Select The Best Answer For The Question.14. Which Fraction Has A Value That's Equal To $\frac{7}{8}$?A. $\frac{49}{64}$B. \$\frac{15}{8}$[/tex\]C. $\frac{21}{24}$D. $\frac{56}{8}$

Introduction

Fractions are an essential part of mathematics, and understanding how to compare and simplify them is crucial for solving various mathematical problems. In this article, we will delve into the world of fractions and explore the concept of equivalent fractions. We will examine a specific question that asks us to identify the fraction that has a value equal to $\frac{7}{8}$. Our goal is to analyze each option carefully and determine which one is the correct answer.

Understanding Equivalent Fractions

Equivalent fractions are fractions that have the same value, even though they may look different. To determine if two fractions are equivalent, we can multiply or divide both the numerator and the denominator by the same number. This operation does not change the value of the fraction.

For example, consider the fraction $\frac{1}{2}$. We can multiply both the numerator and the denominator by 2 to get $\frac{2}{4}$. Since we multiplied both numbers by the same value, the fraction remains the same. Therefore, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions.

Analyzing the Options

Now that we understand equivalent fractions, let's analyze each option carefully.

Option A: $\frac{49}{64}$

To determine if this fraction is equivalent to $\frac{7}{8}$, we can multiply both the numerator and the denominator by the same number. Let's try multiplying both numbers by 8.

$\frac{49}{64} \times \frac{8}{8} = \frac{392}{512}$

Since we multiplied both numbers by 8, the fraction remains the same. However, we can simplify the fraction further by dividing both numbers by their greatest common divisor, which is 8.

$\frac{392}{512} = \frac{49}{64}$

As we can see, the fraction $\frac{49}{64}$ is indeed equivalent to $\frac{7}{8}$.

Option B: $\frac{15}{8}$

To determine if this fraction is equivalent to $\frac{7}{8}$, we can multiply both the numerator and the denominator by the same number. Let's try multiplying both numbers by 8.

$\frac{15}{8} \times \frac{8}{8} = \frac{120}{64}$

Since we multiplied both numbers by 8, the fraction remains the same. However, we can simplify the fraction further by dividing both numbers by their greatest common divisor, which is 8.

$\frac{120}{64} = \frac{15}{8}$

As we can see, the fraction $\frac{15}{8}$ is not equivalent to $\frac{7}{8}$.

Option C: $\frac{21}{24}$

To determine if this fraction is equivalent to $\frac{7}{8}$, we can multiply both the numerator and the denominator by the same number. Let's try multiplying both numbers by 8.

$\frac{21}{24} \times \frac{8}{8} = \frac{168}{192}$

Since we multiplied both numbers by 8, the fraction remains the same. However, we can simplify the fraction further by dividing both numbers by their greatest common divisor, which is 8.

$\frac{168}{192} = \frac{21}{24}$

As we can see, the fraction $\frac{21}{24}$ is not equivalent to $\frac{7}{8}$.

Option D: $\frac{56}{8}$

To determine if this fraction is equivalent to $\frac{7}{8}$, we can multiply both the numerator and the denominator by the same number. Let's try multiplying both numbers by 8.

$\frac{56}{8} \times \frac{8}{8} = \frac{448}{64}$

Since we multiplied both numbers by 8, the fraction remains the same. However, we can simplify the fraction further by dividing both numbers by their greatest common divisor, which is 8.

$\frac{448}{64} = \frac{56}{8}$

As we can see, the fraction $\frac{56}{8}$ is not equivalent to $\frac{7}{8}$.

Conclusion

After analyzing each option carefully, we can conclude that the correct answer is Option A: $\frac{49}{64}$. This fraction is equivalent to $\frac{7}{8}$, as we demonstrated by multiplying both numbers by 8 and simplifying the fraction further.

Final Thoughts

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Q: What is an equivalent fraction?

A: An equivalent fraction is a fraction that has the same value as another fraction, even though they may look different. To determine if two fractions are equivalent, we can multiply or divide both the numerator and the denominator by the same number.

Q: How do I determine if two fractions are equivalent?

A: To determine if two fractions are equivalent, we can multiply or divide both the numerator and the denominator by the same number. If the resulting fraction is the same as the original fraction, then the two fractions are equivalent.

Q: Can I simplify an equivalent fraction?

A: Yes, we can simplify an equivalent fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). This will result in a simpler fraction that has the same value as the original fraction.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder. We can use the GCD to simplify a fraction and make it easier to work with.

Q: Can I multiply or divide both the numerator and the denominator by any number?

A: No, we can only multiply or divide both the numerator and the denominator by the same number. If we multiply or divide both numbers by different numbers, the resulting fraction will not be equivalent to the original fraction.

Q: What is the difference between equivalent fractions and similar fractions?

A: Equivalent fractions have the same value, while similar fractions have the same ratio of numerator to denominator. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions, while $\frac{1}{2}$ and $\frac{3}{6}$ are similar fractions.

Q: Can I use equivalent fractions to solve real-world problems?

A: Yes, equivalent fractions can be used to solve real-world problems. For example, if we need to divide a pizza into equal-sized slices, we can use equivalent fractions to determine the number of slices and the size of each slice.

Q: What are some common applications of equivalent fractions?

A: Equivalent fractions have many common applications in mathematics and real-world problems, such as:

• Simplifying fractions
• Adding and subtracting fractions
• Multiplying and dividing fractions
• Solving equations and inequalities
• Working with ratios and proportions

Q: Can I use a calculator to find equivalent fractions?

A: Yes, we can use a calculator to find equivalent fractions. However, it's often more efficient and effective to use mental math or simple calculations to find equivalent fractions.

Q: What are some common mistakes to avoid when working with equivalent fractions?

A: Some common mistakes to avoid when working with equivalent fractions include:

• Multiplying or dividing both the numerator and the denominator by different numbers
• Not simplifying fractions when possible
• Not using the greatest common divisor (GCD) to simplify fractions
• Not checking if two fractions are equivalent before using them in a calculation

Conclusion

Equivalent fractions are an essential concept in mathematics, and understanding how to work with them is crucial for solving various mathematical problems. By following the tips and guidelines outlined in this article, you can develop a deeper understanding of equivalent fractions and improve your math skills.