Fractions and Ratio: Area Fractions and Scale Factors

Methods in this video

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1. 1

   Equal pieces first, then count

   ▶ 0:57

   When to use it: Find a shaded fraction, matching shaded fractions, extra shading or a shaded area. You need equal area parts, half cells, simple rearrangement or different ways of dividing the same whole.

   • Name the whole shape. Count equal areas, not just the number of visible pieces.
   • Split big pieces or move small pieces without gaps or overlaps. Subtract only the blanks from a frame. Keep half cells exact.
   • Divide shaded parts by all parts. Match the area units across drawings, then subtract existing shading if asked for more.
2. 2

   Multiply for every direction

   ▶ 5:19

   When to use it: A map scale, matching side lengths or changed cuboid dimensions are given. Find a perimeter, area, volume or the mass of a solid made from the same material.

   • Match the sides and units. On a map, change each side to its real length first.
   • For similar shapes, multiply perimeter by k and area by k squared. For volume, multiply the three direction factors.
   • The factors may differ in each direction. Mass follows volume only for the same material at the same density.