Equivalent Fractions and Ordering

Understanding Fractions#

A fraction represents a part of a whole or a part of a set. In Grade 4, you will deepen your understanding of fractions and learn to work with them in more sophisticated ways.

Parts of a Fraction#

A fraction has two parts:

• Numerator — the top number, showing how many parts are selected
• Denominator — the bottom number, showing how many equal parts the whole is divided into

In the fraction 3/8:

• The denominator 8 tells you the whole is divided into 8 equal parts
• The numerator 3 tells you that 3 of those parts are selected

Fractions on a Number Line#

Fractions can be placed on a number line between 0 and 1 (or beyond 1 for fractions greater than one whole). To place 3/4 on a number line:

1. Divide the space between 0 and 1 into 4 equal parts
2. Count 3 parts from 0
3. Mark the point — this is 3/4

Number lines help you see the relative size of fractions and understand that fractions are numbers, not just parts of a pizza.

Types of Fractions#

Proper fraction: Numerator is less than the denominator (less than 1 whole). Examples: 1/2, 3/4, 5/8

Improper fraction: Numerator is greater than or equal to the denominator (equal to or greater than 1 whole). Examples: 5/4, 7/3, 8/8

Mixed number: A whole number combined with a proper fraction. Examples: 1 1/2, 2 3/4, 3 1/8

Converting: 5/4 = 1 1/4 (5 divided by 4 = 1 remainder 1 → 1 and 1/4)

Fractions as Division#

A fraction also represents division: 3/4 means 3 ÷ 4. If you share 3 pizzas equally among 4 people, each person gets 3/4 of a pizza.