Multiplication of Fractions

Content Standards

In this lesson, learners will demonstrate an understanding of multiplication of fractions and whole numbers, as well as multiplication of two fractions, representing the process and results in visual (area models), contextual (word problems), and numerical formats.

Performance Standards

Students will be able to:

Identify and represent fraction multiplication using unit squares/area models.
Explain key terms (multiplier, multiplicand, numerator, denominator) and the a/b × c/d = (a×c)/(b×d) rule.
Compute products of (fraction × whole number) and (fraction × fraction), and simplify to lowest form using cancellation.
Apply fraction multiplication to real-world contexts (rate × time, sharing/partitioning, area).

Alignment Standards

Reference: NCERT Book Alignment

The lesson is aligned with the NCERT Grade 7 Mathematics Textbook, Chapter 8: Working with Fractions. Section 8.1: Multiplications of Fractions

Learning Objectives

By the end of the lesson, students will be able to:

Model products like 1/2×1/4 and 3/4×2/5 using a unit square (area model).
Explain why multiplying numerators and denominators gives the correct product and when the product is greater than / less than the factors.
Calculate and simplify products (e.g., 12/7×5/24=5/14 ) using cancellation before multiplying.
Solve contextual problems (e.g., distance = rate × time), including fractional hours and mixed numbers, and convert improper ↔ mixed fractions.

Prerequisites (Prior Knowledge)

Equivalent fractions and simplifying fractions.
Addition of unit fractions and understanding unit rate (e.g., “3 km per hour”).
Area of rectangles (area = length × breadth) and mixed number ↔ improper fraction conversion.

Introduction

In this session, students explore how and why we multiply fractions. Using stories (Aaron walking; tortoise pace), visuals (unit square/area model), and rules (multiply numerators & denominators, cancellation), learners connect context → model → computation, then apply the ideas to real-life scenarios (cost/time, sharing, area).

Timeline (40 Minutes)

Title	Approximate Duration	Procedure	Reference Material
Engage	5	Hook (Think–Pair–Share): “Aaron walks 3 km in 1 hour. How far in 1/5 hour?” Collect quick estimates; surface strategies (repeated addition vs. fraction of a rate).	Slides
Explore	10	Hands-on Visuals: Use unit squares to model 1/2×1/4 and 3/4×2/5. Students shade rows/columns to see parts of a whole; discuss the grid has (denominator × denominator) parts.	Slides
Explain	10	Direct Instruction & Worked Examples: 1) Fraction × Whole via rate: 2/5×3=6/5 (Aaron, fractional hours). 2) Fraction × Fraction rule: a/b×c/d=ac/bd 3) Cancellation before multiplying: 12/7 × 5/24 = 1/7 × 5/2 = 5/14 4) When is the product bigger/smaller? (both >1; both between 0 and 1; mixed).	Slides and Virtual Lab
Evaluate	10	Ask students to complete a self-evaluation task on the LMS	Virtual Lab
Extend	5	Application & Reflection: Water tank example.	Slides

Multiplication of Fractions

Introduction

In this lesson, students will learn how to multiply fractions and multiply a fraction by a whole number to find “parts of parts” and solve real-life problems. Through interactive examples, visual area models, and everyday scenarios (like distance = speed × time, sharing, and cost), students will explore why we multiply numerators and denominators and when the product is bigger or smaller than the factors.

Theory

Introduction: Why multiply fractions?

Hook: If Aaron walks 3 km in 1 hour, how far does he walk in 1/5 hour?
We often need a fraction of a quantity (e.g., part of an hour, a piece of land, a portion of a recipe). Multiplying fractions let us compute a fraction of a fraction or a fraction of a whole, such as:

Distance in fractional time,
Splitting resources among families,
Find an area where both sides are fractional.

Example scenario: Aaron’s tortoise walks 1/4 km per hour. In 1/2 hour, it covers 1/2 × 1/4 = 1/8 km. This shows “part of a part.”

What is the multiplication of fractions?

