, making it easier to compare or add them together.

Finding the Least Common Denominator

To find the LCD of two fractions, we need to list the multiples of each denominator and find the smallest number that is common to both lists.

Multiples of 9

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...

Multiples of 18

The multiples of 18 are: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, ...

Finding the LCD

From the lists above, we can see that the smallest number that is common to both lists is 18. Therefore, the least common denominator of $\frac{4}{9}$ and $\frac{17}{18}$ is 18.

Renaming Fractions with the Least Common Denominator

Now that we have found the LCD, we can rename the fractions $\frac{4}{9}$ and $\frac{17}{18}$ using the least common denominator.

Renaming $\frac{4}{9}$

To rename $\frac{4}{9}$ using the LCD of 18, we need to multiply the numerator and denominator by 2.

$\frac{4}{9} \times \frac{2}{2} = \frac{8}{18}$

Renaming $\frac{17}{18}$

Since the denominator of $\frac{17}{18}$ is already 18, we do not need to multiply it by anything. The fraction $\frac{17}{18}$ is already in its simplest form.

Conclusion

In this article, we learned how to rename the fractions $\frac{4}{9}$ and $\frac{17}{18}$ using the least common denominator. We found that the LCD of these fractions is 18 and used it to rename the fractions. By renaming fractions with the least common denominator, we can make it easier to compare or add them together.

Examples

Here are some examples of renaming fractions with the least common denominator:

Example 1

Rename $\frac{3}{8}$ and $\frac{5}{12}$ using the least common denominator.

The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...

The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

The least common denominator of $\frac{3}{8}$ and $\frac{5}{12}$ is 24.

$\frac{3}{8} \times \frac{3}{3} = \frac{9}{24}$

$\frac{5}{12} \times \frac{2}{2} = \frac{10}{24}$

Example 2

Rename $\frac{2}{5}$ and $\frac{3}{10}$ using the least common denominator.

The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...

The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...

The least common denominator of $\frac{2}{5}$ and $\frac{3}{10}$ is 10.

$\frac{2}{5} \times \frac{2}{2} = \frac{4}{10}$

$\frac{3}{10}$ is already in its simplest form.

Practice Problems

Here are some practice problems to help you understand how to rename fractions with the least common denominator:

Problem 1

Rename $\frac{6}{8}$ and $\frac{9}{12}$ using the least common denominator.

Problem 2

Rename $\frac{4}{9}$ and $\frac{16}{18}$ using the least common denominator.

Problem 3

Rename $\frac{3}{4}$ and $\frac{5}{8}$ using the least common denominator.

Answer Key

Problem 1

The least common denominator of $\frac{6}{8}$ and $\frac{9}{12}$ is 24.

$\frac{6}{8} \times \frac{3}{3} = \frac{18}{24}$

$\frac{9}{12} \times \frac{2}{2} = \frac{18}{24}$

Problem 2

The least common denominator of $\frac{4}{9}$ and $\frac{16}{18}$ is 18.

$\frac{4}{9} \times \frac{2}{2} = \frac{8}{18}$

$\frac{16}{18}$ is already in its simplest form.

Problem 3

The least common denominator of $\frac{3}{4}$ and $\frac{5}{8}$ is 8.

$\frac{3}{4} \times \frac{2}{2} = \frac{6}{8}$

$\frac{5}{8}$ is already in its simplest form.

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Introduction

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

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

A: The least common denominator (LCD) is the smallest number that is a multiple of both denominators of the fractions. It is used to rename fractions with different denominators to have the same denominator, making it easier to compare or add them together.

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 number that is common to both lists.

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 LCD by finding the product of the two denominators and then dividing it by their greatest common divisor (GCD).

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 is always a good idea to understand the concept behind finding the LCD, so you can apply it to more complex problems.

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

A: To rename a fraction with the LCD, you need to multiply the numerator and denominator of the fraction by the same number, so that the denominator becomes the LCD.

Q: What if the denominator of the fraction is already the least common denominator?

A: If the denominator of the fraction is already the LCD, then the fraction is already in its simplest form and you do not need to rename it.

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. By renaming the fractions with the LCD, you can add or subtract them easily.

Q: What are some examples of renaming fractions with the least common denominator?

A: Here are some examples of renaming fractions with the LCD:

Example 1

Rename $\frac{3}{8}$ and $\frac{5}{12}$ using the least common denominator.

The LCD of $\frac{3}{8}$ and $\frac{5}{12}$ is 24.

$\frac{3}{8} \times \frac{3}{3} = \frac{9}{24}$

$\frac{5}{12} \times \frac{2}{2} = \frac{10}{24}$

Example 2

Rename $\frac{2}{5}$ and $\frac{3}{10}$ using the least common denominator.

The LCD of $\frac{2}{5}$ and $\frac{3}{10}$ is 10.

$\frac{2}{5} \times \frac{2}{2} = \frac{4}{10}$

$\frac{3}{10}$ is already in its simplest form.

Conclusion

In this article, we answered some frequently asked questions about renaming fractions with the least common denominator. We also provided some examples of renaming fractions with the LCD. By understanding how to rename fractions with the LCD, you can make it easier to compare or add them together.

Practice Problems

Here are some practice problems to help you understand how to rename fractions with the least common denominator:

Problem 1

Rename $\frac{6}{8}$ and $\frac{9}{12}$ using the least common denominator.

Problem 2

Rename $\frac{4}{9}$ and $\frac{16}{18}$ using the least common denominator.

Problem 3

Rename $\frac{3}{4}$ and $\frac{5}{8}$ using the least common denominator.

Answer Key

Problem 1

The LCD of $\frac{6}{8}$ and $\frac{9}{12}$ is 24.

$\frac{6}{8} \times \frac{3}{3} = \frac{18}{24}$

$\frac{9}{12} \times \frac{2}{2} = \frac{18}{24}$

Problem 2

The LCD of $\frac{4}{9}$ and $\frac{16}{18}$ is 18.

$\frac{4}{9} \times \frac{2}{2} = \frac{8}{18}$

$\frac{16}{18}$ is already in its simplest form.

Problem 3

The LCD of $\frac{3}{4}$ and $\frac{5}{8}$ is 8.

$\frac{3}{4} \times \frac{2}{2} = \frac{6}{8}$

$\frac{5}{8}$ is already in its simplest form.

Introduction

What is the Least Common Denominator?

Finding the Least Common Denominator

Multiples of 9

Multiples of 18

Finding the LCD

Renaming Fractions with the Least Common Denominator

Renaming 49\frac{4}{9}94​

Renaming 1718\frac{17}{18}1817​

Conclusion

Examples

Example 1

Example 2

Practice Problems

Problem 1

Problem 2

Problem 3

Answer Key

Problem 1

Problem 2

Problem 3

Introduction

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

Q: How do I find the least common denominator?

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

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

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

Q: What if the denominator of the fraction is already the least common denominator?

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

Q: What are some examples of renaming fractions with the least common denominator?

Example 1

Example 2

Conclusion

Practice Problems

Problem 1

Problem 2

Problem 3

Answer Key

Problem 1

Problem 2

Problem 3

Renaming $\frac{4}{9}$

Renaming $\frac{17}{18}$