Fractions Lesson: Numerators, Denominators, and Simplification

Lesson Overview

• What Is a Fraction?
• Visual Representation of Fractions
• Understanding Numerator and Denominator
• Simplifying Fractions
• Equivalent Fractions
• Comparing and Recognizing Equivalent Fractions
• Table of Simplified and Equivalent Fractions

Fractions are a fundamental concept in math that represent parts of a whole. We use fractions in everyday life - whether we are sharing a pizza, telling time, or measuring ingredients. Understanding fractions and how they can be simplified or expressed in equivalent forms helps us solve problems more accurately and efficiently.

What Is a Fraction?

A fraction is a number that represents a part of a whole. It has two main parts:

• Numerator (Top Number): Tells how many parts are being considered.
• Denominator (Bottom Number): Tells how many total equal parts the whole is divided into.

Example:

If a rectangle is divided into 5 equal parts and 2 parts are shaded, the fraction representing the shaded area is:

Visual Representation of Fractions

Fractions can be shown using diagrams. These visuals help us understand how parts of a whole are represented.

Example:

A circle is divided into 7 equal parts, and 2 parts are shaded.

Understanding Numerator and Denominator

The numerator and denominator work together to describe a part-whole relationship.

Simplifying Fractions

Simplifying a fraction means writing it in its lowest terms. This is done by dividing both the numerator and the denominator by their Greatest Common Factor (GCF).

Steps to Simplify a Fraction:

1. Find the GCF of the numerator and denominator.
2. Divide both numbers by the GCF.

Example:

Simplify 3/15

• GCF of 3 and 15 = 3
• 3 ÷ 3 = 1
• 15 ÷ 3 = 5
• Simplified Form = 1/5

Take This Quiz -

Fractions and Equivalent Fractions

Equivalent Fractions

Equivalent fractions are different fractions that represent the same value.

How to Find Equivalent Fractions:

• Multiply or divide both the numerator and denominator by the same number.

Example:

1/2 is equivalent to:

• (1 × 2) / (2 × 2) = 2/4
• (1 × 3) / (2 × 3) = 3/6
• (1 × 4) / (2 × 4) = 4/8

Comparing and Recognizing Equivalent Fractions

To check if two fractions are equivalent:

1. Simplify both fractions.
2. If they simplify to the same value, they are equivalent.

Example:

Are 12/36 and 1/3 equivalent?

• Simplify 12/36
  GCF = 12
  12 ÷ 12 = 1
  36 ÷ 12 = 3
  
  Yes, they are equivalent.

Table of Simplified and Equivalent Fractions

Take This Quiz -

Fraction Math Quiz