Method for Finding Equivalent Fractions

Oct 13, 2025 by miodeya.com 34 views

Introduction

Fractions are a fundamental concept in mathematics, representing a part of a whole. In this article, we will explore the concept of equivalent fractions, which are fractions that have the same value but differ in their numerator and denominator. We will form three fractions equivalent to each of the given fractions, demonstrating the process of finding equivalent fractions.

What are Equivalent Fractions?

Equivalent fractions are fractions that have the same value but differ in their numerator and denominator. For example, the fractions $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent because they represent the same value, but they have different numerators and denominators. Equivalent fractions can be formed by multiplying or dividing both the numerator and denominator by the same non-zero number.

Method for Finding Equivalent Fractions

To find equivalent fractions, we can follow these steps:

Multiply both the numerator and denominator by the same non-zero number.
Simplify the resulting fraction, if possible.
Repeat the process to form three equivalent fractions.

Forming Equivalent Fractions

a. $\frac{1}{2}$

To form three equivalent fractions for $\frac{1}{2}$ , we can multiply both the numerator and denominator by 2, 3, and 4, respectively.

$\frac{1}{2} \times \frac{2}{2} = \frac{2}{4}$
$\frac{1}{2} \times \frac{3}{3} = \frac{3}{6}$
$\frac{1}{2} \times \frac{4}{4} = \frac{4}{8}$

b. $\frac{2}{5}$

To form three equivalent fractions for $\frac{2}{5}$ , we can multiply both the numerator and denominator by 2, 3, and 4, respectively.

$\frac{2}{5} \times \frac{2}{2} = \frac{4}{10}$
$\frac{2}{5} \times \frac{3}{3} = \frac{6}{15}$
$\frac{2}{5} \times \frac{4}{4} = \frac{8}{20}$

c. $\frac{4}{5}$

To form three equivalent fractions for $\frac{4}{5}$ , we can multiply both the numerator and denominator by 2, 3, and 4, respectively.

$\frac{4}{5} \times \frac{2}{2} = \frac{8}{10}$
$\frac{4}{5} \times \frac{3}{3} = \frac{12}{15}$
$\frac{4}{5} \times \frac{4}{4} = \frac{16}{20}$

d. $\frac{3}{7}$

To form three equivalent fractions for $\frac{3}{7}$ , we can multiply both the numerator and denominator by 2, 3, and 4, respectively.

$\frac{3}{7} \times \frac{2}{2} = \frac{6}{14}$
$\frac{3}{7} \times \frac{3}{3} = \frac{9}{21}$
$\frac{3}{7} \times \frac{4}{4} = \frac{12}{28}$

e. $\frac{7}{10}$

To form three equivalent fractions for $\frac{7}{10}$ , we can multiply both the numerator and denominator by 2, 3, and 4, respectively.

$\frac{7}{10} \times \frac{2}{2} = \frac{14}{20}$
$\frac{7}{10} \times \frac{3}{3} = \frac{21}{30}$
$\frac{7}{10} \times \frac{4}{4} = \frac{28}{40}$

f. $\frac{8}{12}$

To form three equivalent fractions for $\frac{8}{12}$ , we can multiply both the numerator and denominator by 2, 3, and 4, respectively.

$\frac{8}{12} \times \frac{2}{2} = \frac{16}{24}$
$\frac{8}{12} \times \frac{3}{3} = \frac{24}{36}$
$\frac{8}{12} \times \frac{4}{4} = \frac{32}{48}$

g. $\frac{12}{20}$

To form three equivalent fractions for $\frac{12}{20}$ , we can multiply both the numerator and denominator by 2, 3, and 4, respectively.

$\frac{12}{20} \times \frac{2}{2} = \frac{24}{40}$
$\frac{12}{20} \times \frac{3}{3} = \frac{36}{60}$
$\frac{12}{20} \times \frac{4}{4} = \frac{48}{80}$

h. $\frac{5}{9}$

To form three equivalent fractions for $\frac{5}{9}$ , we can multiply both the numerator and denominator by 2, 3, and 4, respectively.

