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AA.3 Identify fractions in models

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What are fractions?

A fraction represents a part of a whole. It tells us how many equal parts of something we are looking at.

Key Terms:
  • Numerator (Top Number): Counts how many parts you have.
  • Denominator (Bottom Number): Shows how many equal parts the whole is divided into.
  • Fraction Bar (Line): Separates the numerator and denominator.

For example, in the fraction 34, you have 3 parts out of a whole split into 4 equal parts.

Note

Think of the denominator as the "down" number—it tells you how many parts the whole is divided "down" into.

Identifying fractions in shapes

To identify a fraction from a model, follow these steps:

Steps:
  1. Look at the whole shape. Is it a circle, rectangle, or another shape divided into parts?
  2. Count all the equal parts. This number is your denominator.
  3. Count the shaded or marked parts. This number is your numerator.
  4. Write the fraction with the numerator on top and the denominator on the bottom.
Example:

A rectangle divided into 8 equal parts with 5 parts shaded represents the fraction 58.

Note

The parts must be equal for it to be a fair fraction. If the parts are different sizes, you cannot write a fraction for them.

Common fractions with different shapes

The same fraction can be shown using many different shapes. The important part is that the shaded area matches the fraction.

Fraction Examples from 12 to 110:
  • One-Half (12): A circle cut into two equal pieces, with one piece shaded.
  • One-Third (13): A rectangle divided into three equal rows, with one row shaded.
  • One-Fourth (14): A square split into four smaller squares, with one square shaded.
  • One-Fifth (15): A strip divided into five equal parts, with the first part colored.
  • One-Tenth (110): A long bar divided into ten equal sections, with one section marked.
Note

Even if the shape changes, the fraction 12 always means "one out of two equal parts." Look for the relationship between the part and the whole.

Fractions with numerators greater than one

A fraction can represent more than one part of a divided whole. When the numerator is greater than 1, it means you have multiple equal parts.

Understanding the Parts:
  • In 23, the denominator 3 means the whole is divided into 3 equal parts.
  • The numerator 2 means you are looking at 2 of those 3 equal parts.
  • This does not mean two wholes, but two parts from one whole.
Examples in Models:
  • A circle divided into 3 equal slices with 2 slices shaded = 23
  • A rectangle divided into 5 equal columns with 3 columns shaded = 35
  • A strip divided into 8 equal sections with 7 sections colored = 78
Note

Remember: The denominator (bottom number) defines the size of the part. The numerator (top number) defines how many of those parts you have. For 34, you have three "one-fourth" pieces.

Fractions greater than one whole

Sometimes, a model shows more than one whole shape. You can use fractions to describe this.

Example:

If you have two identical pizzas, and each is cut into 4 slices, eating all the slices of one pizza plus one slice from the second means you ate 54 pizzas.

How to Identify:
  1. Count how many wholes are completely filled or shaded.
  2. For the last, incomplete whole, identify the fraction that is shaded.
  3. Combine them. Two whole circles plus a third circle split into fourths with one part shaded is 14, making a total of 14.
Note

When the numerator is larger than the denominator, the fraction represents an amount greater than one whole.

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