Which Phrase Should Be Inserted On The Line To Correctly Compare The Two Fractions? Use The Models To Help.\[$\frac{4}{5} \longrightarrow \frac{16}{20}\$\]- \[$\frac{4}{5}\$\]- \[$\frac{16}{20}\$\]A. Is Greater Than B. Cannot

Understanding the Basics of Fractions

Fractions are a fundamental concept in mathematics, representing a part of a whole. They consist of two parts: the numerator, which is the top number, and the denominator, which is the bottom number. In this article, we will explore how to compare fractions, using models to help us understand the concept.

What is Equivalent Ratio?

Equivalent ratios are fractions that have the same value, but with different numerators and denominators. For example, $\frac{4}{5}$ and $\frac{16}{20}$ are equivalent ratios because they represent the same value, but with different numerators and denominators.

Modeling Equivalent Ratios

To compare fractions, we can use models to help us visualize the concept. Let's consider the following example:

• We have a pizza that is divided into 5 equal parts. Each part represents $\frac{1}{5}$ of the pizza.
• We also have a pizza that is divided into 20 equal parts. Each part represents $\frac{1}{20}$ of the pizza.

Comparing Fractions Using Models

Now, let's compare the two fractions: $\frac{4}{5}$ and $\frac{16}{20}$. We can use the models to help us understand the concept.

• If we have 4 parts of the first pizza, we can represent it as $\frac{4}{5}$.
• If we have 16 parts of the second pizza, we can represent it as $\frac{16}{20}$.

Which Phrase Should be Inserted on the Line?

Now that we have compared the two fractions using models, we can determine which phrase should be inserted on the line.

• If $\frac{4}{5}$ is greater than $\frac{16}{20}$, we would insert the phrase "is greater than".
• If $\frac{4}{5}$ is not greater than $\frac{16}{20}$, we would insert the phrase "cannot".

Using the Models to Help Us Understand

Let's use the models to help us understand the concept.

• If we have 4 parts of the first pizza, we can represent it as $\frac{4}{5}$.
• If we have 16 parts of the second pizza, we can represent it as $\frac{16}{20}$.

Comparing the Fractions

Now that we have compared the two fractions using models, we can determine which phrase should be inserted on the line.

• If $\frac{4}{5}$ is greater than $\frac{16}{20}$, we would insert the phrase "is greater than".
• If $\frac{4}{5}$ is not greater than $\frac{16}{20}$, we would insert the phrase "cannot".

Conclusion

In conclusion, comparing fractions using models can help us understand the concept. By using the models, we can determine which phrase should be inserted on the line. In this case, we can see that $\frac{4}{5}$ is not greater than $\frac{16}{20}$, so the correct phrase to insert on the line is "cannot".

Answer

The correct answer is B. cannot.

Why is it Important to Compare Fractions?

Comparing fractions is an important concept in mathematics because it helps us understand the value of different fractions. By comparing fractions, we can determine which fraction is greater or lesser than another fraction. This concept is essential in real-life situations, such as cooking, measuring ingredients, and calculating proportions.

Real-Life Applications of Comparing Fractions

Comparing fractions has many real-life applications. For example:

• In cooking, comparing fractions can help us determine the correct amount of ingredients to use.
• In measuring ingredients, comparing fractions can help us determine the correct amount of ingredients to use.
• In calculating proportions, comparing fractions can help us determine the correct proportion of ingredients to use.

Conclusion

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Q: What is the difference between equivalent ratios and comparing fractions?

A: Equivalent ratios are fractions that have the same value, but with different numerators and denominators. Comparing fractions, on the other hand, is the process of determining which fraction is greater or lesser than another fraction.

Q: How do I compare fractions with different denominators?

A: To compare fractions with different denominators, you can use the following steps:

1. Find the least common multiple (LCM) of the two denominators.
2. Convert both fractions to have the LCM as the denominator.
3. Compare the numerators of the two fractions.

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

A: The least common multiple (LCM) is the smallest number that is a multiple of both numbers. For example, the LCM of 4 and 6 is 12.

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

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

1. List the multiples of each number.
2. Find the smallest number that is a multiple of both numbers.

Q: What is the difference between adding and comparing fractions?

A: Adding fractions is the process of combining two or more fractions to get a total value. Comparing fractions, on the other hand, is the process of determining which fraction is greater or lesser than another fraction.

Q: Can I compare fractions with different signs?

A: Yes, you can compare fractions with different signs. To compare fractions with different signs, you can use the following steps:

1. Determine the sign of the difference between the two fractions.
2. Compare the absolute values of the two fractions.

Q: How do I compare fractions with decimals?

A: To compare fractions with decimals, you can convert the decimal to a fraction and then compare the two fractions.

Q: What is the difference between comparing fractions and comparing decimals?

A: Comparing fractions is the process of determining which fraction is greater or lesser than another fraction. Comparing decimals, on the other hand, is the process of determining which decimal is greater or lesser than another decimal.

Q: Can I compare fractions with mixed numbers?

A: Yes, you can compare fractions with mixed numbers. To compare fractions with mixed numbers, you can convert the mixed number to an improper fraction and then compare the two fractions.

Q: How do I compare fractions with negative numbers?

A: To compare fractions with negative numbers, you can use the following steps:

1. Determine the sign of the difference between the two fractions.
2. Compare the absolute values of the two fractions.

Q: What is the difference between comparing fractions and solving equations?

A: Comparing fractions is the process of determining which fraction is greater or lesser than another fraction. Solving equations, on the other hand, is the process of finding the value of a variable that makes an equation true.

Q: Can I compare fractions with variables?

A: Yes, you can compare fractions with variables. To compare fractions with variables, you can use the following steps:

1. Determine the value of the variable.
2. Compare the two fractions.

Q: How do I compare fractions with exponents?

A: To compare fractions with exponents, you can use the following steps:

1. Determine the value of the exponent.
2. Compare the two fractions.

Q: What is the difference between comparing fractions and graphing?

A: Comparing fractions is the process of determining which fraction is greater or lesser than another fraction. Graphing, on the other hand, is the process of visualizing the relationship between two or more variables.

Q: Can I compare fractions with graphs?

A: Yes, you can compare fractions with graphs. To compare fractions with graphs, you can use the following steps:

1. Determine the value of the variable.
2. Compare the two fractions.

Conclusion

In conclusion, comparing fractions is an important concept in mathematics that has many real-life applications. By understanding how to compare fractions, you can determine which fraction is greater or lesser than another fraction. This concept is essential in real-life situations, such as cooking, measuring ingredients, and calculating proportions.