Mathematics
Grade 10
15 min
Multiply three or more fractions and whole numbers
Multiply three or more fractions and whole numbers
What you'll learn
- Solve multiplication problems involving three fractions with at least 80% accuracy.
- Apply the concept of multiplying fractions to solve word problems involving three or more fractions and whole numbers, demonstrating understanding by showing their work and arriving at a correct solution in at least 3 out of 4 problems.
- Explain the steps involved in multiplying three fractions, using mathematical vocabulary (numerator, denominator, product) correctly in at least two sentences.
- Calculate the product of a whole number and two fractions, expressing the answer in simplest form at least 75% of the time.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the volume of rectangular prisms and other polyhedra with fractional side lengths.
Apply fractional scaling factors to determine the new volume of a three-dimensional figure.
Convert whole numbers and mixed numbers into improper fractions to solve multi-term multiplication problems for volume.
Utilize cross-cancellation to efficiently multiply three or more fractions in geometric contexts.
Solve multi-step word problems involving the volume of composite 3D figures with fractional dimensions.
Prove how a fractional scaling factor affects the volume of a prism by a factor of k-cubed.
Ever wondered how architects calculate the exact concrete needed for a foundation with dimensions like 15 yards by 10 1/2 yards by 1/3 yard? Let's find out! 🏗️...
2
Key Concepts & Vocabulary
TermDefinitionExample
VolumeThe measure of the three-dimensional space enclosed by a closed surface. For a rectangular prism, it is the product of its length, width, and height.A box with sides 3 cm, 4 cm, and 5 cm has a volume of 3 * 4 * 5 = 60 cubic centimeters (cm³).
Rectangular PrismA polyhedron with six rectangular faces, twelve edges, and eight vertices. Opposite faces are parallel and congruent.A standard brick, a shoebox, or a fish tank.
Improper FractionA fraction in which the numerator is greater than or equal to the denominator. Mixed numbers must be converted to improper fractions before multiplication.The mixed number 3 1/4 is converted to the improper fraction (3*4 + 1)/4 = 13/4.
Cross-CancellationA method to simplify the multiplication of fractions by dividing any numerator...
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Core Formulas
Multiplication of Three or More Fractions
\frac{a}{b} \times \frac{c}{d} \times \frac{e}{f} = \frac{a \times c \times e}{b \times d \times f}
To multiply three or more fractions, multiply all the numerators together to get the new numerator, and multiply all the denominators together to get the new denominator. Always convert whole numbers and mixed numbers to improper fractions first.
Volume of a Rectangular Prism
V = l \times w \times h
The volume (V) of a rectangular prism is the product of its length (l), width (w), and height (h). This formula inherently requires multiplying three numbers, which can be fractions, whole numbers, or a mix.
Volume Scaling Principle
V_{new} = k^3 \times V_{original}
When a 3D figure is scaled by a factor of 'k', its new vo...
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Sign Up Free to ContinueSample Practice Questions
Challenging
A wooden box with no lid is shaped like a rectangular prism. Its outer dimensions are length 10 1/2 in, width 8 in, and height 6 in. The wood is 1/4 inch thick on all sides and the bottom. What is the interior volume of the box?
A.504 cubic inches
B.450 cubic inches
C.1725/4 cubic inches
D.1665/4 cubic inches
Challenging
The volume of a large rectangular prism is 1250 cm³. A smaller, geometrically similar prism has a volume of 80 cm³. What fractional scaling factor `k` was used to reduce the large prism to the small one?
A.2/5
B.4/25
C.8/125
D.1/2
Challenging
A student is asked to prove the volume scaling principle. They start with an original prism of volume V₁ = lwh. They create a new prism with dimensions l' = kl, w' = kw, and h' = kh. Which of the following steps correctly completes the proof that V₂ = k³V₁?
A.V₂ = l'w'h' = (kl)(kw)(kh) = k(lwh) = kV₁
B.V₂ = l'w'h' = (l+k)(w+k)(h+k) = (lwh) + k³ = V₁ + k³
C.V₂ = l'w'h' = (kl)(kw)(kh) = (k*k*k)(l*w*h) = k³(lwh) = k³V₁
D.V₂ = l'w'h' = k(l) + k(w) + k(h) = k(l+w+h)
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Frequently asked questions
What grade level is "Multiply three or more fractions and whole numbers"?
Multiply three or more fractions and whole numbers is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Multiply three or more fractions and whole numbers?
You'll be able to: Solve multiplication problems involving three fractions with at least 80% accuracy; Apply the concept of multiplying fractions to solve word problems involving three or more fractions and whole numbers, demonstrating….
Is "Multiply three or more fractions and whole numbers" 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 Multiply three or more fractions and whole numbers?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.