Write A Fraction Equivalent To 3 5 \frac{3}{5} 5 3 ​ .

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1.1 Introduction

Fractions are a fundamental concept in mathematics, representing a part of a whole. In this discussion, we will explore how to write a fraction equivalent to $\frac{3}{5}$. This involves understanding the concept of equivalent fractions and how to manipulate them to obtain a new fraction with the same value.

1.2 Understanding Equivalent Fractions

Equivalent fractions are fractions that have the same value, but with different numerators and denominators. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they both represent the same part of a whole. To write a fraction equivalent to $\frac{3}{5}$, we need to find a fraction with the same value, but with different numerators and denominators.

1.3 Multiplying the Numerator and Denominator

One way to write a fraction equivalent to $\frac{3}{5}$ is to multiply the numerator and denominator by the same number. This will not change the value of the fraction, but will give us a new fraction with the same value. For example, if we multiply the numerator and denominator of $\frac{3}{5}$ by 2, we get:

$$\frac{3}{5} \times \frac{2}{2} = \frac{6}{10}$$

1.4 Simplifying the Fraction

The fraction $\frac{6}{10}$ can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 6 and 10 is 2. Dividing both the numerator and denominator by 2 gives us:

$$\frac{6}{10} = \frac{3}{5}$$

1.5 Writing a Fraction Equivalent to $\frac{3}{5}$

To write a fraction equivalent to $\frac{3}{5}$, we can multiply the numerator and denominator by the same number. Let's try multiplying the numerator and denominator by 3:

$$\frac{3}{5} \times \frac{3}{3} = \frac{9}{15}$$

1.6 Simplifying the Fraction

The fraction $\frac{9}{15}$ can be simplified by dividing both the numerator and denominator by their GCD. In this case, the GCD of 9 and 15 is 3. Dividing both the numerator and denominator by 3 gives us:

$$\frac{9}{15} = \frac{3}{5}$$

1.7 Conclusion

In this discussion, we have explored how to write a fraction equivalent to $\frac{3}{5}$. We have seen that multiplying the numerator and denominator by the same number will give us a new fraction with the same value. We have also seen that simplifying the fraction by dividing both the numerator and denominator by their GCD will give us the simplest form of the fraction. By following these steps, we can write a fraction equivalent to $\frac{3}{5}$.

1.8 Example Problems

1.8.1 Problem 1

Write a fraction equivalent to $\frac{2}{3}$.

1.8.2 Solution

To write a fraction equivalent to $\frac{2}{3}$, we can multiply the numerator and denominator by the same number. Let's try multiplying the numerator and denominator by 2:

$$\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}$$

The fraction $\frac{4}{6}$ can be simplified by dividing both the numerator and denominator by their GCD. In this case, the GCD of 4 and 6 is 2. Dividing both the numerator and denominator by 2 gives us:

$$\frac{4}{6} = \frac{2}{3}$$

1.8.3 Problem 2

Write a fraction equivalent to $\frac{4}{5}$.

1.8.4 Solution

To write a fraction equivalent to $\frac{4}{5}$, we can multiply the numerator and denominator by the same number. Let's try multiplying the numerator and denominator by 2:

$$\frac{4}{5} \times \frac{2}{2} = \frac{8}{10}$$

The fraction $\frac{8}{10}$ can be simplified by dividing both the numerator and denominator by their GCD. In this case, the GCD of 8 and 10 is 2. Dividing both the numerator and denominator by 2 gives us:

$$\frac{8}{10} = \frac{4}{5}$$

1.9 Final Answer

The final answer is: $\boxed{\frac{9}{15}}$

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2.1 Introduction

In the previous discussion, we explored how to write a fraction equivalent to $\frac{3}{5}$. In this Q&A article, we will answer some common questions related to writing fractions equivalent to $\frac{3}{5}$.

2.2 Q&A

2.2.1 Q: How do I write a fraction equivalent to $\frac{3}{5}$?

A: To write a fraction equivalent to $\frac{3}{5}$, you can multiply the numerator and denominator by the same number. For example, if you multiply the numerator and denominator by 2, you get:

$$\frac{3}{5} \times \frac{2}{2} = \frac{6}{10}$$

2.2.2 Q: Can I simplify the fraction after multiplying the numerator and denominator?

A: Yes, you can simplify the fraction after multiplying the numerator and denominator. To simplify the fraction, you need to divide both the numerator and denominator by their greatest common divisor (GCD). For example, if you multiply the numerator and denominator by 2, you get:

$$\frac{3}{5} \times \frac{2}{2} = \frac{6}{10}$$

You can simplify the fraction by dividing both the numerator and denominator by 2:

$$\frac{6}{10} = \frac{3}{5}$$

2.2.3 Q: What if I multiply the numerator and denominator by a number that is not a multiple of the denominator?

A: If you multiply the numerator and denominator by a number that is not a multiple of the denominator, you will get a fraction that is not equivalent to the original fraction. For example, if you multiply the numerator and denominator of $\frac{3}{5}$ by 3, you get:

$$\frac{3}{5} \times \frac{3}{3} = \frac{9}{15}$$

This fraction is not equivalent to the original fraction $\frac{3}{5}$.

2.2.4 Q: Can I write a fraction equivalent to $\frac{3}{5}$ by dividing the numerator and denominator by a number?

A: No, you cannot write a fraction equivalent to $\frac{3}{5}$ by dividing the numerator and denominator by a number. To write a fraction equivalent to $\frac{3}{5}$, you need to multiply the numerator and denominator by the same number.

2.2.5 Q: How do I know if a fraction is equivalent to $\frac{3}{5}$?

A: To determine if a fraction is equivalent to $\frac{3}{5}$, you need to check if the fraction has the same value as $\frac{3}{5}$. You can do this by multiplying the numerator and denominator of the fraction by the same number and simplifying the fraction. If the simplified fraction is equal to $\frac{3}{5}$, then the original fraction is equivalent to $\frac{3}{5}$.

2.3 Example Problems

2.3.1 Problem 1

Write a fraction equivalent to $\frac{2}{3}$.

2.3.2 Solution

To write a fraction equivalent to $\frac{2}{3}$, you can multiply the numerator and denominator by the same number. Let's try multiplying the numerator and denominator by 2:

$$\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}$$

The fraction $\frac{4}{6}$ can be simplified by dividing both the numerator and denominator by their GCD. In this case, the GCD of 4 and 6 is 2. Dividing both the numerator and denominator by 2 gives us:

$$\frac{4}{6} = \frac{2}{3}$$

2.3.3 Problem 2

Write a fraction equivalent to $\frac{4}{5}$.

2.3.4 Solution

To write a fraction equivalent to $\frac{4}{5}$, you can multiply the numerator and denominator by the same number. Let's try multiplying the numerator and denominator by 2:

$$\frac{4}{5} \times \frac{2}{2} = \frac{8}{10}$$

The fraction $\frac{8}{10}$ can be simplified by dividing both the numerator and denominator by their GCD. In this case, the GCD of 8 and 10 is 2. Dividing both the numerator and denominator by 2 gives us:

$$\frac{8}{10} = \frac{4}{5}$$

2.4 Final Answer

The final answer is: $\boxed{\frac{9}{15}}$