Compare These Fractions. Choose The Sign That Makes The Statement True.$\frac{2}{5} \quad ? \quad \frac{19}{20}$A. $\ \textless \ $ B. $\ \textgreater \ $ C. $=$

Introduction

Comparing fractions is an essential skill in mathematics, and it's often used in various real-world applications. In this article, we will compare two fractions, $\frac{2}{5}$ and $\frac{19}{20}$, and determine which sign makes the statement true. We will also explore the concept of equivalent fractions and how to compare them.

Understanding Fractions

A fraction is a way to represent a part of a whole. It consists of two parts: the numerator (the top number) and the denominator (the bottom number). The numerator represents the number of equal parts we have, and the denominator represents the total number of parts the whole is divided into.

For example, the fraction $\frac{2}{5}$ means we have 2 equal parts out of a total of 5 parts.

Comparing Fractions

To compare two fractions, we need to determine which one is larger or smaller. We can do this by comparing the numerators and denominators of the fractions.

Method 1: Cross-Multiplication

One way to compare fractions is by cross-multiplying. This involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.

For example, to compare $\frac{2}{5}$ and $\frac{19}{20}$, we can cross-multiply as follows:

$$\frac{2}{5} \times 20 = 40$$

$$\frac{19}{20} \times 5 = 19$$

Since 40 is greater than 19, we can conclude that $\frac{2}{5}$ is greater than $\frac{19}{20}$.

Method 2: Equivalent Fractions

Another way to compare fractions is by finding equivalent fractions. Equivalent fractions are fractions that have the same value, but different numerators and denominators.

For example, the fraction $\frac{2}{5}$ is equivalent to $\frac{4}{10}$, since both fractions have the same value.

To compare $\frac{2}{5}$ and $\frac{19}{20}$, we can find equivalent fractions as follows:

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

$$\frac{19}{20} = \frac{38}{40}$$

Since $\frac{4}{10}$ is less than $\frac{38}{40}$, we can conclude that $\frac{2}{5}$ is less than $\frac{19}{20}$.

Conclusion

In conclusion, comparing fractions is an essential skill in mathematics. We can compare fractions using cross-multiplication or equivalent fractions. In this article, we compared the fractions $\frac{2}{5}$ and $\frac{19}{20}$ and determined that $\frac{2}{5}$ is less than $\frac{19}{20}$.

Answer

The correct answer is B. $\ \textgreater \ $.

Why is this answer correct?

This answer is correct because $\frac{2}{5}$ is less than $\frac{19}{20}$. To determine which sign makes the statement true, we need to compare the fractions. Since $\frac{2}{5}$ is less than $\frac{19}{20}$, the correct sign is $\ \textgreater \ $.

Real-World Applications

Comparing fractions has many real-world applications. For example, in cooking, we often need to compare fractions to determine the amount of ingredients needed. In finance, we need to compare fractions to determine the interest rates on loans. In science, we need to compare fractions to determine the concentration of solutions.

Tips and Tricks

Here are some tips and tricks to help you compare fractions:

• Use cross-multiplication to compare fractions.
• Find equivalent fractions to compare fractions.
• Compare the numerators and denominators of the fractions.
• Use a number line to visualize the fractions.

Conclusion

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Q: What is the best way to compare fractions?

A: The best way to compare fractions is by using cross-multiplication or finding equivalent fractions. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa. Finding equivalent fractions involves finding fractions that have the same value, but different numerators and denominators.

Q: How do I know which fraction is larger or smaller?

A: To determine which fraction is larger or smaller, you need to compare the numerators and denominators of the fractions. If the numerator of one fraction is larger than the numerator of the other fraction, and the denominator of one fraction is smaller than the denominator of the other fraction, then the fraction with the larger numerator and smaller denominator is larger.

Q: What is an equivalent fraction?

A: An equivalent fraction is a fraction that has the same value as another fraction, but different numerators and denominators. For example, the fraction $\frac{2}{5}$ is equivalent to $\frac{4}{10}$, since both fractions have the same value.

Q: How do I find equivalent fractions?

A: To find equivalent fractions, you can multiply or divide the numerator and denominator of a fraction by the same number. For example, to find an equivalent fraction of $\frac{2}{5}$, you can multiply the numerator and denominator by 2, resulting in $\frac{4}{10}$.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way to represent a part of a whole, while a decimal is a way to represent a number as a sum of powers of 10. Fractions and decimals can be converted to each other by dividing the numerator by the denominator.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you can divide the numerator by the denominator. For example, to convert the fraction $\frac{2}{5}$ to a decimal, you can divide 2 by 5, resulting in 0.4.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you can express the decimal as a sum of powers of 10. For example, the decimal 0.4 can be expressed as the fraction $\frac{4}{10}$.

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

A: Comparing fractions has many real-world applications, including cooking, finance, and science. In cooking, we often need to compare fractions to determine the amount of ingredients needed. In finance, we need to compare fractions to determine the interest rates on loans. In science, we need to compare fractions to determine the concentration of solutions.

Q: What are some tips and tricks for comparing fractions?

A: Here are some tips and tricks for comparing fractions:

• Use cross-multiplication to compare fractions.
• Find equivalent fractions to compare fractions.
• Compare the numerators and denominators of the fractions.
• Use a number line to visualize the fractions.

Conclusion

In conclusion, comparing fractions is an essential skill in mathematics. We can compare fractions using cross-multiplication or equivalent fractions. In this article, we answered some frequently asked questions about comparing fractions and provided some tips and tricks for comparing fractions.