Choose The Symbol That Correctly Compares These Mixed Numbers.${ 11 \frac{2}{7} \quad ? \quad 11 \frac{4}{6} }$A. { \ \textless \ $}$ B. { = $}$ C. { \ \textgreater \ $}$

Mar 8, 2025 by ADMIN 178 views

**Comparing Mixed Numbers: A Step-by-Step Guide**

Introduction

Mixed numbers are a combination of a whole number and a fraction. They are used to represent a value that is part of a whole. In this article, we will discuss how to compare mixed numbers and choose the correct symbol to represent the relationship between them.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form of:

${ a \frac{b}{c} }$

Where:

${ a }$ is the whole number part
${ b }$ is the numerator of the fraction
${ c }$ is the denominator of the fraction

For example, ${ 11 \frac{2}{7} }$ is a mixed number where ${ a = 11 }$ , ${ b = 2 }$ , and ${ c = 7 }$ .

Comparing Mixed Numbers

To compare mixed numbers, we need to compare the whole number part and the fraction part separately. We can use the following steps:

Compare the whole number part: If the whole number part of one mixed number is greater than the whole number part of the other mixed number, then the first mixed number is greater.
Compare the fraction part: If the whole number part is the same, then we need to compare the fraction part. If the fraction part of one mixed number is greater than the fraction part of the other mixed number, then the first mixed number is greater.

Comparing the Whole Number Part

To compare the whole number part, we simply compare the numbers. For example, if we have two mixed numbers:

${ 11 \frac{2}{7} \quad ? \quad 11 \frac{4}{6} }$

We can see that the whole number part is the same, which is 11. Therefore, we need to compare the fraction part.

Comparing the Fraction Part

To compare the fraction part, we need to compare the numerators and denominators separately. We can use the following steps:

Compare the numerators: If the numerator of one fraction is greater than the numerator of the other fraction, then the first fraction is greater.
Compare the denominators: If the numerators are the same, then we need to compare the denominators. If the denominator of one fraction is greater than the denominator of the other fraction, then the first fraction is smaller.

Comparing the Fractions

Let's compare the fractions in the example:

${ 11 \frac{2}{7} \quad ? \quad 11 \frac{4}{6} }$

We can see that the numerators are 2 and 4, respectively. Since 4 is greater than 2, the fraction ${ \frac{4}{6} }$ is greater than the fraction ${ \frac{2}{7} }$ .

Choosing the Correct Symbol

Based on the comparison, we can choose the correct symbol to represent the relationship between the mixed numbers:

${ 11 \frac{2}{7} \quad ? \quad 11 \frac{4}{6} }$

Since the fraction ${ \frac{4}{6} }$ is greater than the fraction ${ \frac{2}{7} }$ , we can choose the symbol ${ \textgreater }$ to represent the relationship.

Conclusion

In conclusion, comparing mixed numbers involves comparing the whole number part and the fraction part separately. We can use the steps outlined above to compare the whole number part and the fraction part. By choosing the correct symbol to represent the relationship between the mixed numbers, we can accurately compare them.

Common Mistakes to Avoid

When comparing mixed numbers, it's easy to make mistakes. Here are some common mistakes to avoid:

Comparing the whole number part only: Make sure to compare the whole number part and the fraction part separately.
Comparing the fractions incorrectly: Make sure to compare the numerators and denominators separately.
Choosing the wrong symbol: Make sure to choose the correct symbol to represent the relationship between the mixed numbers.

Practice Problems

Here are some practice problems to help you practice comparing mixed numbers:

Compare the mixed numbers ${ 12 \frac{3}{4} }$ and ${ 12 \frac{5}{8} }$ .
Compare the mixed numbers ${ 15 \frac{2}{3} }$ and ${ 15 \frac{4}{5} }$ .
Compare the mixed numbers ${ 18 \frac{1}{2} }$ and ${ 18 \frac{3}{4} }$ .

Answer Key

Here are the answers to the practice problems:

${ 12 \frac{3}{4} }$ is greater than ${ 12 \frac{5}{8} }$ .
${ 15 \frac{4}{5} }$ is greater than ${ 15 \frac{2}{3} }$ .
${ 18 \frac{3}{4} }$ is greater than ${ 18 \frac{1}{2} }$ .

Conclusion

Q: What is the first step in comparing mixed numbers?

A: The first step in comparing mixed numbers is to compare the whole number part. If the whole number part of one mixed number is greater than the whole number part of the other mixed number, then the first mixed number is greater.

Q: How do I compare the fraction part of mixed numbers?

A: To compare the fraction part of mixed numbers, you need to compare the numerators and denominators separately. If the numerator of one fraction is greater than the numerator of the other fraction, then the first fraction is greater. If the numerators are the same, then you need to compare the denominators. If the denominator of one fraction is greater than the denominator of the other fraction, then the first fraction is smaller.

Q: What if the whole number part and the fraction part are the same?

A: If the whole number part and the fraction part are the same, then the two mixed numbers are equal.

Q: Can I compare mixed numbers with different denominators?

A: Yes, you can compare mixed numbers with different denominators. To do this, you need to find a common denominator for the two fractions. Once you have a common denominator, you can compare the fractions.

Q: How do I choose the correct symbol to represent the relationship between mixed numbers?

A: To choose the correct symbol to represent the relationship between mixed numbers, you need to compare the whole number part and the fraction part separately. If the first mixed number is greater, then you can choose the symbol ${ \textgreater }$ . If the second mixed number is greater, then you can choose the symbol ${ \textless }$ . If the two mixed numbers are equal, then you can choose the symbol ${ = }$ .

Q: What are some common mistakes to avoid when comparing mixed numbers?

A: Some common mistakes to avoid when comparing mixed numbers include:

Comparing the whole number part only
Comparing the fractions incorrectly
Choosing the wrong symbol to represent the relationship between the mixed numbers

Q: How can I practice comparing mixed numbers?

A: You can practice comparing mixed numbers by using the steps outlined above and by working through practice problems. Some examples of practice problems include:

Comparing the mixed numbers ${ 12 \frac{3}{4} }$ and ${ 12 \frac{5}{8} }$
Comparing the mixed numbers ${ 15 \frac{2}{3} }$ and ${ 15 \frac{4}{5} }$
Comparing the mixed numbers ${ 18 \frac{1}{2} }$ and ${ 18 \frac{3}{4} }$

Q: What are some real-world applications of comparing mixed numbers?

A: Comparing mixed numbers has many real-world applications, including:

Measuring ingredients for a recipe
Calculating the cost of materials for a project
Determining the amount of time it will take to complete a task

Q: Can I use a calculator to compare mixed numbers?

A: Yes, you can use a calculator to compare mixed numbers. However, it's often faster and more efficient to compare mixed numbers by hand using the steps outlined above.

Q: How can I teach others to compare mixed numbers?

A: You can teach others to compare mixed numbers by using the steps outlined above and by providing practice problems for them to work through. Some additional tips for teaching others to compare mixed numbers include:

Using visual aids, such as diagrams or charts, to help illustrate the concept
Providing examples of real-world applications of comparing mixed numbers
Encouraging students to work through practice problems on their own and to ask questions if they need help