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Recognize equivalent fractions with models

Equivalent fractions name the same quantity or the same point on a number line, even when a whole is divided into different numbers of equal parts; for example, 1/21/2 and 2/42/4 describe the same amount. Area models, fraction strips, and number lines reveal that partitioning each part into smaller equal parts changes both numerator and denominator while preserving the value, countering the misconception that a larger denominator always means a larger fraction. The focus is on familiar fractions with small denominators, not generalized algebraic rules for arbitrary numbers.

Detailed Explanation: Recognize equivalent fractions with models

Equivalent fractions show the same amount, even when the whole is divided into a different number of equal parts.

Example: Are 12\frac{1}{2} and 24\frac{2}{4} equivalent?

  1. Look at 12\frac{1}{2}:

    • The denominator, 22, means the whole is split into 2 equal parts.

    • The numerator, 11, means 1 part is shaded.

shadednot shaded \boxed{\text{shaded}}\boxed{\text{not shaded}}
  1. Look at 24\frac{2}{4}:

    • The denominator, 44, means the whole is split into 4 equal parts.

    • The numerator, 22, means 2 parts are shaded.

shadedshadednot shadednot shaded \boxed{\text{shaded}}\boxed{\text{shaded}}\boxed{\text{not shaded}}\boxed{\text{not shaded}}
  1. Compare the shaded amounts. In the second model, each half was split into 2 smaller pieces. The 1 shaded half became 2 shaded fourths.

Therefore,

12=24\frac{1}{2}=\frac{2}{4}

The fractions are equivalent because they name the same amount. A larger denominator does not always mean a larger fraction; it may mean the whole was divided into more, smaller parts.

Learn by doing: Recognize equivalent fractions with models

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    Fractions - Equivalent Fraction From Image Pair (Circle)

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