Mathematics
Grade 8
15 min
Multiply two fractions using models
Multiply two fractions using models
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1
Introduction & Learning Objectives
Learning Objectives
Visually represent a single fraction using an area model.
Construct an area model to illustrate the multiplication of two proper fractions.
Identify the product of two fractions by interpreting the overlapping region of an area model.
Connect the visual representation of fraction multiplication to the standard algebraic algorithm.
Solve problems involving the multiplication of two fractions by drawing and analyzing area models.
Simplify the resulting product fraction from an area model.
Ever wondered how to visually 'see' what happens when you multiply fractions? 🤔 Get ready to uncover the power of models!
In this lesson, you'll learn to multiply two fractions by drawing and interpreting area models. This visual approach will deepen your...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number representing a part of a whole, expressed as a numerator over a denominator.In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator, meaning 3 out of 4 equal parts.
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $\frac{2}{5}$, the numerator is 2, meaning we are considering 2 parts.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In $\frac{2}{5}$, the denominator is 5, meaning the whole is divided into 5 equal parts.
Unit SquareA square with sides of length 1 unit, representing one whole in an area model.When multiplying fractions, we start with a square that represents the value '1'.
Area ModelA visual r...
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Core Formulas
Algebraic Rule for Multiplying Fractions
$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
To multiply two fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. This rule is what the area model visually demonstrates.
Representing the First Fraction in an Area Model
Divide a unit square vertically into 'b' equal columns, then shade 'a' of these columns to represent $\frac{a}{b}$.
This step establishes the first fraction as a portion of the whole unit square along one dimension.
Representing the Second Fraction in an Area Model
Divide the *same* unit square horizontally into 'd' equal rows, then shade 'c' of these rows (using a differe...
5 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
A school survey finds that 3/5 of students play a sport. Of those student-athletes, 1/4 play a fall sport. You are asked to model the probability that a randomly selected student is a student-athlete who plays a fall sport. What is the simplified fraction representing this probability?
A.4/9
B.3/20
C.1/5
D.4/20
Challenging
An area model is described as follows: A unit square is divided into 6 vertical columns, and the first 5 are shaded. The same square is divided into 4 horizontal rows, and the top 3 are shaded. What is the simplified product represented by the overlapping region?
A.15/24
B.8/10
C.3/4
D.5/8
Challenging
The tutorial specifies that area models are used for multiplying proper fractions. A student is asked to model 3/2 x 1/3. Why is the standard area model, starting with a single unit square, problematic for this calculation?
A.The product will be greater than 1, which is fine.
B.It is impossible to divide a square into 2 columns.
C.The first fraction, 3/2, is greater than one whole, but the model begins with only one unit square.
D.The denominators are different.
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