Multiply fractions by whole numbers: word problems

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...

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...

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.