Scaling mixed numbers by fractions

Learning Objectives Calculate the new dimensions of a 3D figure when its original mixed number dimensions are scaled by a fraction. Convert mixed numbers to improper fractions as a primary step for accurate scaling calculations. Apply the principle of scaling to determine the new volume of a 3D figure. Apply the principle of scaling to determine the new surface area of a 3D figure. Analyze and prove the relationship between a linear scale factor and the resulting changes in volume and surface area. Solve multi-step word problems involving the scaling of 3D figures with mixed number dimensions. Ever wondered how architects create miniature models of giant skyscrapers? 🏛️ They scale every single measurement down, often using fractions! This tutorial connects a foundational ar...

TermDefinitionExample Mixed NumberA number consisting of an integer and a proper fraction.4 1/2, which represents four whole units and one half of another unit. Improper FractionA fraction in which the numerator is greater than or equal to the denominator.9/2, which is the improper fraction equivalent of 4 1/2. Scale Factor (k)The constant ratio by which all dimensions of an object are multiplied to create a similar figure. A scale factor between 0 and 1 results in a reduction.A scale factor of 2/3 means the new figure's dimensions will be 2/3 the size of the original. Similar FiguresTwo geometric figures that have the same shape but potentially different sizes. The ratio of their corresponding linear measurements is constant and equal to the scale factor.A 2x2x2 cube and a 4x4x4 cub...

Converting Mixed Numbers to Improper Fractions a b/c = (a * c + b) / c This conversion is the mandatory first step before multiplying. It consolidates the mixed number into a single fractional form, which is necessary for accurate calculations with other fractions. Scaling Linear Dimensions New Dimension = Original Dimension × k To find a new scaled dimension (like length, width, or height), multiply the original dimension by the scale factor, k. Scaling Volume of Similar Figures New Volume = Original Volume × k³ When all linear dimensions are scaled by a factor k, the volume of the new figure is the original volume multiplied by the cube of the scale factor. This is because volume is a three-dimensional measurement. Scaling Surface Area of Similar Figures New...