Identify the given fraction

Oct 13, 2025 by talynt.org 68 views

$Identify the given fraction$

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Introduction

In mathematics, equivalent fractions are fractions that have the same value, but their numerators and denominators are different. One way to find equivalent fractions is by using the division process. This method involves dividing the numerator and the denominator of a given fraction by the same number to obtain a new fraction that is equivalent to the original one. In this article, we will explore how to find the first three equivalent fractions for each of the given fractions using the division process.

Step-by-Step Process

To find equivalent fractions using the division process, follow these steps:

Identify the given fraction: Start by identifying the given fraction for which you want to find equivalent fractions.
Find the greatest common divisor (GCD): Determine the greatest common divisor (GCD) of the numerator and the denominator of the given fraction. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.
Divide the numerator and the denominator by the GCD: Divide the numerator and the denominator of the given fraction by the GCD to obtain a new fraction.
Repeat the process: Repeat steps 2 and 3 to find the next two equivalent fractions.

Finding Equivalent Fractions

a) $\frac{6}{12}$

To find the first three equivalent fractions for $\frac{6}{12}$ , follow the steps outlined above.

Identify the given fraction: The given fraction is $\frac{6}{12}$ .
Find the GCD: The GCD of 6 and 12 is 6.
Divide the numerator and the denominator by the GCD: Divide 6 and 12 by 6 to obtain $\frac{1}{2}$ .
Repeat the process: Repeat steps 2 and 3 to find the next two equivalent fractions.

To find the next equivalent fraction, divide 6 and 12 by 2 to obtain $\frac{3}{6}$ . To find the third equivalent fraction, divide 6 and 12 by 1 to obtain $\frac{6}{12}$ .

The first three equivalent fractions for $\frac{6}{12}$ are $\frac{1}{2}$ , $\frac{3}{6}$ , and $\frac{6}{12}$ .

b) $\frac{8}{16}$

To find the first three equivalent fractions for $\frac{8}{16}$ , follow the steps outlined above.

Identify the given fraction: The given fraction is $\frac{8}{16}$ .
Find the GCD: The GCD of 8 and 16 is 8.
Divide the numerator and the denominator by the GCD: Divide 8 and 16 by 8 to obtain $\frac{1}{2}$ .
Repeat the process: Repeat steps 2 and 3 to find the next two equivalent fractions.

To find the next equivalent fraction, divide 8 and 16 by 4 to obtain $\frac{2}{4}$ . To find the third equivalent fraction, divide 8 and 16 by 2 to obtain $\frac{4}{8}$ .

The first three equivalent fractions for $\frac{8}{16}$ are $\frac{1}{2}$ , $\frac{2}{4}$ , and $\frac{4}{8}$ .

c) $\frac{12}{18}$

To find the first three equivalent fractions for $\frac{12}{18}$ , follow the steps outlined above.

Identify the given fraction: The given fraction is $\frac{12}{18}$ .
Find the GCD: The GCD of 12 and 18 is 6.
Divide the numerator and the denominator by the GCD: Divide 12 and 18 by 6 to obtain $\frac{2}{3}$ .
Repeat the process: Repeat steps 2 and 3 to find the next two equivalent fractions.

To find the next equivalent fraction, divide 12 and 18 by 3 to obtain $\frac{4}{6}$ . To find the third equivalent fraction, divide 12 and 18 by 2 to obtain $\frac{6}{9}$ .

The first three equivalent fractions for $\frac{12}{18}$ are $\frac{2}{3}$ , $\frac{4}{6}$ , and $\frac{6}{9}$ .

d) $\frac{18}{24}$

To find the first three equivalent fractions for $\frac{18}{24}$ , follow the steps outlined above.

Identify the given fraction: The given fraction is $\frac{18}{24}$ .
Find the GCD: The GCD of 18 and 24 is 6.
Divide the numerator and the denominator by the GCD: Divide 18 and 24 by 6 to obtain $\frac{3}{4}$ .
Repeat the process: Repeat steps 2 and 3 to find the next two equivalent fractions.

To find the next equivalent fraction, divide 18 and 24 by 4 to obtain $\frac{9}{12}$ . To find the third equivalent fraction, divide 18 and 24 by 2 to obtain $\frac{9}{12}$ .

The first three equivalent fractions for $\frac{18}{24}$ are $\frac{3}{4}$ , $\frac{9}{12}$ , and $\frac{9}{12}$ .

e) $\frac{20}{30}$

To find the first three equivalent fractions for $\frac{20}{30}$ , follow the steps outlined above.

Identify the given fraction: The given fraction is $\frac{20}{30}$ .
Find the GCD: The GCD of 20 and 30 is 10.
Divide the numerator and the denominator by the GCD: Divide 20 and 30 by 10 to obtain $\frac{2}{3}$ .
Repeat the process: Repeat steps 2 and 3 to find the next two equivalent fractions.

To find the next equivalent fraction, divide 20 and 30 by 5 to obtain $\frac{4}{6}$ . To find the third equivalent fraction, divide 20 and 30 by 2 to obtain $\frac{10}{15}$ .

