Write A Fraction For Each Statement.4. 2 Copies Of 1 6 \frac{1}{6} 6 1 ​ Is 5. 3 Copies Of 1 3 \frac{1}{3} 3 1 ​ Is 6. 4 Copies Of 1 5 \frac{1}{5} 5 1 ​ Is 7. 2 Copies Of 1 10 \frac{1}{10} 10 1 ​ Is 8. 7 Copies Of 1 12 \frac{1}{12} 12 1 ​ Is 9. 3

What are Fractions?

A fraction is a way to represent a part of a whole. It consists of two parts: a numerator and a denominator. The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into. For example, the fraction 1/2 represents one half of a whole.

Understanding Equivalent Fractions

Equivalent fractions are fractions that have the same value, but may look different. For example, 1/2 and 2/4 are equivalent fractions because they both represent the same part of a whole. In this article, we will explore how to write equivalent fractions for each of the given statements.

2 copies of $\frac{1}{6}$ is

To find the equivalent fraction for 2 copies of $\frac{1}{6}$, we need to multiply the numerator and denominator by 2.

$\frac{1}{6} \times 2 = \frac{2}{12}$

However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2.

$\frac{2}{12} = \frac{1}{6}$

So, 2 copies of $\frac{1}{6}$ is still $\frac{1}{6}$.

3 copies of $\frac{1}{3}$ is

To find the equivalent fraction for 3 copies of $\frac{1}{3}$, we need to multiply the numerator and denominator by 3.

$\frac{1}{3} \times 3 = \frac{3}{9}$

However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3.

$\frac{3}{9} = \frac{1}{3}$

So, 3 copies of $\frac{1}{3}$ is still $\frac{1}{3}$.

4 copies of $\frac{1}{5}$ is

To find the equivalent fraction for 4 copies of $\frac{1}{5}$, we need to multiply the numerator and denominator by 4.

$\frac{1}{5} \times 4 = \frac{4}{20}$

However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4.

$\frac{4}{20} = \frac{1}{5}$

So, 4 copies of $\frac{1}{5}$ is still $\frac{1}{5}$.

2 copies of $\frac{1}{10}$ is

To find the equivalent fraction for 2 copies of $\frac{1}{10}$, we need to multiply the numerator and denominator by 2.

$\frac{1}{10} \times 2 = \frac{2}{20}$

However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2.

$\frac{2}{20} = \frac{1}{10}$

So, 2 copies of $\frac{1}{10}$ is still $\frac{1}{10}$.

7 copies of $\frac{1}{12}$ is

To find the equivalent fraction for 7 copies of $\frac{1}{12}$, we need to multiply the numerator and denominator by 7.

$\frac{1}{12} \times 7 = \frac{7}{84}$

However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 7.

$\frac{7}{84} = \frac{1}{12}$

So, 7 copies of $\frac{1}{12}$ is still $\frac{1}{12}$.

Conclusion

In this article, we have explored how to write equivalent fractions for each of the given statements. We have seen that multiplying the numerator and denominator by a certain number does not always result in a simplified fraction. In some cases, we need to simplify the fraction by dividing both the numerator and denominator by their greatest common divisor. By understanding equivalent fractions, we can better understand the concept of fractions and how to work with them.

Frequently Asked Questions

Q: What is a fraction?

A: A fraction is a way to represent a part of a whole. It consists of two parts: a numerator and a denominator.

Q: What is an equivalent fraction?

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

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and denominator by their greatest common divisor.

Q: What is the greatest common divisor?

A: The greatest common divisor is the largest number that divides both the numerator and denominator of a fraction.

Glossary

• Numerator: The number on top of a fraction that tells us how many equal parts we have.
• Denominator: The number on the bottom of a fraction that tells us how many parts the whole is divided into.
• Equivalent fraction: A fraction that has the same value, but may look different.
• Greatest common divisor: The largest number that divides both the numerator and denominator of a fraction.

References

• [1] Khan Academy. (n.d.). Fractions. Retrieved from https://www.khanacademy.org/math/fractions
• [2] Math Open Reference. (n.d.). Fractions. Retrieved from https://www.mathopenref.com/fractions.html

About the Author

Q: What is a fraction?

A: A fraction is a way to represent a part of a whole. It consists of two parts: a numerator and a denominator. The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into.

Q: What is an equivalent fraction?

A: An equivalent fraction is a fraction that has the same value, but may look different. For example, 1/2 and 2/4 are equivalent fractions because they both represent the same part of a whole.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and denominator by their greatest common divisor. The greatest common divisor is the largest number that divides both the numerator and denominator of a fraction.

Q: What is the greatest common divisor?

A: The greatest common divisor is the largest number that divides both the numerator and denominator of a fraction. For example, the greatest common divisor of 6 and 12 is 6, because 6 is the largest number that divides both 6 and 12.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly. Once you have the LCM, you can convert both fractions to have the LCM as the denominator, and then add them together.

Q: How do I subtract fractions with different denominators?

A: To subtract fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly. Once you have the LCM, you can convert both fractions to have the LCM as the denominator, and then subtract them together.

Q: How do I multiply fractions?

A: To multiply fractions, you simply multiply the numerators together and multiply the denominators together. For example, to multiply 1/2 and 3/4, you would multiply 1 and 3 together to get 3, and multiply 2 and 4 together to get 8, resulting in 3/8.

Q: How do I divide fractions?

A: To divide fractions, you need to invert the second fraction (i.e. flip the numerator and denominator) and then multiply the fractions together. For example, to divide 1/2 by 3/4, you would invert 3/4 to get 4/3, and then multiply 1/2 and 4/3 together to get 4/6, which can be simplified to 2/3.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. For example, 2 1/2 is a mixed number that represents 2 whole units and 1/2 of another unit.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, to convert 2 1/2 to an improper fraction, you would multiply 2 by 2 to get 4, and then add 1 to get 5, resulting in the improper fraction 5/2.

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator and then write the remainder as a fraction. For example, to convert 5/2 to a mixed number, you would divide 5 by 2 to get 2 with a remainder of 1, resulting in the mixed number 2 1/2.

Q: What is a decimal fraction?

A: A decimal fraction is a fraction that has a decimal value. For example, 0.5 is a decimal fraction that represents 1/2.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you need to divide the numerator by the denominator. For example, to convert 1/2 to a decimal, you would divide 1 by 2 to get 0.5.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you need to find the greatest common divisor of the decimal value and the denominator, and then divide both the numerator and denominator by the greatest common divisor. For example, to convert 0.5 to a fraction, you would find the greatest common divisor of 0.5 and 1 to be 0.5, and then divide both the numerator and denominator by 0.5 to get 1/2.

Q: What is a percentage fraction?

A: A percentage fraction is a fraction that represents a percentage value. For example, 25% is a percentage fraction that represents 1/4.

Q: How do I convert a fraction to a percentage?

A: To convert a fraction to a percentage, you need to divide the numerator by the denominator and then multiply the result by 100. For example, to convert 1/4 to a percentage, you would divide 1 by 4 to get 0.25, and then multiply 0.25 by 100 to get 25%.

Q: How do I convert a percentage to a fraction?

A: To convert a percentage to a fraction, you need to divide the percentage value by 100 and then simplify the result. For example, to convert 25% to a fraction, you would divide 25 by 100 to get 1/4.

Conclusion

In this article, we have answered some of the most frequently asked questions about fractions. We have covered topics such as equivalent fractions, simplifying fractions, adding and subtracting fractions, multiplying and dividing fractions, mixed numbers, improper fractions, decimal fractions, and percentage fractions. We hope that this article has been helpful in answering your questions and providing you with a better understanding of fractions.