Scaling whole numbers by fractions

Learning Objectives Calculate the new dimensions of a 3D figure by scaling its whole number dimensions with a given fraction. Explain the effect of a fractional scale factor (k) on the surface area (k²) and volume (k³) of a 3D solid. Compute the new surface area of a scaled 3D figure without recalculating from the new dimensions. Compute the new volume of a scaled 3D figure using the original volume and the scale factor. Determine the fractional scale factor relating two similar 3D figures with whole number dimensions. Solve problems involving scaling 3D objects, such as architectural models or product packaging. Ever wondered how architects create a tiny, perfect model of a huge skyscraper? 🏙️ They use the power of scaling with fractions! This tutorial explores how multipl...

TermDefinitionExample Scale Factor (k)A fraction that represents the ratio of the new dimension to the original dimension. If k < 1, it's a reduction. If k > 1, it's an enlargement.To scale a cube with a side length of 10 cm down to a cube with a side length of 5 cm, the scale factor is 5/10, which simplifies to k = 1/2. Similar SolidsThree-dimensional figures that have the same shape, and all their corresponding dimensions are proportional by the same scale factor.A rectangular prism of 2x4x6 is similar to one of 3x6x9 because all dimensions are scaled by a factor of 3/2. Linear DimensionA one-dimensional measurement of an object, such as length, width, height, or radius.The height of a cylinder is 12 inches. This is a linear dimension. Surface AreaThe total area of all t...

Linear Scaling Rule L_{new} = L_{original} \times k To find a new linear dimension (like length, width, height, or radius), multiply the original whole number dimension by the fractional scale factor 'k'. Surface Area Scaling Rule A_{new} = A_{original} \times k^2 To find the new surface area, multiply the original surface area by the square of the scale factor. You do not need to find the new dimensions first. Volume Scaling Rule V_{new} = V_{original} \times k^3 To find the new volume, multiply the original volume by the cube of the scale factor. This is often much faster than recalculating from new dimensions.