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AA.1 Identify fractions of shapes

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What are fractions?

Fractions are numbers that represent equal parts of a whole or a group. A fraction is written with two numbers separated by a line: the top number is called the numerator, and the bottom number is called the denominator.

Examples:
  • 12 means 1 part out of 2 equal parts
  • 34 means 3 parts out of 4 equal parts
  • 23 means 2 parts out of 3 equal parts
Note

The numerator shows how many parts you have. The denominator shows how many equal parts make the whole.

How to identify fractions of shapes

When a shape is divided into equal parts, each part represents a fraction of the whole shape. To identify the fraction, count the shaded (or chosen) parts and compare them to the total number of equal parts.

Steps:
  • Look at the shape and check that it is divided into equal parts.
  • Count the total number of parts β†’ this is the denominator.
  • Count the shaded (or selected) parts β†’ this is the numerator.
  • Write the fraction with numerator over denominator.
Note

Fractions must always be based on equal parts. If the parts are not equal, the fraction does not represent the whole correctly.

Common fractions you will see in shapes

These are fractions that often appear when shapes are divided into equal parts:

Examples:
  • Circle divided into 2 equal parts β†’ each part is 12
  • Square divided into 4 equal parts β†’ each part is 14
  • Rectangle divided into 3 equal parts β†’ each part is 13
Note

When more than one part is shaded, the numerator changes. For example, shading 2 out of 4 equal parts of a square makes the fraction 24, which is also equal to 12.

Using fractions in sentences

Fractions can be used to describe parts of shapes or groups in everyday language. Practice explaining fractions with full sentences.

Examples:
  • β€œOne out of two parts of the circle is shaded.” β†’ 12 of the circle is shaded.
  • β€œThree out of four parts of the square are shaded.” β†’ 34 of the square is shaded.
  • β€œTwo out of three parts of the rectangle are shaded.” β†’ 23 of the rectangle is shaded.
Note

When writing or speaking about fractions, always connect the numerator to the denominator clearly. This helps explain what part of the whole is being described.