Convert each fraction to have the common denominator

Oct 13, 2025 by vinooalluri.com 36 views

$Convert each fraction to have the common denominator$

Comparing Fractions: Who Hikes Farther?

When it comes to comparing fractions, it's essential to understand the concept of equivalent ratios. In this article, we'll explore how to use a fraction comparison strategy to determine who hikes farther between Jonah and Jane.

Understanding the Problem

Jonah hikes 9/10 mile along the Rock Edge Trail, while Jane hikes 7/8 mile along the same trail. To determine who hikes farther, we need to compare these two fractions.

Fraction Comparison Strategy

To compare fractions, we can use the following steps:

Find a common denominator: The common denominator is the least common multiple (LCM) of the two denominators. In this case, the denominators are 10 and 8.
Convert each fraction to have the common denominator: Once we have the common denominator, we can convert each fraction to have that denominator.
Compare the numerators: With the fractions having the same denominator, we can compare the numerators to determine which fraction is larger.

Step 1: Find a Common Denominator

The least common multiple (LCM) of 10 and 8 is 40. Therefore, the common denominator is 40.

Step 2: Convert Each Fraction to Have the Common Denominator

To convert 9/10 to have a denominator of 40, we multiply both the numerator and denominator by 4:

9/10 = (9 × 4) / (10 × 4) = 36/40

To convert 7/8 to have a denominator of 40, we multiply both the numerator and denominator by 5:

7/8 = (7 × 5) / (8 × 5) = 35/40

Step 3: Compare the Numerators

Now that both fractions have the same denominator, we can compare the numerators:

36/40 > 35/40

Since 36 is greater than 35, we can conclude that 36/40 is the larger fraction.

Conclusion

Using the fraction comparison strategy, we can determine that Jonah hikes farther than Jane. To summarize:

Jonah hikes 9/10 mile along the Rock Edge Trail, which is equivalent to 36/40 miles.
Jane hikes 7/8 mile along the same trail, which is equivalent to 35/40 miles.
Since 36/40 is greater than 35/40, Jonah hikes farther than Jane.

Real-World Applications

Comparing fractions is a fundamental concept in mathematics that has numerous real-world applications. In this article, we've seen how to use a fraction comparison strategy to determine who hikes farther between Jonah and Jane. This concept can be applied to various situations, such as:

Comparing the prices of different products
Determining the amount of time spent on a task
Calculating the area of a shape

By understanding how to compare fractions, we can make informed decisions and solve problems in a variety of contexts.

Common Misconceptions

When comparing fractions, it's essential to avoid common misconceptions. Some of these misconceptions include:

Assuming that the larger numerator always means the larger fraction
Failing to find a common denominator
Not converting fractions to have the same denominator

By avoiding these misconceptions, we can ensure that our fraction comparisons are accurate and reliable.

Conclusion

In conclusion, comparing fractions is a crucial concept in mathematics that has numerous real-world applications. By using a fraction comparison strategy, we can determine who hikes farther between Jonah and Jane. This concept can be applied to various situations, and by understanding how to compare fractions, we can make informed decisions and solve problems in a variety of contexts.
Frequently Asked Questions: Comparing Fractions

In our previous article, we explored how to use a fraction comparison strategy to determine who hikes farther between Jonah and Jane. In this article, we'll answer some frequently asked questions about comparing fractions.

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

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. In the context of comparing fractions, the LCM is used to find a common denominator.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can use the following steps:

List the multiples of each number.
Identify the smallest number that appears in both lists.
The LCM is the smallest number that appears in both lists.

For example, to find the LCM of 10 and 8, you can list the multiples of each number:

Multiples of 10: 10, 20, 30, 40 Multiples of 8: 8, 16, 24, 32, 40

The LCM of 10 and 8 is 40.

Q: Why do I need to find a common denominator?

A: Finding a common denominator allows you to compare fractions with the same denominator. This makes it easier to compare the numerators and determine which fraction is larger.

Q: Can I compare fractions with different denominators?

A: While it's possible to compare fractions with different denominators, it's not always easy. If the denominators are not multiples of each other, you may need to find a common denominator to compare the fractions.

Q: How do I convert a fraction to have a different denominator?

A: To convert a fraction to have a different denominator, you can multiply both the numerator and denominator by the same number. This will give you a new fraction with the desired denominator.

For example, to convert 1/2 to have a denominator of 4, you can multiply both the numerator and denominator by 2:

1/2 = (1 × 2) / (2 × 2) = 2/4

Q: What if the numerators are equal?

A: If the numerators are equal, the fractions are equivalent. This means that the two fractions represent the same value.

For example, 1/2 and 2/4 are equivalent fractions because they have the same numerator and denominator.

Q: Can I compare mixed numbers?

A: Yes, you can compare mixed numbers. To compare mixed numbers, you can convert them to improper fractions and then compare the fractions.

For example, to compare 2 1/2 and 3 1/4, you can convert each mixed number to an improper fraction:

2 1/2 = 5/2 3 1/4 = 13/4

You can then compare the fractions:

5/2 < 13/4

Since 5/2 is less than 13/4, 2 1/2 is less than 3 1/4.

Q: What if I have a fraction with a zero numerator?

A: If you have a fraction with a zero numerator, the fraction is equal to zero. This is because any number multiplied by zero is equal to zero.

For example, 0/4 = 0

Conclusion

Comparing fractions is a fundamental concept in mathematics that has numerous real-world applications. By understanding how to compare fractions, you can make informed decisions and solve problems in a variety of contexts. We hope this article has helped you to better understand how to compare fractions and answer some of the most frequently asked questions about this topic.