Danielle Said She Read 1 2 \frac{1}{2} 2 1 ​ Of A Book. Select All The Fractions That Are Equivalent To 1 2 \frac{1}{2} 2 1 ​ .1. 3 6 \frac{3}{6} 6 3 ​ 2. 5 10 \frac{5}{10} 10 5 ​ 3. 6 12 \frac{6}{12} 12 6 ​ 4. 3 5 \frac{3}{5} 5 3 ​ 5.

Equivalent Fractions: Understanding Danielle's Book Reading

In mathematics, equivalent fractions are fractions that have the same value, even though they may look different. Danielle, a book lover, claims to have read half of a book. We can represent this as a fraction, $\frac{1}{2}$. In this article, we will explore equivalent fractions to Danielle's book reading experience and identify which fractions are equivalent to $\frac{1}{2}$.

What are Equivalent Fractions?

Equivalent fractions are fractions that have the same value, but may have different numerators and denominators. To determine if two fractions are equivalent, we can divide both the numerator and the denominator of one fraction by their greatest common divisor (GCD). If the resulting fraction is the same as the other fraction, then the two fractions are equivalent.

Finding Equivalent Fractions

To find equivalent fractions to $\frac{1}{2}$, we can start by listing the multiples of the numerator and the denominator. The multiples of 1 are 1, 2, 3, 4, 5, and so on. The multiples of 2 are 2, 4, 6, 8, 10, and so on. We can then create fractions by dividing the numerator by the denominator, using these multiples.

Option 1: $\frac{3}{6}$

To determine if $\frac{3}{6}$ is equivalent to $\frac{1}{2}$, we can divide both the numerator and the denominator of $\frac{3}{6}$ by their GCD, which is 3. This results in $\frac{1}{2}$, which is equivalent to Danielle's book reading experience.

Option 2: $\frac{5}{10}$

To determine if $\frac{5}{10}$ is equivalent to $\frac{1}{2}$, we can divide both the numerator and the denominator of $\frac{5}{10}$ by their GCD, which is 5. This results in $\frac{1}{2}$, which is equivalent to Danielle's book reading experience.

Option 3: $\frac{6}{12}$

To determine if $\frac{6}{12}$ is equivalent to $\frac{1}{2}$, we can divide both the numerator and the denominator of $\frac{6}{12}$ by their GCD, which is 6. This results in $\frac{1}{2}$, which is equivalent to Danielle's book reading experience.

Option 4: $\frac{3}{5}$

To determine if $\frac{3}{5}$ is equivalent to $\frac{1}{2}$, we can divide both the numerator and the denominator of $\frac{3}{5}$ by their GCD, which is 1. This results in $\frac{3}{5}$, which is not equivalent to Danielle's book reading experience.

Option 5: $\frac{4}{8}$

To determine if $\frac{4}{8}$ is equivalent to $\frac{1}{2}$, we can divide both the numerator and the denominator of $\frac{4}{8}$ by their GCD, which is 4. This results in $\frac{1}{2}$, which is equivalent to Danielle's book reading experience.

In conclusion, the equivalent fractions to Danielle's book reading experience, $\frac{1}{2}$, are $\frac{3}{6}$, $\frac{5}{10}$, $\frac{6}{12}$, and $\frac{4}{8}$. These fractions have the same value as $\frac{1}{2}$ and can be used to represent Danielle's book reading experience.

The correct answer is:

1. $\frac{3}{6}$
2. $\frac{5}{10}$
3. $\frac{6}{12}$
4. $\frac{4}{8}$
   Equivalent Fractions: A Q&A Guide

In our previous article, we explored equivalent fractions and identified the fractions that are equivalent to $\frac{1}{2}$. In this article, we will answer some frequently asked questions about equivalent fractions to provide a deeper understanding of this mathematical concept.

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

A: Equivalent fractions and equivalent ratios are related concepts, but they are not the same thing. Equivalent fractions are fractions that have the same value, but may have different numerators and denominators. Equivalent ratios, on the other hand, are ratios that have the same value, but may have different numbers.

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

A: To determine if two fractions are equivalent, you can divide both the numerator and the denominator of one fraction by their greatest common divisor (GCD). If the resulting fraction is the same as the other fraction, then the two fractions are equivalent.

Q: Can equivalent fractions have different denominators?

A: Yes, equivalent fractions can have different denominators. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions, even though they have different denominators.

Q: Can equivalent fractions have different numerators?

A: Yes, equivalent fractions can have different numerators. For example, $\frac{1}{2}$ and $\frac{3}{6}$ are equivalent fractions, even though they have different numerators.

Q: How do I simplify equivalent fractions?

A: To simplify equivalent fractions, you can divide both the numerator and the denominator by their greatest common divisor (GCD). This will result in a simplified fraction that is equivalent to the original fraction.

Q: Can equivalent fractions be used in real-world applications?

A: Yes, equivalent fractions can be used in real-world applications. For example, if you are baking a cake and need to divide it into equal parts, you can use equivalent fractions to ensure that each part is the same size.

Q: Can equivalent fractions be used in algebra?

A: Yes, equivalent fractions can be used in algebra. For example, if you are solving an equation and need to simplify a fraction, you can use equivalent fractions to find a simpler form of the fraction.

Mistake 1: Assuming that equivalent fractions have the same denominator

A: Equivalent fractions do not have to have the same denominator. For example, $\frac{1}{2}$ and $\frac{3}{6}$ are equivalent fractions, even though they have different denominators.

Mistake 2: Assuming that equivalent fractions have the same numerator

A: Equivalent fractions do not have to have the same numerator. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions, even though they have different numerators.

Mistake 3: Not simplifying equivalent fractions

A: Equivalent fractions can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). This will result in a simplified fraction that is equivalent to the original fraction.

In conclusion, equivalent fractions are an important concept in mathematics that can be used in a variety of real-world applications. By understanding equivalent fractions, you can simplify complex fractions and solve equations more easily. We hope that this Q&A guide has provided you with a deeper understanding of equivalent fractions and how to use them in your daily life.

The correct answers to the Q&A guide are:

1. Equivalent fractions and equivalent ratios are related concepts, but they are not the same thing.
2. To determine if two fractions are equivalent, you can divide both the numerator and the denominator of one fraction by their greatest common divisor (GCD).
3. Yes, equivalent fractions can have different denominators.
4. Yes, equivalent fractions can have different numerators.
5. To simplify equivalent fractions, you can divide both the numerator and the denominator by their greatest common divisor (GCD).
6. Yes, equivalent fractions can be used in real-world applications.
7. Yes, equivalent fractions can be used in algebra.
8. Equivalent fractions do not have to have the same denominator.
9. Equivalent fractions do not have to have the same numerator.
10. Equivalent fractions can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).