Multiply two fractions: word problems

Learning Objectives Translate word problems involving 3D figures into mathematical expressions requiring fraction multiplication. Calculate the volume of a rectangular prism when its dimensions are given as fractions or mixed numbers. Determine a fractional portion of a 3D figure's volume or surface area. Solve problems involving scaling the dimensions of a 3D figure by a fractional factor. Apply fraction multiplication to solve problems related to the capacity of 3D containers. Interpret the meaning of a fractional answer in the context of a geometric word problem. Ever wondered how much space is left in a cereal box that's only 3/4 full? 🥣 Let's explore how fractions define the 3D world around us! This tutorial bridges the gap between basic fraction operat...

TermDefinitionExample VolumeThe amount of three-dimensional space an object occupies, measured in cubic units.The volume of a cube with a side length of 1/2 meter is (1/2) * (1/2) * (1/2) = 1/8 cubic meters. Rectangular PrismA three-dimensional solid shape which has six faces that are rectangles.A standard textbook, a shoebox, or a fish tank. Fractional ScalingThe process of changing the size of an object by multiplying its dimensions by a fraction.Scaling a cube with a 2-inch side by a factor of 3/4 results in a new side length of 2 * (3/4) = 3/2 inches. CapacityThe maximum amount that a three-dimensional container can hold. It is often used interchangeably with volume.A tank with a volume of 50 cubic meters has a capacity of 50 cubic meters. If it's 2/5 full, it contains 50 * (2/5)...

Multiplication of Fractions \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} To multiply two fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. This is used to find a 'fraction of a fraction'. Volume of a Rectangular Prism V = l \times w \times h The volume (V) of a rectangular prism is found by multiplying its length (l), width (w), and height (h). This formula is fundamental when the dimensions are given as fractions. Volume Scaling by a Factor V_{new} = V_{original} \times k^3 If every dimension of a 3D figure is scaled by a factor 'k', the new volume is the original volume multiplied by k cubed. This is because the scaling factor is applied to a...