Form Three Fractions Equivalent To Each Of The Following:a. 1 2 \frac{1}{2} 2 1 ​ B. 2 5 \frac{2}{5} 5 2 ​ C. 4 5 \frac{4}{5} 5 4 ​ D. 3 7 \frac{3}{7} 7 3 ​ E. 7 10 \frac{7}{10} 10 7 ​ F. 8 12 \frac{8}{12} 12 8 ​ G. 12 20 \frac{12}{20} 20 12 ​ H.

Form Three Fractions Equivalent to Each of the Following

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.

Equivalent Fractions

Equivalent fractions are fractions that have the same value but differ in their numerator and denominator. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they represent the same value, but with different numerators and denominators. To form equivalent fractions, we can multiply or divide the numerator and denominator by the same number.

Forming Equivalent Fractions

To form equivalent fractions, we can follow these steps:

1. Identify the given fraction: The first step is to identify the given fraction that we want to form equivalent fractions for.
2. Determine the multiplier: We need to determine the multiplier that we will use to form the equivalent fractions. This can be any number, but it must be a positive integer.
3. Multiply the numerator and denominator: We multiply the numerator and denominator of the given fraction by the multiplier to form the equivalent fraction.
4. Simplify the fraction: We simplify the equivalent fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Forming Equivalent Fractions for Each of the Given Fractions

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

To form three equivalent fractions for $\frac{1}{2}$, we can use the following multipliers: 2, 3, and 4.

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

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

To form three equivalent fractions for $\frac{2}{5}$, we can use the following multipliers: 2, 3, and 4.

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

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

To form three equivalent fractions for $\frac{4}{5}$, we can use the following multipliers: 2, 3, and 4.

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

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

To form three equivalent fractions for $\frac{3}{7}$, we can use the following multipliers: 2, 3, and 4.

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

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

To form three equivalent fractions for $\frac{7}{10}$, we can use the following multipliers: 2, 3, and 4.

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

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

To form three equivalent fractions for $\frac{8}{12}$, we can use the following multipliers: 2, 3, and 4.

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

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

To form three equivalent fractions for $\frac{12}{20}$, we can use the following multipliers: 2, 3, and 4.

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

Conclusion

In this article, we have formed three equivalent fractions for each of the given fractions. We have demonstrated the process of finding equivalent fractions by multiplying or dividing the numerator and denominator by the same number. We have also simplified the equivalent fractions by dividing both the numerator and denominator by their greatest common divisor (GCD). Equivalent fractions are an important concept in mathematics, and understanding how to form them is essential for solving problems involving fractions.

References

• [1] Khan Academy. (n.d.). Equivalent Fractions. Retrieved from https://www.khanacademy.org/math/fraction-equivalence-and-ordering/equivalent-fractions/v/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

Keywords

• Equivalent fractions
• Fractions
• Mathematics
• Algebra
• Geometry
• Fractions equivalent
• Fractions simplification
• Greatest common divisor (GCD)
• Numerator
• Denominator
• Multiplier
• Simplification
  Form Three Fractions Equivalent to Each of the Following: Q&A

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 answer some frequently asked questions (FAQs) related to equivalent fractions.

Q&A

Q1: What are equivalent fractions?

A1: Equivalent fractions are fractions that have the same value but differ in their numerator and denominator. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they represent the same value, but with different numerators and denominators.

Q2: How do I form equivalent fractions?

A2: To form equivalent fractions, you can multiply or divide the numerator and denominator by the same number. For example, to form an equivalent fraction for $\frac{1}{2}$, you can multiply the numerator and denominator by 2 to get $\frac{2}{4}$.

Q3: What is the greatest common divisor (GCD)?

A3: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction without leaving a remainder. For example, the GCD of 12 and 20 is 4.

Q4: How do I simplify a fraction?

A4: To simplify a fraction, you need to divide both the numerator and denominator by their greatest common divisor (GCD). For example, to simplify $\frac{12}{20}$, you can divide both the numerator and denominator by 4 to get $\frac{3}{5}$.

Q5: What is the difference between equivalent fractions and similar fractions?

A5: 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 and denominator but differ in their order. For example, $\frac{1}{2}$ and $\frac{2}{1}$ are similar fractions, but not equivalent fractions.

Q6: Can I form equivalent fractions for fractions with different denominators?

A6: Yes, you can form equivalent fractions for fractions with different denominators. For example, to form an equivalent fraction for $\frac{1}{3}$, you can multiply the numerator and denominator by 4 to get $\frac{4}{12}$.

Q7: How do I determine if two fractions are equivalent?

A7: To determine if two fractions are equivalent, you can cross-multiply the numerators and denominators. If the resulting product is equal, then the two fractions are equivalent. For example, to determine if $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent, you can cross-multiply the numerators and denominators to get $1 \times 4 = 4$ and $2 \times 2 = 4$. Since the resulting products are equal, then the two fractions are equivalent.

Q8: Can I form equivalent fractions for fractions with negative numerators or denominators?

A8: Yes, you can form equivalent fractions for fractions with negative numerators or denominators. For example, to form an equivalent fraction for $-\frac{1}{2}$, you can multiply the numerator and denominator by -2 to get $\frac{2}{4}$.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) related to equivalent fractions. We have covered topics such as the definition of equivalent fractions, how to form equivalent fractions, the greatest common divisor (GCD), simplifying fractions, and determining if two fractions are equivalent. We hope that this article has provided you with a better understanding of equivalent fractions and how to work with them.

References

• [1] Khan Academy. (n.d.). Equivalent Fractions. Retrieved from https://www.khanacademy.org/math/fraction-equivalence-and-ordering/equivalent-fractions/v/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

Keywords

• Equivalent fractions
• Fractions
• Mathematics
• Algebra
• Geometry
• Fractions equivalent
• Fractions simplification
• Greatest common divisor (GCD)
• Numerator
• Denominator
• Multiplier
• Simplification
• Negative fractions
• Cross-multiplication