Mathematics
Grade 5
15 min
Multiply two unit fractions using models
Multiply two unit fractions using models
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1
Introduction & Learning Objectives
Learning Objectives
Identify and define unit fractions.
Represent a unit fraction using an area model.
Explain how an area model visually represents the multiplication of fractions.
Use an area model to multiply two unit fractions.
Determine the product of two unit fractions from an area model.
Relate the visual product from a model to the numerical product of two unit fractions.
Ever wonder how much of a pizza you get if you share a slice that's already a fraction of the whole? 🍕 Let's find out how models help us see these tiny parts!
In this lesson, you'll learn to multiply two unit fractions using visual area models. This skill helps you understand how parts of parts combine and lays the foundation for more complex fraction operations, making math more co...
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Key Concepts & Vocabulary
TermDefinitionExample
Unit FractionA fraction where the numerator (top number) is 1. It represents one part of a whole that has been divided into equal parts.$ rac{1}{2}$, $ rac{1}{3}$, $ rac{1}{5}$ are all unit fractions.
Area ModelA visual representation, often a rectangle or square, divided into smaller equal parts to show fractions and their operations.A square divided into 4 equal parts with one part shaded represents $ rac{1}{4}$.
WholeThe entire quantity or object, represented by the undivided model (e.g., a full square or rectangle).A whole pizza before any slices are taken.
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $ rac{1}{4}$, the numerator is 1, meaning we are considering 1 part.
DenominatorThe bottom number in a frac...
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Core Formulas
Representing the First Unit Fraction
To represent $ rac{1}{a}$ in an area model, divide a whole rectangle into $a$ equal rows and shade one of those rows.
This step visually establishes the first fraction by showing one part out of 'a' total parts of the whole.
Representing the Second Unit Fraction
To multiply $ rac{1}{a} imes rac{1}{b}$ using an area model, after representing $ rac{1}{a}$, divide the *entire* whole rectangle into $b$ equal columns and shade one of those columns.
This step applies the second fraction to the whole, creating a grid and showing 'a fraction of a fraction' through overlapping areas.
Finding the Product from the Model
The product $ rac{1}{a} imes rac{1}{b}$ is represented by the area where the shaded row (for $ rac{1}...
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Challenging
The product of two unit fractions, 1/a × 1/b, is 1/24. Which of the following could NOT be the pair of unit fractions multiplied?
A.1/4 and 1/6
B.1/3 and 1/8
C.1/2 and 1/12
D.1/4 and 1/8
Challenging
Imagine you use a model to find 1/2 × 1/3. Then you use a model to find 1/2 × 1/8. What happens to the size of the product when you multiply 1/2 by a unit fraction with a larger denominator?
A.The product gets larger.
B.The product gets smaller.
C.The product stays the same.
D.The product becomes a whole number.
Challenging
Why does the area model for multiplication work? What is the fundamental idea it represents?
A.It shows taking a 'part of a part,' which is the definition of fraction multiplication.
B.It is a way to count squares that is easier than multiplying numbers.
C.It works because the area of a rectangle is length times width.
D.It visually represents adding the same fraction repeatedly.
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