Mathematics
Grade 10
15 min
Scaling fractions by fractions
Scaling fractions by fractions
What you'll learn
- Identify whether multiplying a whole number by a fraction greater than one will result in a product greater than or less than the original whole number, and explain why.
- Solve multiplication problems involving fractions and fractions (e.g., 1/2 x 2/3) using visual models (area models, number lines) with at least 80% accuracy.
- Explain, using a real-world example, how scaling a recipe up or down involves multiplying fractions by fractions.
- Apply the rule for multiplying fractions (numerator times numerator, denominator times denominator) to solve at least 3 out of 4 fraction multiplication problems correctly.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Calculate the new dimensions of a 3D figure when scaled by a fractional factor.
Determine the new surface area of a 3D figure by applying the square of a fractional scaling factor.
Determine the new volume of a 3D figure by applying the cube of a fractional scaling factor.
Solve for an original dimension or scale factor given the measurements of a scaled 3D figure.
Prove the relationship between a fractional scale factor and the resulting changes in surface area and volume for cubes and prisms.
Apply fractional scaling principles to solve complex, multi-step word problems involving similar 3D figures.
Ever wondered how architects create a perfect miniature model of a skyscraper, or how 3D printers shrink a design to fit in your hand? 🏗️ It's all abou...
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Key Concepts & Vocabulary
TermDefinitionExample
Scale Factor (k)The constant ratio between the corresponding linear measurements of two similar figures. When the scale factor is a fraction less than 1 (e.g., 1/2, 2/3), the new figure is a reduction of the original.If a cube with a side length of 10 cm is scaled by a factor of k = 1/2, the new cube will have a side length of 10 * (1/2) = 5 cm.
Similar 3D FiguresTwo 3D figures that have the same shape but are different sizes. The ratio of all their corresponding linear dimensions (like height, radius, or edge length) is equal to the scale factor.Two spheres are always similar. A cone with radius 3 and height 4 is similar to a cone with radius 6 and height 8, with a scale factor of 2.
Linear Dimension ScalingThe principle that any linear dimension (length, width, hei...
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Core Formulas
Linear Scaling Formula
Dimension_{new} = k \cdot Dimension_{original}
Use this to find any new linear measurement (like length, radius, or height) after scaling. 'k' is the fractional scale factor.
Surface Area Scaling Formula
Area_{new} = k^2 \cdot Area_{original}
Use this to find the new surface area of a figure. Remember to square the entire fractional scale factor, both numerator and denominator.
Volume Scaling Formula
Volume_{new} = k^3 \cdot Volume_{original}
Use this to find the new volume of a figure. Remember to cube the entire fractional scale factor.
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Challenging
A rectangular prism is scaled by a factor of k=2/3. The process is then repeated on the new prism with a scale factor of m=1/2. What is the overall linear scale factor that relates the final prism to the original prism?
A.1/3
B.7/6
C.1/27
D.1/9
Challenging
The volume of a sphere is reduced, resulting in a new volume that is 125/216 of the original. The surface area of the new, smaller sphere is 75π. What was the surface area of the original sphere?
A.90π
B.108π
C.125π
D.216π
Challenging
A sculptor has a block of marble in the shape of a rectangular prism with a volume of V and surface area of A. She carves a smaller, similar prism from it using a scale factor of 4/5. She then wishes to paint the new prism. What is the ratio of the new prism's volume to its new surface area?
A.(4/5) * (V/A)
B.(16/25) * (V/A)
C.(64/125) * (V/A)
D.(5/4) * (V/A)
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Frequently asked questions
What grade level is "Scaling fractions by fractions"?
Scaling fractions by fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Scaling fractions by fractions?
You'll be able to: Identify whether multiplying a whole number by a fraction greater than one will result in a product greater than or less than the original whole number, and explain why; Solve multiplication problems involving fractions and….
Is "Scaling fractions by fractions" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Scaling fractions by fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.