Mathematics
Grade 6
15 min
Multiply two fractions using models
Multiply two fractions using models
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1
Introduction & Learning Objectives
Learning Objectives
Visually represent fractions using a unit square model.
Construct an area model to represent the multiplication of two fractions.
Identify the product of two fractions by interpreting the overlapping shaded region in an area model.
Write the product of two fractions as a new fraction based on their area model.
Explain how an area model demonstrates the multiplication of two fractions.
Solve fraction multiplication problems using area models and express the answer in simplest form.
Have you ever wondered how much of a recipe you'd make if you only used a fraction of the ingredients? 🍰 Or how much of a garden plot is used if you plant flowers in a fraction of a fraction of it?
In this lesson, you'll learn a powerful visual method called an '...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole. It is written as a numerator (top number) over a denominator (bottom number).In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator. It means 3 out of 4 equal parts.
NumeratorThe top number in a fraction, which tells you how many parts of the whole are being considered or selected.In $\frac{2}{5}$, the numerator is 2, meaning we are looking at 2 parts.
DenominatorThe bottom number in a fraction, which tells you 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. In fraction models, it represents the 'whole' or '1'.When multiplying frac...
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Core Formulas
General 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.
Constructing an Area Model for Fraction Multiplication
1. Draw a unit square. 2. Divide the square vertically into 'd' parts for the first fraction $\frac{a}{d}$ and shade 'a' parts. 3. Divide the same square horizontally into 'f' parts for the second fraction $\frac{c}{f}$ and shade 'c' parts. 4. The product is the number of squares that are shaded by BOTH fractions (numerator) over the total number of small squares created (deno...
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Challenging
An area model is built for $\frac{x}{y} \times \frac{p}{q}$. The model has 12 total small squares, and 2 of them are in the overlapping shaded region. If y and q are both greater than 1, which of these could be the two fractions being multiplied?
A.\frac{1}{6} \times \frac{2}{2}
B.\frac{2}{12} \times \frac{1}{1}
C.\frac{1}{3} \times \frac{2}{4}
D.\frac{2}{1} \times \frac{1}{12}
Challenging
A recipe for one batch of cookies requires $\frac{3}{4}$ cup of flour. You decide to make only $\frac{1}{2}$ of the batch. If you were to model this situation to find out how much flour you need, what would the overlapping shaded area of the model represent?
A.The total flour for two batches.
B.The amount of flour needed for half the recipe.
C.The original amount of flour, $\frac{3}{4}$ cup.
D.The fraction of the batch being made, $\frac{1}{2}$.
Challenging
The product of two fractions is modeled, resulting in 8 overlapping shaded squares out of a total of 40 small squares. The first fraction had a denominator of 5. What must the second fraction be?
A.\frac{4}{8}
B.\frac{2}{10}
C.\frac{8}{5}
D.\frac{2}{4}
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