Mathematics
Grade 10
15 min
Multiples of fractions
Multiples of fractions
What you'll learn
- Identify multiples of a given fraction by skip counting and writing them in a list.
- Solve multiplication problems involving whole numbers and fractions using visual models like number lines or fraction bars with 80% accuracy.
- Explain, in their own words, the relationship between repeated addition of a fraction and multiplying that fraction by a whole number.
- Apply the concept of multiples of fractions to solve real-world word problems involving quantities like ingredients in a recipe or distances traveled, showing all work.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the new dimensions of a 3D figure when its original dimensions are multiplied by a fractional scale factor.
Determine the fractional scale factor relating two similar three-dimensional figures.
Prove and apply the relationship between the linear scale factor (k), the surface area ratio (k^2), and the volume ratio (k^3) for similar solids.
Compute the new surface area of a solid after scaling its dimensions by a fractional multiple.
Compute the new volume of a solid after scaling its dimensions by a fractional multiple.
Solve for original dimensions, surface area, or volume given the properties of a fractionally scaled model.
Ever wonder how an architect's tiny model represents a massive skyscraper, or how a 3D printer creates a perfect half...
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Key Concepts & Vocabulary
TermDefinitionExample
Similar SolidsTwo three-dimensional figures that have the same shape, and all of their corresponding linear dimensions (like height, radius, or edge length) are proportional.A sphere with a radius of 2 cm is similar to a sphere with a radius of 6 cm. A cube with a side length of 5 inches is similar to a cube with a side length of 2.5 inches.
Scale Factor (k)The constant ratio of corresponding linear dimensions of two similar solids. If k > 1, it's an enlargement. If 0 < k < 1, it's a reduction.If a cone has a height of 10m and a similar cone has a height of 4m, the scale factor from the larger cone to the smaller is k = 4/10 = 2/5.
Fractional MultipleThe result of multiplying a quantity by a fraction. In this context, it refers to the new dimension...
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Core Formulas
Linear Scaling Rule
Dimension_{new} = k \cdot Dimension_{original}
To find any new linear dimension (length, width, height, radius) of a scaled figure, multiply the original dimension by the scale factor k.
Surface Area Scaling Rule
Area_{new} = k^2 \cdot Area_{original}
To find the new surface area of a scaled figure, multiply the original surface area by the square of the scale factor (k^2). This is because area is a two-dimensional measurement.
Volume Scaling Rule
Volume_{new} = k^3 \cdot Volume_{original}
To find the new volume of a scaled figure, multiply the original volume by the cube of the scale factor (k^3). This is because volume is a three-dimensional measurement.
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Challenging
A rectangular prism is scaled by a factor of 3/4. The resulting prism is then scaled again by a factor of 2/3. What is the final volume as a fraction of the original volume?
A.1/8
B.5/7
C.1/2
D.6/12
Challenging
The surface area of a solid is scaled by an unknown fractional multiple, x/y. The volume of the same solid is scaled by a fractional multiple of 8/27. What is the value of x/y?
A.2/3
B.4/9
C.4/6
D.16/81
Challenging
An architectural model of a skyscraper is made with a scale of 1/200. The volume of the model is 0.15 m³. The actual skyscraper will be constructed using concrete that costs $120 per cubic meter. What is the total cost of the concrete required for the actual skyscraper?
A.$1,200,000
B.$3,600,000
C.$144,000,000
D.$2,400,000
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Frequently asked questions
What grade level is "Multiples of fractions"?
Multiples of fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Multiples of fractions?
You'll be able to: Identify multiples of a given fraction by skip counting and writing them in a list; Solve multiplication problems involving whole numbers and fractions using visual models like number lines or fraction bars with 80% accuracy….
Is "Multiples of 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 Multiples of fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.