Equivalent Fractions

Definition

Equivalent fractions are fractions that represent the same numerical value, even though the numerator and denominator may be different. They are fractions that depict the same portion or amount of a whole.

5 Must Know Facts For Your Next Test

1. Equivalent fractions can be generated by multiplying or dividing both the numerator and denominator by the same non-zero number.
2. Visualizing fractions using area models or number lines can help identify equivalent fractions.
3. When adding or subtracting fractions, they must be converted to equivalent fractions with a common denominator.
4. Solving equations with fractions often requires finding equivalent fractions to isolate the variable.
5. Equivalent fractions are crucial for accurately comparing, ordering, and performing operations with fractions.

Review Questions

• How can you generate equivalent fractions from a given fraction?
  • To generate equivalent fractions from a given fraction, you can multiply or divide both the numerator and denominator by the same non-zero number. For example, if you have the fraction $\frac{2}{3}$, you can multiply both the numerator and denominator by 2 to get the equivalent fraction $\frac{4}{6}$. This process preserves the value of the fraction while creating a new representation with different numerator and denominator.
• Explain how equivalent fractions are used when adding or subtracting fractions with different denominators.
  • When adding or subtracting fractions with different denominators, the fractions must first be converted to equivalent fractions with a common denominator. This is necessary to ensure that the fractions represent the same unit and can be combined or subtracted. The common denominator is typically the least common multiple of the original denominators. By converting the fractions to equivalent fractions with the same denominator, the numerators can then be added or subtracted, and the resulting fraction will be in simplest form.
• Describe how equivalent fractions are utilized when solving equations that involve fractions.
  • In solving equations with fractions, equivalent fractions are essential for isolating the variable. To solve an equation like $\frac{x}{4} = \frac{3}{8}$, you would first need to find an equivalent fraction for $\frac{3}{8}$ that has a denominator of 4. This could be done by multiplying both the numerator and denominator of $\frac{3}{8}$ by 2, resulting in the equivalent fraction $\frac{6}{16}$. Now, since both fractions have a common denominator of 4, you can solve for the variable $x$ by cross-multiplying and solving for the unknown.

Related terms

Fraction:

A fraction is a numerical quantity that represents a part of a whole, expressed as a ratio of two integers - the numerator and the denominator.

Simplifying Fractions: Simplifying a fraction involves reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common factor.

Equivalent Ratio: An equivalent ratio is a pair of ratios that represent the same proportional relationship, even though the individual numbers may be different.