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Represent fractions with area models

An area model represents a whole, typically a rectangle or circle, partitioned into equal-area parts; the denominator names the total number of equal parts, and the numerator names the parts represented or shaded. It supports fractions involving halves, thirds, and fourths, including combinations that compose one whole, while excluding unequal partitions, fractions greater than one, and fraction operations or comparisons requiring more advanced understanding.

Detailed Explanation: Represent fractions with area models

An area model shows a fraction by dividing a shape into equal parts.

  • The denominator tells how many equal parts are in the whole.
  • The numerator tells how many parts to shade or show.

Example: Represent 34\frac{3}{4}

  1. Draw a rectangle to represent one whole.

  2. The denominator is 44, so divide the rectangle into 4 equal parts.

x ∣ x ∣ x ∣ x\boxed{\phantom{x}\ \vert \ \phantom{x}\ \vert \ \phantom{x}\ \vert \ \phantom{x}}

  1. The numerator is 33, so shade 3 of the 4 parts.

■ ∣ ■ ∣ ■ ∣ □\boxed{\blacksquare\ \vert \ \blacksquare\ \vert \ \blacksquare\ \vert \ \square}

The shaded area represents 34\frac{3}{4}. There are 4 equal parts altogether, and 3 parts are shaded.

Learn by doing: Represent fractions with area models

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