Fractions that are equivalent to ⅔

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What are Equivalent Fractions?

Equivalent fractions are fractions that have the same value or represent the same amount, but have different numerators and denominators. They are different ways of expressing the same quantity. For example, ½, 2/4, and 4/8 are all equivalent fractions because they represent the same value, which is half of a whole.

How to Find Fractions Equivalent to ⅔

There are several methods to find fractions equivalent to ⅔. Let's explore three common methods:
a. Multiplying by a Whole Number
One way to find equivalent fractions is by multiplying both the numerator and the denominator of ⅔ by the same whole number. This method is effective when we want to find fractions with a higher denominator. For example, to find an equivalent fraction of ⅔ with a denominator of 12, we can multiply both the numerator and the denominator by 6, which gives us 4/6. This fraction is equivalent to ⅔ as it represents the same portion of a whole.
b. Dividing by a Common Factor
Another method to find equivalent fractions is by dividing both the numerator and the denominator of ⅔ by their greatest common factor (GCF). The GCF is the largest number that evenly divides both the numerator and the denominator. For example, the GCF of 2 and 3 (numerator and denominator of ⅔) is 1. Dividing both by 1 does not change the value of the fraction, so ⅔ remains equivalent.
c. Using Cross Multiplication
Cross multiplication is a method used to find equivalent fractions when we have a proportion, such as when comparing two fractions. To find an equivalent fraction of ⅔, we can set up a proportion with a known equivalent fraction, such as 4/6, and then cross multiply to find the missing numerator or denominator. This method can be useful when we have a known equivalent fraction and want to find other equivalent fractions.
Simplifying Equivalent Fractions
Once we have found fractions equivalent to ⅔, we can simplify them to their lowest terms, also known as simplest form. Simplifying fractions involves dividing both the numerator and the denominator by their greatest common factor (GCF) until no further common factors remain. For example, the fraction 4/6, which is equivalent to ⅔, can be simplified by dividing both the numerator and the denominator by 2, resulting in the simplest form of ⅔.
Examples of Finding Fractions Equivalent to ⅔
Let's look at some examples of finding fractions equivalent to ⅔ using the methods discussed above:
Example 1: Multiplying by a Whole Number
To find an equivalent fraction of ⅔ with a denominator of 12, we can multiply both the numerator and denominator by 4, which gives us 8/12. This fraction is equivalent to ⅔ as it represents the same portion of a whole.
Example 2: Dividing by a Common Factor
To find an equivalent fraction of ⅔ by dividing both the numerator and denominator by their greatest common factor, we can divide both by 1 (since the GCF of 2 and 3 is 1), which gives us ⅔ itself. This shows that ⅔ is already in its simplest form and cannot be further simplified.
Example 3: Using Cross Multiplication
To find an equivalent fraction of ⅔ using cross multiplication, we can set up a proportion with a known equivalent fraction, such as 4/6, and then cross multiply to find the missing numerator or denominator. Cross multiplying gives us 2x6 = 3x4, which simplifies to 12 = 12. This shows that 4/6 is equivalent to ⅔.

Common Fractions Equivalent to ⅔

There are several common fractions that are equivalent to ⅔. Some of the most commonly used ones include:
4/6
6/9
8/12
10/15
12/18

How to Simplify Fractions Equivalent to ⅔

Equivalent fractions can often be simplified or reduced to their simplest form. To simplify fractions, we need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by that number. For example, for the fraction 4/6, the GCD of 4 and 6 is 2, so we can divide both the numerator and denominator by 2 to get 2/3, which is the simplest form of the fraction.

How to Convert Fractions to Equivalent Fractions

Fractions can also be converted to equivalent fractions by multiplying or dividing both the numerator and denominator by the same number. To convert a fraction to an equivalent fraction, we can choose any non-zero number and multiply or divide both the numerator and denominator by that number. For example, to convert ⅔ to an equivalent fraction with a denominator of 12, we can multiply both the numerator and denominator by 6, which gives us 4/6, and then further simplify it to 2/3.

