Mathematics
Grade 10
15 min
Scaling whole numbers by fractions
Scaling whole numbers by fractions
What you'll learn
- Identify whether scaling a whole number by a fraction greater than 1 will result in a product greater than or less than the original whole number with 80% accuracy.
- Solve multiplication problems involving whole numbers and fractions (including fractions greater than 1) using visual models (e.g., area models, number lines) and/or equations with 75% accuracy.
- Explain, in their own words, how multiplying a whole number by a fraction changes the size of the whole number, providing at least two specific examples.
- Apply the concept of scaling to solve word problems involving real-world scenarios with fractions and whole numbers, achieving a score of 70% or higher on a related assessment.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the new dimensions of a 3D figure by scaling its whole number dimensions with a given fraction.
Explain the effect of a fractional scale factor (k) on the surface area (k²) and volume (k³) of a 3D solid.
Compute the new surface area of a scaled 3D figure without recalculating from the new dimensions.
Compute the new volume of a scaled 3D figure using the original volume and the scale factor.
Determine the fractional scale factor relating two similar 3D figures with whole number dimensions.
Solve problems involving scaling 3D objects, such as architectural models or product packaging.
Ever wondered how architects create a tiny, perfect model of a huge skyscraper? 🏙️ They use the power of scaling with fractions!
This tutorial explores how multipl...
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Key Concepts & Vocabulary
TermDefinitionExample
Scale Factor (k)A fraction that represents the ratio of the new dimension to the original dimension. If k < 1, it's a reduction. If k > 1, it's an enlargement.To scale a cube with a side length of 10 cm down to a cube with a side length of 5 cm, the scale factor is 5/10, which simplifies to k = 1/2.
Similar SolidsThree-dimensional figures that have the same shape, and all their corresponding dimensions are proportional by the same scale factor.A rectangular prism of 2x4x6 is similar to one of 3x6x9 because all dimensions are scaled by a factor of 3/2.
Linear DimensionA one-dimensional measurement of an object, such as length, width, height, or radius.The height of a cylinder is 12 inches. This is a linear dimension.
Surface AreaThe total area of all t...
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Core Formulas
Linear Scaling Rule
L_{new} = L_{original} \times k
To find a new linear dimension (like length, width, height, or radius), multiply the original whole number dimension by the fractional scale factor 'k'.
Surface Area Scaling Rule
A_{new} = A_{original} \times k^2
To find the new surface area, multiply the original surface area by the square of the scale factor. You do not need to find the new dimensions first.
Volume Scaling Rule
V_{new} = V_{original} \times k^3
To find the new volume, multiply the original volume by the cube of the scale factor. This is often much faster than recalculating from new dimensions.
4 more steps in this tutorial
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Challenging
A company wants to reduce the volume of its product packaging to 64/125 of the original volume to save on shipping. The cost of the cardboard is directly proportional to the surface area. By what fractional factor will the cost of cardboard for one package be reduced?
A.4/5
B.64/125
C.16/25
D.8/25
Challenging
An architectural model of a building is created with a scale factor of 1/50. This model is then used to create a larger display model, which is scaled up from the first model by a factor of 5/2. What is the overall scale factor of the final display model relative to the original building?
A.1/20
B.1/125
C.4/25
D.1/25
Challenging
The surface area of a pyramid is increased to 49/16 of its original area. If an edge of the original pyramid's base was 8 cm, what is the length of the corresponding edge on the new, larger pyramid?
A.14 cm
B.12.25 cm
C.24.5 cm
D.16 cm
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Frequently asked questions
What grade level is "Scaling whole numbers by fractions"?
Scaling whole numbers by fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Scaling whole numbers by fractions?
You'll be able to: Identify whether scaling a whole number by a fraction greater than 1 will result in a product greater than or less than the original whole number with 80% accuracy; Solve multiplication problems involving whole numbers and….
Is "Scaling whole numbers 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 whole numbers by fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.