Mathematics
Grade 5
15 min
Multiply two fractions using models
Multiply two fractions using models
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1
Introduction & Learning Objectives
Learning Objectives
Represent a fraction multiplication problem using an area model.
Construct an area model to show the product of two fractions.
Identify the total number of parts and the number of overlapping parts in an area model.
Write the product of two fractions as a new fraction based on an area model.
Explain how an area model visually demonstrates fraction multiplication.
Solve real-world problems involving fraction multiplication using models.
Have you ever wondered what happens when you take a 'fraction of a fraction'? 🤔 Imagine cutting a pizza into slices, and then taking only a part of one of those slices!
In this lesson, you'll learn how to multiply two fractions by drawing and understanding visual models. This will help you see exactly why t...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole. It is written as a numerator over a denominator.1/2 (one-half), 3/4 (three-fourths)
NumeratorThe top number in a fraction that tells you how many parts of the whole you have.In 2/3, the numerator is 2, meaning you have 2 parts.
DenominatorThe bottom number in a fraction that tells you how many equal parts the whole is divided into.In 2/3, the denominator is 3, meaning the whole is divided into 3 equal parts.
Area ModelA visual representation, often a square or rectangle, divided into smaller parts to show fractions and their products.A square divided into rows and columns to show 1/2 x 1/3.
ProductThe result obtained when two or more numbers are multiplied together.The product of 2 and 3 is 6 (2 x 3 = 6). The produc...
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Core Formulas
Setting Up an Area Model for Fraction Multiplication
To multiply two fractions $\frac{a}{b} \times \frac{c}{d}$ using an area model, draw a square or rectangle. Divide it vertically into 'b' equal parts and shade 'a' parts. Then, divide the same square horizontally into 'd' equal parts and shade 'c' parts using a different direction or color.
This rule helps you visually represent each fraction in the multiplication problem within the same whole. One fraction's parts are shown by vertical divisions, and the other's by horizontal divisions.
Identifying the Product from an Area Model
The product of two fractions $\frac{a}{b} \times \frac{c}{d}$ is represented by the fraction $\frac{\text{number of overlapping shaded parts}}{\text...
4 more steps in this tutorial
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Challenging
An area model shows the product of two fractions is 6/15. The model was created by shading 2 of 3 vertical columns. What was the second fraction that was represented by horizontal rows?
A.2/5
B.3/5
C.6/5
D.4/12
Challenging
If you create an area model for a/b x c/d, how is the total number of small rectangles in the model (the denominator of the product) related to the denominators of the original fractions (b and d)?
A.The total number of rectangles is the sum of b and d.
B.The total number of rectangles is the greater of b or d.
C.The total number of rectangles is the least common multiple of b and d.
D.The total number of rectangles is the product of b and d.
Challenging
The standard algorithm for multiplying fractions is (a/b) x (c/d) = (a x c) / (b x d). How does the area model visually prove that you must multiply the denominators?
A.The model shows that dividing the whole into 'b' columns and 'd' rows creates a total of 'b x d' smaller, equal-sized parts, which defines the new denominator.
B.The model shows that the overlapping parts (a x c) are more important than the total number of parts.
C.The model proves you should add the denominators because you are using two different fractions.
D.The model doesn't show anything about the denominators; it only shows the numerators.
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