Mathematics
Grade 10
15 min
Scaling mixed numbers by fractions
Scaling mixed numbers by fractions
What you'll learn
- Identify whether multiplying a mixed number by a fraction greater than 1 will result in a product larger or smaller than the original mixed number, and explain your reasoning.
- Solve multiplication problems involving mixed numbers scaled by fractions using visual models (e.g., area models, number lines) with at least 80% accuracy.
- Apply the standard algorithm to multiply a mixed number by a fraction, expressing the answer in simplest form, on a worksheet with 4 problems and achieving 75% accuracy.
- Explain, in your own words, how multiplying by a fraction is different from multiplying by a whole number, providing at least two specific examples.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the new dimensions of a 3D figure when its original mixed number dimensions are scaled by a fraction.
Convert mixed numbers to improper fractions as a primary step for accurate scaling calculations.
Apply the principle of scaling to determine the new volume of a 3D figure.
Apply the principle of scaling to determine the new surface area of a 3D figure.
Analyze and prove the relationship between a linear scale factor and the resulting changes in volume and surface area.
Solve multi-step word problems involving the scaling of 3D figures with mixed number dimensions.
Ever wondered how architects create miniature models of giant skyscrapers? 🏛️ They scale every single measurement down, often using fractions!
This tutorial connects a foundational ar...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of an integer and a proper fraction.4 1/2, which represents four whole units and one half of another unit.
Improper FractionA fraction in which the numerator is greater than or equal to the denominator.9/2, which is the improper fraction equivalent of 4 1/2.
Scale Factor (k)The constant ratio by which all dimensions of an object are multiplied to create a similar figure. A scale factor between 0 and 1 results in a reduction.A scale factor of 2/3 means the new figure's dimensions will be 2/3 the size of the original.
Similar FiguresTwo geometric figures that have the same shape but potentially different sizes. The ratio of their corresponding linear measurements is constant and equal to the scale factor.A 2x2x2 cube and a 4x4x4 cub...
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Core Formulas
Converting Mixed Numbers to Improper Fractions
a b/c = (a * c + b) / c
This conversion is the mandatory first step before multiplying. It consolidates the mixed number into a single fractional form, which is necessary for accurate calculations with other fractions.
Scaling Linear Dimensions
New Dimension = Original Dimension × k
To find a new scaled dimension (like length, width, or height), multiply the original dimension by the scale factor, k.
Scaling Volume of Similar Figures
New Volume = Original Volume × k³
When all linear dimensions are scaled by a factor k, the volume of the new figure is the original volume multiplied by the cube of the scale factor. This is because volume is a three-dimensional measurement.
Scaling Surface Area of Similar Figures
New...
4 more steps in this tutorial
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Challenging
The volume of a sphere is scaled from an original volume of 972π cubic units to a new volume of 36π cubic units. If the original radius was 4 1/2 units, what was the fractional scale factor 'k' applied?
A.1/3
B.1/9
C.1/27
D.2/3
Easy
According to the tutorial, what is the mandatory first step before multiplying a mixed number dimension by a fractional scale factor?
A.Multiply the whole number and the fraction separately, then add the results.
B.Convert the mixed number into an improper fraction.
C.Find the reciprocal of the scale factor.
D.Calculate the volume of the original figure.
Easy
A three-dimensional figure is scaled by a factor of 3/4. What does this scale factor indicate about the new figure?
A.The new figure is a reduction of the original.
B.The new figure is an enlargement of the original.
C.The new figure has the same volume as the original.
D.The new figure is not similar to the original.
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Frequently asked questions
What grade level is "Scaling mixed numbers by fractions"?
Scaling mixed numbers by fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Scaling mixed numbers by fractions?
You'll be able to: Identify whether multiplying a mixed number by a fraction greater than 1 will result in a product larger or smaller than the original mixed number, and explain your reasoning; Solve multiplication problems involving mixed….
Is "Scaling mixed 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 mixed numbers by fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.