The first three equivalent fractions for $\frac{20}{30}$ are $\frac{2}{3}$ , $\frac{4}{6}$ , and $\frac{10}{15}$ .

f) $\frac{24}{36}$

To find the first three equivalent fractions for $\frac{24}{36}$ , follow the steps outlined above.

Identify the given fraction: The given fraction is $\frac{24}{36}$ .
Find the GCD: The GCD of 24 and 36 is 12.
Divide the numerator and the denominator by the GCD: Divide 24 and 36 by 12 to obtain $\frac{2}{3}$ .
Repeat the process: Repeat steps 2 and 3 to find the next two equivalent fractions.

To find the next equivalent fraction, divide 24 and 36 by 6 to obtain $\frac{4}{6}$ . To find the third equivalent fraction, divide 24 and 36 by 3 to obtain $\frac{8}{12}$ .

The first three equivalent fractions for $\frac{24}{36}$ are $\frac{2}{3}$ , $\frac{4}{6}$ , and $\frac{8}{12}$ .

Conclusion

In this article, we explored how to find the first three equivalent fractions for each of the given fractions using the division process. We followed a step-by-step approach to identify the given fraction, find the greatest common divisor (GCD), divide the numerator and the denominator by the GCD, and repeat the process to find the next two equivalent fractions. The first three equivalent fractions for each of the given fractions are:

$\frac{6}{12}$ : $\frac{1}{2}$ , $\frac{3}{6}$ , and $\frac{6}{12}$
$\frac{8}{16}$ : $\frac{1}{2}$ , $\frac{2}{4}$ , and $\frac{4}{8}$
$\frac{12}{18}$ : $\frac{2}{3}$ , $\frac{4}{6}$ , and $\frac{6}{9}$
$\frac{18}{24}$ : $\frac{3}{4}$ , $\frac{9}{12}$ , and $\frac{9}{12}$
$\frac{20}{30}$ : $\frac{2}{3}$ , $\frac{4}{6}$ , and $\frac{10}{15}$
$\frac{24}{36}$ : $\frac{2}{3}$ , $\frac{4}{6}$ , and $\frac{8}{12}$

By following the steps outlined in this article, you can find the first three equivalent fractions for any given fraction using the division process.

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Introduction

In our previous article, we explored how to find the first three equivalent fractions for each of the given fractions using the division process. In this article, we will address some of the most frequently asked questions about equivalent fractions.

Q&A

Q: What are equivalent fractions?

A: Equivalent fractions are fractions that have the same value, but their numerators and denominators are different.

Q: Why are equivalent fractions important?

A: Equivalent fractions are important because they help us to simplify fractions and make them easier to work with. They also help us to compare fractions and determine which one is larger or smaller.

Q: How do I find equivalent fractions?

A: There are several ways to find equivalent fractions, including:

Division process: Divide the numerator and the denominator of a given fraction by the same number to obtain a new fraction that is equivalent to the original one.
Multiplication process: Multiply the numerator and the denominator of a given fraction by the same number to obtain a new fraction that is equivalent to the original one.
Finding the greatest common divisor (GCD): Find the GCD of the numerator and the denominator of a given fraction and divide both numbers by the GCD to obtain a new fraction that is equivalent to the original one.

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

A: The GCD is the largest number that divides both the numerator and the denominator of a given fraction without leaving a remainder.

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

A: There are several ways to find the GCD of two numbers, including:

Listing the factors: List the factors of each number and find the largest factor that is common to both numbers.
Using the Euclidean algorithm: Use the Euclidean algorithm to find the GCD of two numbers.
Using a calculator: Use a calculator to find the GCD of two numbers.

Q: What are some examples of equivalent fractions?

A: Some examples of equivalent fractions include:

$\frac{1}{2}$ and $\frac{2}{4}$
$\frac{2}{3}$ and $\frac{4}{6}$
$\frac{3}{4}$ and $\frac{9}{12}$

Q: How do I compare equivalent fractions?

A: To compare equivalent fractions, you can compare their numerators or denominators. If the numerators are the same, then the fractions are equal. If the numerators are different, then the fraction with the larger numerator is larger.

Q: Can equivalent fractions be used to solve real-world problems?

A: Yes, equivalent fractions can be used to solve real-world problems. For example, if you are baking a cake and you need to divide it into equal parts, you can use equivalent fractions to determine how many parts the cake will be divided into.

Conclusion

In this article, we addressed some of the most frequently asked questions about equivalent fractions. We discussed what equivalent fractions are, why they are important, and how to find them using the division process, multiplication process, and finding the greatest common divisor (GCD). We also provided some examples of equivalent fractions and discussed how to compare them. By understanding equivalent fractions, you can solve real-world problems and make math more accessible and fun.

Additional Resources

Math textbooks: Check out math textbooks for more information on equivalent fractions.
Online resources: Visit online resources such as Khan Academy, Mathway, and Wolfram Alpha for more information on equivalent fractions.
Math apps: Download math apps such as Photomath, Math Tricks, and Math Games for more information on equivalent fractions.

By following the steps outlined in this article and using the additional resources provided, you can become more confident and proficient in finding equivalent fractions and solving real-world problems.