Applications of Equivalent Fractions

Equivalent fractions are fractions that have the same value or represent the same portion of a whole, but have different numerators and denominators. For example, ½ and 2/4 are equivalent fractions as they both represent half of a whole. Equivalent fractions can be found by multiplying or dividing both the numerator and denominator of a fraction by the same non-zero integer.
Equivalent Fractions in Comparing and Ordering Fractions
Equivalent fractions are commonly used in comparing and ordering fractions. When comparing fractions, it can be helpful to convert them into equivalent fractions with a common denominator. For example, when comparing ⅓ and ½, we can convert ⅓ to an equivalent fraction with a denominator of 6 by multiplying both the numerator and denominator by 2, giving us 2/6. Now we can easily compare 2/6 and ½, and see that ½ is greater.
Similarly, when ordering fractions with different denominators, finding equivalent fractions with a common denominator can simplify the process. By converting fractions to equivalent fractions with the same denominator, we can easily arrange them in ascending or descending order. This skill is important in various mathematical concepts such as fractions, decimals, and percentages.
Equivalent Fractions in Adding and Subtracting Fractions

Equivalent fractions are also crucial in adding and subtracting fractions with different denominators. In order to add or subtract fractions with different denominators, we need to find equivalent fractions with a common denominator. By converting fractions to equivalent fractions with the same denominator, we can add or subtract them easily.
For example, to add ⅓ and ¼, we can find equivalent fractions with a common denominator of 12, such as 4/12 and 3/12. Now we can add the numerators, giving us 7/12 as the sum. Similarly, for subtraction, we can find equivalent fractions with a common denominator and subtract the numerators to obtain the result.
Equivalent Fractions in Multiplying and Dividing Fractions
Equivalent fractions are also used in multiplying and dividing fractions. When multiplying fractions, we can simplify the process by finding equivalent fractions with smaller numerators and denominators. For example, to multiply ⅔ and ⅝, we can simplify both fractions to equivalent fractions with smaller numerators and denominators, such as 2/3 and 5/8. Now we can easily multiply the numerators and denominators to obtain the product.
In division, equivalent fractions can help us simplify complex fractions. For example, when dividing ¾ by ⅔, we can simplify both fractions to equivalent fractions with smaller numerators and denominators, such as 3/4 and 2/3. Now we can invert the divisor (2/3) and multiply it by the dividend (3/4) to obtain the quotient.
Equivalent Fractions in Real-World Applications
Equivalent fractions have practical applications in various real-world scenarios. For example, in cooking, recipes often require measurements in fractions, and understanding equivalent fractions can help in adjusting and converting recipe measurements accurately. For instance, if a recipe calls for 1/2 cup of flour, but you only have a 1/4 cup measuring cup, you can use the knowledge of equivalent fractions to know that you need to fill the 1/4 cup measuring cup twice to get an equivalent measurement of 1/2 cup.
Another real-world application of equivalent fractions is in measurements and conversions. For example, in construction or woodworking, understanding equivalent fractions can be useful in cutting materials to specific lengths or dimensions. It can also be helpful in measuring and dividing spaces or areas accurately.

FAQs

Q: What are fractions equivalent to ⅔?
A: Common fractions equivalent to ⅔ include 4/6, 6/9, 8/12, 10/15, and 12/18, among others.
Q: How do I find fractions equivalent to ⅔?
A: To find fractions equivalent to ⅔, you can multiply or divide both the numerator and denominator by the same number. For example, you can multiply both the numerator and denominator by 2 to get 4/6, which is an equivalent fraction. Similarly, you can divide both the numerator and denominator by 3 to get 2/3, which is also an equivalent fraction.
Q: Can I simplify fractions equivalent to ⅔?
A: Yes, you can simplify fractions equivalent to ⅔. To simplify fractions, find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by that number. For example, for the fraction 4/6, the GCD of 4 and 6 is 2, so you can divide both the numerator and denominator by 2 to get 2/3, which is the simplest form of the fraction.
Q: How can I convert fractions to equivalent fractions?
A: You can convert fractions to equivalent fractions by multiplying or dividing both the numerator and denominator by the same number. To do this, choose any non-zero number and multiply or divide both the numerator and denominator by that number. For example, to convert ⅔ to an equivalent fraction with a denominator of 12, you can multiply both the numerator and denominator by 6, which gives you 4/6, and then further simplify it to 2/3.
Q: Where can I use fractions equivalent to ⅔ in real life?
A: Equivalent fractions are used in various real-life applications, such as cooking, measuring, and resizing. For example, in a recipe that requires 2/3 cup of an ingredient, you can use an equivalent fraction like 4/6 or 8/12 if you have a different measuring cup. Equivalent fractions are also used in scaling or resizing objects, such as enlarging or reducing the size of a drawing or a map.

Conclusion

Understanding fractions equivalent to ⅔ is an important mathematical concept that has practical applications in various aspects of everyday life. By knowing how to find, simplify, and convert fractions to equivalent fractions, you can confidently use them in different situations where fractions are commonly used. Whether in cooking, measuring, or resizing, the ability to work with equivalent fractions is a valuable skill that can enhance your understanding of mathematics and its real-life applications.