Multiplying fractions means taking a fraction of another fraction/whole. We multiply the numerators together and the denominators together:

Key components:

Numerator (top number): how many parts are taken.
Denominator (bottom number): total equal parts in the whole.

Case 1: Fraction × Whole Number (3 x 2/5)

Step 1: Rewrite the whole number as a fraction: 3=3/1

Step 2: Multiply numerators and denominators: 2/5 x 3/1 = 6/5

Step 3: Simplify and/or convert to a mixed number: 6/5= 1 1/5

Solved example (rate × time):
Aaron walks 3 km in 1 hour. In 2/5 hours, the distance =
2/5X 3 = 6/5 Km = 1 1/5 Km

Case 2: Fraction × Fraction (3/4 x 2/5)

Step 1: Multiply numerators: 3 × 2 = 6

Step 2: Multiply denominators: 4 X 5 = 20

Step 3: Write the product: 6 /20

Step 4: Simplify if possible: 6/20= 3/10

Case 3: Cancellation tip (before multiplying):

12/7 × 5/24 = 1/7 × 5/2 = 5/14

Case 4: When is the product bigger/smaller?

If both factors > 1 → product greater than both.
If both between 0 and 1 → product smaller than both.
If one between 0 and 1 and one > 1 → product is between them.

Visual Representation: Use a unit square (area model):

Divide the square into b equal rows to represent a/b
Divide the same square into d equal columns to represent c/d
The overlap (shaded intersection) has a x c small squares out of b x d total, giving

Applications / Why is it Useful?

Distance & time fractional hours at a constant speed (e.g., 2/5 x 3 km).
Sharing/recipes: take a fraction of a portion (e.g., half of a quarter cake).
Area: rectangle with fractional length and breadth.
Budgeting/pricing: fractional hours of internet time, tutoring, or rental.

Vocabulary

This is the list of vocabulary terms used throughout the lesson.

Fraction: A number representing a part of a whole, written numerator denominator.
Numerator: The top number; counts how many parts are taken.
Denominator: The bottom number; total equal parts in the whole.
Multiplier: The factor by which we multiply.
Multiplicand: The quantity being multiplied.
Product: The result of multiplication.
Area Model / Unit Square: A visual grid representing fractions as shaded portions of a whole square.
Cancellation (Common Factors): Dividing numerator and denominator by common factors before multiplying to simplify.
Simplest (Lowest) Form: A fraction whose numerator and denominator share no common factor other than 1.
Mixed Number: A whole number with a proper fraction.
Improper Fraction: Numerator ≥ denominator.
Unit Rate: Amount per one unit (e.g., 3 km per hour).

Multiplication of Fractions

Introduction

In this virtual lab, students will explore the concept of multiplication of fractions using the PictoBlox 3D & XR environment. Fractions represent parts of a whole and multiplying them shows us “parts of parts.” Through interactive visuals, learners will see how numerators and denominators multiply step by step. Real-life contexts like walking distances, sharing food, and costs make the concept meaningful. The activity combines visual models, practice problems, and gamified quizzes for a complete learning experience.

Key Features

Clean scene-by-scene UI with Next/Back navigation and scene map
Real-time 3D block/grid animations showing numerator × numerator and denominator × denominator
Instant feedback panels

Step-by-Step Procedure for VR Experience

Step-by-step Procedure for VR Experience

1) Access the Virtual Lab

Click Start to enter Scene 1.

2) Scene-by-Scene Flow

Scene 1 – Informative: Concept of multiplying fractions with visual overlay.
Scene 2 – Simulative: Multiply numerators (top parts).
Scene 3 – Simulative: Multiply denominators (bottom parts).
Scene 4 – Informative: Display full solution (e.g., 1/2 × 2/4 = 2/8).
Scene 5 – Interactive: Practice with 1/2 × 1/3 → correct = 1/6.
Scene 6 – Interactive: Practice with 1/3 × 2/3 → correct = 2/9.

3) Quiz