Equivalent Fractions

Definition

Equivalent fractions are two or more fractions that represent the same value or amount, even though the numerators and denominators may be different. They are fractions that have the same proportional relationship between the numerator and denominator.

5 Must Know Facts For Your Next Test

1. Equivalent fractions have the same value, but different numerators and denominators.
2. To generate equivalent fractions, you can multiply or divide the numerator and denominator by the same non-zero number.
3. Equivalent fractions are important for performing operations with fractions, such as addition, subtraction, multiplication, and division.
4. Fractions with the same denominator are automatically equivalent, as long as the numerators are different.
5. Equivalent fractions can be used to represent the same quantity in different ways, which is useful in problem-solving and simplifying calculations.

Review Questions

• Explain how to generate equivalent fractions and provide an example.
  • To generate equivalent fractions, you can multiply or divide the numerator and denominator by the same non-zero number. For example, the fraction $\frac{1}{2}$ is equivalent to $\frac{2}{4}$, $\frac{3}{6}$, and $\frac{4}{8}$, because each of these fractions can be obtained by multiplying the numerator and denominator of $\frac{1}{2}$ by the same number (2, 3, or 4). The key is that the relationship between the numerator and denominator is maintained, preserving the fraction's value.
• Describe how equivalent fractions can be used to compare and order fractions.
  • Equivalent fractions can be used to compare and order fractions by finding a common denominator. Once the fractions have a common denominator, you can compare the numerators to determine the relative size of the fractions. For example, to compare $\frac{1}{3}$ and $\frac{2}{5}$, you can find equivalent fractions with a common denominator of 15, such as $\frac{5}{15}$ and $\frac{6}{15}$. Since 5 is less than 6, $\frac{1}{3}$ is less than $\frac{2}{5}$. This process of finding equivalent fractions with a common denominator allows you to accurately compare and order fractions.
• Explain the importance of equivalent fractions in performing operations with fractions, such as addition and subtraction.
  • Equivalent fractions are crucial for performing operations with fractions, such as addition and subtraction. When adding or subtracting fractions, they must have a common denominator. By finding equivalent fractions with a common denominator, you can then add or subtract the numerators while maintaining the same overall value. This allows for accurate and meaningful calculations with fractions. For example, to add $\frac{1}{2}$ and $\frac{1}{4}$, you can find equivalent fractions with a common denominator of 4, resulting in $\frac{2}{4}$ and $\frac{1}{4}$. Then, you can add the numerators to get $\frac{3}{4}$, which is the sum of the original fractions.

Related terms

Simplifying Fractions: The process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common factor.

Fraction Equivalence: The concept that two or more fractions can represent the same quantity or value, despite having different numerators and denominators.

Fraction Comparison: The ability to determine which of two or more fractions is greater, lesser, or equal in value.