Learn how to determine what fraction is equivalent to 8/12! Explore the concept of equivalent fractions, common denominators, and more in this informative guide.

## Introduction

Fractions are a critical concept in mathematics, and they are used in various fields of study, including physics, engineering, and finance. Equivalent fractions are fractions that have the same value, but they are written differently. For instance, 2/4 is equivalent to 1/2 because both fractions represent the same amount. In this article, we will explore the concept of equivalent fractions and how to determine which fraction is equivalent to 8/12.

## Simplifying Fractions

Simplifying fractions refers to reducing a fraction to its lowest terms. To simplify a fraction, you need to divide the numerator and denominator by their greatest common factor (GCF). For example, to simplify 12/24, you need to find the GCF of 12 and 24, which is 12. Then divide both numerator and denominator by 12. The simplified fraction is 1/2.

To simplify 8/12, we need to find the GCF of 8 and 12, which is 4. We then divide both the numerator and denominator by 4 to simplify the fraction. The simplified fraction is 2/3.

Simplifying fractions is a crucial step in determining equivalent fractions. When you simplify a fraction, you can compare it with other fractions to determine if they are equivalent. The next section will explore the concept of equivalent fractions in more detail.

## Equivalent Fractions

Equivalent fractions are fractions that have the same value but are written differently. For example, 1/2 is equivalent to 2/4, 3/6, and so on. To determine if two fractions are equivalent, you need to simplify them and then compare them. If the simplified fractions are the same, then the fractions are equivalent.

To determine which fraction is equivalent to 8/12, we need to simplify 8/12 to its lowest terms, which is 2/3. We can then compare this fraction with other fractions to determine if they are equivalent. The next section will explore the concept of common denominators, which is a critical step in determining equivalent fractions.

## Equivalent Fractions

In addition to simplifying fractions, another critical concept in determining equivalent fractions is finding the common denominator. The common denominator is the least common multiple of the denominators of two or more fractions. To determine equivalent fractions, you need to convert the fractions to have the same denominator.

For example, let’s say we want to determine which fraction is equivalent to 1/2. We can convert this fraction to have a denominator of 6 by multiplying the numerator and denominator by 3. The resulting fraction is 3/6. Similarly, to determine which fraction is equivalent to 2/3, we can convert this fraction to have a denominator of 6 by multiplying the numerator and denominator by 2. The resulting fraction is 4/6.

To determine which fraction is equivalent to 8/12, we need to find a common denominator for this fraction and another fraction. Let’s say we want to determine which fraction is equivalent to 8/12 and 1/4. We can find a common denominator of 12 by multiplying the denominator of 1/4 by 3. The resulting fraction is 3/12. We can then convert 1/4 to have a denominator of 12 by multiplying the numerator and denominator by 3. The resulting fraction is 3/12.

Now that we have both fractions with a denominator of 12, we can compare them to determine if they are equivalent. We can see that 8/12 is equivalent to 2/3, and 3/12 is equivalent to 1/4. Therefore, the fraction that is equivalent to 8/12 and 1/4 is 2/3 and 3/12.

## Common Denominator

The common denominator is the least common multiple of the denominators of two or more fractions. To find the common denominator of two fractions, you need to find the least common multiple of their denominators. The least common multiple is the smallest number that is a multiple of both denominators.

For example, let’s say we want to find the common denominator of 1/2 and 1/3. The denominator of 1/2 is 2, and the denominator of 1/3 is 3. The multiples of 2 are 2, 4, 6, 8, and so on, while the multiples of 3 are 3, 6, 9, 12, and so on. The least common multiple of 2 and 3 is 6. Therefore, the common denominator of 1/2 and 1/3 is 6.

To determine which fraction is equivalent to 8/12, we need to find a common denominator for this fraction and another fraction. We can find a common denominator by finding the least common multiple of 12 and the denominator of the other fraction. For example, if we want to find the fraction that is equivalent to 8/12 and 1/6, we need to find the least common multiple of 12 and 6, which is 12. We can convert 1/6 to have a denominator of 12 by multiplying the numerator and denominator by 2. The resulting fraction is 2/12.

Now that we have both fractions with a denominator of 12, we can compare them to determine if they are equivalent. We can see that 8/12 is equivalent to 2/3, and 2/12 is equivalent to 1/6. Therefore, the fraction that is equivalent to 8/12 and 1/6 is 2/3 and 1/6.

## Converting Fractions

Converting fractions refers to changing a fraction’s form without changing its value. One way to convert a fraction is to change its denominator. To do this, you need to multiply both the numerator and denominator by the same number. For example, to convert 2/3 to a fraction with a denominator of 12, you need to multiply both the numerator and denominator by 4. The resulting fraction is 8/12.

To determine which fraction is equivalent to 8/12, we can convert 8/12 to other fractions and compare them. For example, we can convert 8/12 to a fraction with a denominator of 24. To do this, we need to multiply both the numerator and denominator by 2. The resulting fraction is 16/24. We can simplify 16/24 to 2/3, which is the same as 8/12. Therefore, 16/24 is equivalent to 8/12.

## Conclusion

In conclusion, equivalent fractions are fractions that have the same value but are written differently. To determine which fraction is equivalent to 8/12, we need to simplify it to its lowest terms, which is 2/3. We can then compare this fraction with other fractions by converting them or finding a common denominator. It is essential to understand equivalent fractions because they are used in many mathematical concepts, such as adding and subtracting fractions, comparing fractions, and solving equations. With this knowledge, you can solve complex mathematical problems with ease and confidence.