$\frac{5}{9} \times \frac{2}{2} = \frac{10}{18}$
$\frac{5}{9} \times \frac{3}{3} = \frac{15}{27}$
$\frac{5}{9} \times \frac{4}{4} = \frac{20}{36}$

Conclusion

Introduction

In our previous article, we explored the concept of equivalent fractions and formed three equivalent fractions for each of the given fractions. In this article, we will address some common questions related to equivalent fractions and provide additional examples to help solidify your understanding.

Q&A

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

A: Equivalent fractions are fractions that have the same value but differ in their numerator and denominator. Similar fractions, on the other hand, are fractions that have the same numerator but differ in their denominator.

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

A: To determine if two fractions are equivalent, you can cross-multiply the fractions and check if the resulting products are equal. For example, to check if $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent, you can cross-multiply as follows:

$\frac{1}{2} \times \frac{4}{4} = \frac{4}{8}$

Since $\frac{4}{8}$ is equal to $\frac{2}{4}$ , we can conclude that $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent.

Q: Can I form equivalent fractions by dividing both the numerator and denominator by the same non-zero number?

A: Yes, you can form equivalent fractions by dividing both the numerator and denominator by the same non-zero number. For example, to form an equivalent fraction for $\frac{4}{8}$ , you can divide both the numerator and denominator by 2 as follows:

$\frac{4}{8} \div \frac{2}{2} = \frac{2}{4}$

Q: How do I simplify a fraction?

A: To simplify a fraction, you can divide both the numerator and denominator by their greatest common divisor (GCD). For example, to simplify $\frac{6}{8}$ , you can find the GCD of 6 and 8, which is 2, and then divide both the numerator and denominator by 2 as follows:

$\frac{6}{8} \div \frac{2}{2} = \frac{3}{4}$

Q: Can I form equivalent fractions for fractions with different signs?

A: Yes, you can form equivalent fractions for fractions with different signs. For example, to form an equivalent fraction for $-\frac{3}{4}$ , you can multiply both the numerator and denominator by -1 as follows:

$-\frac{3}{4} \times \frac{-1}{-1} = \frac{3}{4}$

Q: How do I form equivalent fractions for fractions with decimals?

A: To form equivalent fractions for fractions with decimals, you can convert the decimal to a fraction and then form equivalent fractions. For example, to form an equivalent fraction for $\frac{3}{4}$ , you can convert the decimal 0.75 to a fraction as follows:

$0.75 = \frac{3}{4}$

Then, you can form equivalent fractions for $\frac{3}{4}$ by multiplying both the numerator and denominator by the same non-zero number.

Q: Can I form equivalent fractions for fractions with variables?

A: Yes, you can form equivalent fractions for fractions with variables. For example, to form an equivalent fraction for $\frac{x}{y}$ , you can multiply both the numerator and denominator by the same non-zero number. For example:

$\frac{x}{y} \times \frac{2}{2} = \frac{2x}{2y}$

Q: How do I determine if two fractions are equivalent when they have variables?

A: To determine if two fractions are equivalent when they have variables, you can cross-multiply the fractions and check if the resulting products are equal. For example, to check if $\frac{x}{y}$ and $\frac{2x}{2y}$ are equivalent, you can cross-multiply as follows:

$\frac{x}{y} \times \frac{2y}{2y} = \frac{2x}{2y}$

Since $\frac{2x}{2y}$ is equal to $\frac{2x}{2y}$ , we can conclude that $\frac{x}{y}$ and $\frac{2x}{2y}$ are equivalent.

Conclusion

In this article, we have addressed some common questions related to equivalent fractions and provided additional examples to help solidify your understanding. We have also discussed how to form equivalent fractions for fractions with different signs, decimals, and variables. By following the steps outlined in this article, you can form equivalent fractions for any given fraction and determine if two fractions are equivalent.