Mathematics
Grade 10
15 min
Multiply two fractions using models
Multiply two fractions using models
What you'll learn
- Identify the fractional parts represented by different sections of a visual model (area model, number line) with 80% accuracy.
- Solve multiplication problems involving two fractions (e.g., 1/2 x 1/3) using area models and verify the product with at least 75% accuracy.
- Explain how a visual model represents the multiplication of two fractions, demonstrating an understanding of the concept of 'a fraction of a fraction' in their own words.
- Apply the area model to represent and solve real-world problems involving the multiplication of two fractions with at least 70% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Visually represent the multiplication of two fractions as the base area of a three-dimensional rectangular prism.
Construct a 2D area model for fraction multiplication and extend it conceptually to the volume of a 3D figure.
Calculate the volume of a rectangular prism with fractional edge lengths.
Interpret a shaded 3D model to determine the fractional volume it represents.
Justify the standard algorithm for multiplying fractions using a geometric model based on a unit cube.
Apply fractional scaling to the dimensions of a 3D figure and determine its new base area or volume.
Ever wondered how architects or 3D artists calculate the exact material needed for a scale model of a skyscraper? It all comes down to understanding fractional parts of a larger whole!...
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Key Concepts & Vocabulary
TermDefinitionExample
Unit CubeA cube whose edges are all 1 unit in length. It serves as the fundamental 'whole' (1) from which fractional parts are taken in a 3D context. Its volume is 1 cubic unit.A cube with dimensions 1m x 1m x 1m is a unit cube. Its volume is 1 m³.
Fractional DimensionA length, width, or height of a 3D figure that is expressed as a fraction of a whole unit.A rectangular prism built within a unit cube might have a length of 1/2 unit, a width of 3/4 unit, and a height of 1 unit.
Area Model of MultiplicationA visual representation of multiplication using a rectangle. To model (a/b) * (c/d), a rectangle is divided into 'b' vertical sections and 'd' horizontal sections, and a region of 'a' sections by 'c' sections is shade...
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Core Formulas
Volume of a Rectangular Prism
V = l \cdot w \cdot h
The volume (V) of a rectangular prism is found by multiplying its length (l), width (w), and height (h). When the dimensions are fractions, this formula models the multiplication of those fractions.
Area Model for Fraction Multiplication
\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}
This is the standard algorithm for multiplying two fractions. A geometric model demonstrates this rule by showing that the resulting figure is composed of (a * c) shaded smaller units out of a total of (b * d) possible units that make up the whole.
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Challenging
A rectangular prism has a volume of 12/105 cubic units. The area of its base is the product of 3/5 and 2/7. What is the height of the prism?
A.2/3
B.1/2
C.6/35
D.3/2
Challenging
A rectangular prism has a volume of 24/120 cubic units. Its height is 3/4 of a unit, and its width is 2/5 of a unit. What fraction represents the length of the prism?
A.5/9
B.6/20
C.2/3
D.3/4
Challenging
The base area of a new prism is found by scaling a unit square. The resulting area is 6/35 square units. If the scaling factors were fractions with single-digit, prime denominators, what were the two fractions multiplied?
A.2/5 and 3/7
B.1/5 and 6/7
C.2/7 and 3/6
D.1/6 and 5/7
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What grade level is "Multiply two fractions using models"?
Multiply two fractions using models is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Multiply two fractions using models?
You'll be able to: Identify the fractional parts represented by different sections of a visual model (area model, number line) with 80% accuracy; Solve multiplication problems involving two fractions (e.g., 1/2 x 1/3) using area models and verify….
Is "Multiply two fractions using models" free to practice?
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How many practice questions are included with Multiply two fractions using models?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.