Find The Missing Number In These Equivalent Fractions.$\frac{5}{12} = \frac{}{36}$

Feb 26, 2025 by ADMIN 83 views

Find the Missing Number in Equivalent Fractions

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Introduction

Equivalent fractions are fractions that have the same value, but may appear different. They are often used in mathematics to simplify complex fractions and to compare the values of fractions. In this article, we will explore how to find the missing number in equivalent fractions, using the example of $\frac{5}{12} = \frac{}{36}$ .

Understanding Equivalent Fractions

Equivalent fractions are fractions that have the same value, but may appear different. They are often used in mathematics to simplify complex fractions and to compare the values of fractions. To find the missing number in an equivalent fraction, we need to understand the concept of equivalent fractions and how to simplify them.

Simplifying Fractions

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Once we have found the GCD, we can divide both the numerator and the denominator by the GCD to simplify the fraction.

Example of Simplifying a Fraction

Let's simplify the fraction $\frac{12}{18}$ . To simplify this fraction, we need to find the GCD of 12 and 18. The GCD of 12 and 18 is 6. Once we have found the GCD, we can divide both the numerator and the denominator by the GCD to simplify the fraction.

$\frac{12}{18} = \frac{12 ÷ 6}{18 ÷ 6} = \frac{2}{3}$

Understanding the Concept of Equivalent Fractions

Equivalent fractions are fractions that have the same value, but may appear different. They are often used in mathematics to simplify complex fractions and to compare the values of fractions. To find the missing number in an equivalent fraction, we need to understand the concept of equivalent fractions and how to simplify them.

Finding the Missing Number in Equivalent Fractions

To find the missing number in an equivalent fraction, we need to understand the concept of equivalent fractions and how to simplify them. We can use the following steps to find the missing number in an equivalent fraction:

Step 1: Simplify the Fraction

To simplify a fraction, we need to find the GCD of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Once we have found the GCD, we can divide both the numerator and the denominator by the GCD to simplify the fraction.

Step 2: Find the Missing Number

Once we have simplified the fraction, we can find the missing number in the equivalent fraction. We can do this by multiplying the numerator and the denominator of the simplified fraction by the same number.

Example of Finding the Missing Number in an Equivalent Fraction

Let's find the missing number in the equivalent fraction $\frac{5}{12} = \frac{}{36}$ . To find the missing number, we need to simplify the fraction $\frac{5}{12}$ .

$\frac{5}{12} = \frac{5 ÷ 1}{12 ÷ 1} = \frac{5}{12}$

Since the GCD of 5 and 12 is 1, we cannot simplify the fraction further. However, we can find the missing number in the equivalent fraction by multiplying the numerator and the denominator of the simplified fraction by the same number.

$\frac{5}{12} = \frac{5 × 3}{12 × 3} = \frac{15}{36}$

Therefore, the missing number in the equivalent fraction $\frac{5}{12} = \frac{}{36}$ is 15.

Conclusion

In this article, we have explored how to find the missing number in equivalent fractions. We have used the example of $\frac{5}{12} = \frac{}{36}$ to illustrate the concept of equivalent fractions and how to simplify them. We have also provided a step-by-step guide on how to find the missing number in an equivalent fraction. By following these steps, we can find the missing number in any equivalent fraction.

Frequently Asked Questions

Q: What is an equivalent fraction?

A: An equivalent fraction is a fraction that has the same value, but may appear different.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the GCD of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Once you have found the GCD, you can divide both the numerator and the denominator by the GCD to simplify the fraction.

Q: How do I find the missing number in an equivalent fraction?

A: To find the missing number in an equivalent fraction, you need to simplify the fraction and then multiply the numerator and the denominator of the simplified fraction by the same number.

References

[1] Khan Academy. (n.d.). Equivalent Fractions. Retrieved from https://www.khanacademy.org/math/pre-algebra/pre-algebra-equivalent-fractions
[2] Math Open Reference. (n.d.). Equivalent Fractions. Retrieved from https://www.mathopenref.com/equivalentfractions.html
[3] Purplemath. (n.d.). Equivalent Fractions. Retrieved from https://www.purplemath.com/modules/equivfrac.htm

Note: The references provided are online resources that can be used to learn more about equivalent fractions and how to simplify them.

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Introduction

Equivalent fractions are fractions that have the same value, but may appear different. They are often used in mathematics to simplify complex fractions and to compare the values of fractions. In this article, we will answer some of the most frequently asked questions about equivalent fractions.

Q&A

Q: What is an equivalent fraction?

A: An equivalent fraction is a fraction that has the same value, but may appear different. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they have the same value, but they appear different.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Once you have found the GCD, you can divide both the numerator and the denominator by the GCD to simplify the fraction.

Q: How do I find the missing number in an equivalent fraction?

A: To find the missing number in an equivalent fraction, you need to simplify the fraction and then multiply the numerator and the denominator of the simplified fraction by the same number.

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

A: Equivalent fractions are fractions that have the same value, but may appear different. Similar fractions are fractions that have the same denominator, but may have different numerators.

Q: Can I have multiple equivalent fractions for a single fraction?

A: Yes, you can have multiple equivalent fractions for a single fraction. For example, $\frac{1}{2}$ , $\frac{2}{4}$ , and $\frac{3}{6}$ are all equivalent fractions for the fraction $\frac{1}{2}$ .

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

A: To determine if two fractions are equivalent, you need to simplify both fractions and then compare their values. If the simplified fractions have the same value, then the original fractions are equivalent.

Q: Can I use equivalent fractions to compare the values of fractions?

A: Yes, you can use equivalent fractions to compare the values of fractions. For example, if you have two fractions, $\frac{1}{2}$ and $\frac{2}{4}$ , you can simplify them to $\frac{1}{2}$ and $\frac{1}{2}$ , respectively. Since they have the same value, you can conclude that the two fractions are equal.

Q: How do I use equivalent fractions to solve problems?

A: To use equivalent fractions to solve problems, you need to identify the equivalent fractions that are relevant to the problem and then use them to simplify the problem. For example, if you have a problem that involves the fraction $\frac{1}{2}$ , you can use the equivalent fraction $\frac{2}{4}$ to simplify the problem.