Mathematics
Grade 10
15 min
Complete the fraction multiplication sentence
Complete the fraction multiplication sentence
What you'll learn
- Identify the numerator and denominator in a fraction with 90% accuracy on a worksheet.
- Solve fraction multiplication problems involving proper fractions, improper fractions, and mixed numbers with 80% accuracy on a quiz.
- Explain the process of multiplying fractions, including simplifying before multiplying, in their own words with at least 3 accurate steps.
- Apply fraction multiplication to solve real-world word problems, demonstrating understanding by correctly setting up and solving at least 2 out of 3 problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Relate fractional scale factors to changes in length, surface area, and volume of 3D figures.
Set up and complete fraction multiplication sentences to find unknown dimensions of similar solids.
Use squared fractional scale factors to complete multiplication sentences for surface area ratios.
Apply cubed fractional scale factors to complete multiplication sentences for volume ratios.
Solve problems involving fractional parts of a 3D figure's properties by working backwards from area or volume ratios.
Deconstruct a geometric word problem into a fraction multiplication sentence to find a missing value.
Ever wonder how an architect's small model perfectly represents a giant skyscraper? 🏗️ It's all about scaling with fractions, a concept we'...
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Key Concepts & Vocabulary
TermDefinitionExample
Similar SolidsTwo three-dimensional figures are similar if they have the same shape and all their corresponding dimensions are proportional.A sphere with a radius of 2 cm is similar to a sphere with a radius of 5 cm. A cube with a side length of 3 inches is similar to a cube with a side length of 1 inch.
Scale Factor (k)The constant ratio of corresponding linear dimensions (like height, radius, or side length) of two similar solids. It is often expressed as a fraction.If a large cone has a height of 15m and a similar small cone has a height of 10m, the scale factor from large to small is 10/15, which simplifies to k = 2/3.
Linear DimensionA one-dimensional measurement of a figure, such as length, width, height, radius, or slant height. The ratio of corresponding line...
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Core Formulas
Surface Area Ratio Formula
A_{new} = k^2 \cdot A_{original} = (\frac{a}{b})^2 \cdot A_{original}
Use this formula to find the surface area of a similar solid. Multiply the original surface area by the square of the fractional scale factor (k = a/b).
Volume Ratio Formula
V_{new} = k^3 \cdot V_{original} = (\frac{a}{b})^3 \cdot V_{original}
Use this formula to find the volume of a similar solid. Multiply the original volume by the cube of the fractional scale factor (k = a/b).
Finding the Scale Factor from Ratios
k = \sqrt{\frac{A_{new}}{A_{original}}} \quad \text{or} \quad k = \sqrt[3]{\frac{V_{new}}{V_{original}}}
If you know the surface areas or volumes of two similar solids, you can find the linear scale factor by taking the square root of the area ratio or the cub...
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Challenging
A small, solid silver cube has a mass of 50 grams. A larger, similar cube is made of the same silver and has a surface area that is 4 times greater than the small cube. Assuming mass is proportional to volume, complete the sentence for the mass of the larger cube: `Mass_large = (___) * 50`.
A.4/1
B.8/1
C.2/1
D.16/1
Challenging
Two similar shipping containers are rectangular prisms. The smaller container has a volume of 12 m³ and a length of 3 m. The larger container has a volume of 324 m³. Complete the sentence to find the length of the larger container: `L_large = (___) * 3`.
A.27/1
B.9/1
C.3/1
D.4/1
Challenging
The surface area of a large sphere is 36/25 times the surface area of a similar small sphere. The volume of the large sphere is `V`. Complete the sentence for the volume of the small sphere, `v`, using the surface area ratio as the base: `v = (36/25)^(___) * V`.
A.3/2
B.2/3
C.-2/3
D.-3/2
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Frequently asked questions
What grade level is "Complete the fraction multiplication sentence"?
Complete the fraction multiplication sentence is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Complete the fraction multiplication sentence?
You'll be able to: Identify the numerator and denominator in a fraction with 90% accuracy on a worksheet; Solve fraction multiplication problems involving proper fractions, improper fractions, and mixed numbers with 80% accuracy on a quiz; Explain….
Is "Complete the fraction multiplication sentence" free to practice?
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How many practice questions are included with Complete the fraction multiplication sentence?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.