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K.1 Identify fractions and mixed numbers

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What are fractions?

Fractions represent equal parts of a whole. A fraction tells how many parts of a shape, object, or set are being considered out of the total number of equal parts.

Example:
  • If a circle is divided into 4 equal parts and 1 part is shaded, the shaded fraction is 1/4.
  • The top number (numerator) shows the shaded parts.
  • The bottom number (denominator) shows the total equal parts.
Note

Fractions describe part of a whole, so all parts must be equal in size for the fraction to be accurate.

How to identify fractions in shapes

To identify the fraction of a shape that is shaded, compare the number of shaded parts to the total number of equal parts in the shape.

Steps:
  • Step 1: Count the total number of equal parts.
  • Step 2: Count how many parts are shaded.
  • Step 3: Write the fraction with shaded parts on top (numerator) and total parts on the bottom (denominator).
Example:
  • If a rectangle is divided into 6 equal parts and 3 parts are shaded โ†’ 3/6.
Note

Simplify fractions when possible. For example, 3/6 is equal to 1/2 because both represent half of the whole.

Understanding numerator and denominator

Every fraction has two parts: a numerator and a denominator. These parts tell different things about the fraction.

Parts of a fraction:
  • Numerator โ€“ the number of shaded or chosen parts.
  • Denominator โ€“ the total number of equal parts that make up the whole.
Example:
  • In the fraction 2/5, 2 is the numerator (shaded parts), and 5 is the denominator (total parts).
Note

The numerator and denominator are separated by a fraction bar, which means โ€œdivided by.โ€ For instance, 2/5 means 2 รท 5.

Fractions and mixed numbers

When a whole shape and extra parts are shown, you can write the amount as a mixed numberโ€”a whole number and a fraction combined.

Example:
  • If 1 whole circle and half of another are shaded, it is written as 1 1/2 (read as โ€œone and one-halfโ€).
Note

Mixed numbers are used when you have one or more wholes and a fractional part left over.

Checking your understanding

When identifying fractions, always look for equal parts and carefully count how many are shaded versus unshaded.

Example:
  • A shape has 8 equal parts, and 4 are shaded. The fraction of the shape that is shaded is 4/8 or simplified to 1/2.
Note

If parts are not equal, the shaded portion cannot be represented correctly as a fraction of the whole.