Mathematics
Grade 10
15 min
Multiply fractions by whole numbers: word problems
Multiply fractions by whole numbers: word problems
What you'll learn
- Solve word problems involving multiplying a fraction by a whole number with at least 80% accuracy.
- Explain the steps used to solve a word problem involving multiplying a fraction by a whole number in their own words.
- Apply the concept of repeated addition to represent multiplying a fraction by a whole number with supporting visuals (drawings, diagrams).
- Identify the fraction and whole number in a word problem and determine which operation is needed to solve it with 100% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Analyze word problems involving 3D figures to identify quantities represented by whole numbers (e.g., number of vertices, edges, faces).
Set up multiplication expressions involving fractions and whole numbers to model scenarios related to three-dimensional geometry.
Accurately calculate the product of a fraction and a whole number within the context of geometric properties.
Interpret the fractional part of a whole number quantity in relation to a 3D figure's characteristics.
Apply Euler's formula for polyhedra to determine a whole number quantity (V, E, or F) before performing a fractional calculation.
Solve multi-step word problems that combine properties of prisms, pyramids, and other polyhedra with fractional operations.
Imagine an architectu...
2
Key Concepts & Vocabulary
TermDefinitionExample
PolyhedronA three-dimensional solid figure whose surfaces are flat polygons. These flat surfaces are called faces, the line segments where they meet are edges, and the points where edges meet are vertices.A cube is a polyhedron with 6 square faces, 12 edges, and 8 vertices.
PrismA polyhedron with two parallel, congruent faces called bases, and whose other faces (lateral faces) are parallelograms, formed by connecting corresponding vertices of the bases.A triangular prism has 2 triangular bases and 3 rectangular lateral faces. It has 9 edges and 6 vertices.
PyramidA polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and the apex form a triangle, called a lateral face.A square pyramid has a square base, 4 triangular faces, 8 e...
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Core Formulas
Multiplication of a Fraction and a Whole Number
\frac{a}{b} \times c = \frac{a \times c}{b}
To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number and place the result over the original denominator. The whole number 'c' can be thought of as c/1.
Euler's Formula
V - E + F = 2
Use this formula for any convex polyhedron to find an unknown count of vertices (V), edges (E), or faces (F) when the other two quantities are known. This is often the first step to find the 'whole number' in a problem.
4 more steps in this tutorial
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Challenging
A dodecahedron is a polyhedron with 20 vertices. A model of it requires that 75% of its vertices serve as connection points for a larger structure. Of these connection points, 2/3 must be reinforced with extra material. How many vertices are reinforced?
A.15
B.12
C.10
D.5
Challenging
A cuboctahedron is a polyhedron with 14 faces. A design requires that 4/7 of the faces be made of a translucent material. Of those translucent faces, exactly 1/2 must be tinted blue. How many faces of the cuboctahedron are tinted blue?
A.4
B.8
C.2
D.7
Challenging
A particular convex polyhedron has 30 edges. It is known that the number of its faces is exactly 3/5 of the number of its vertices. If 1/4 of the vertices are to be colored gold, how many vertices are colored gold?
A.20
B.12
C.8
D.5
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Multiply fractions by whole numbers: word problems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Multiply fractions by whole numbers: word problems?
You'll be able to: Solve word problems involving multiplying a fraction by a whole number with at least 80% accuracy; Explain the steps used to solve a word problem involving multiplying a fraction by a whole number in their own words; Apply the….
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How many practice questions are included with Multiply fractions by whole numbers: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.