Equal Ratios and Their Uses

Ratios are put to work moving actual amounts. Four shapes carry the lesson: calculation splitting a whole by a fixed ratio to give two amounts, fill-in-the-blank items completing a box so that the ratios are equal, word problems finding one amount from the ratio and the other, and word problems splitting a whole and answering each part.

In equal ratios the front figure and the back figure move by the same multiplier. Finding first how many times one side has grown and applying that multiplier to the other is the procedure. An answer that filled the box by simply adding the difference between the left and right figures disagrees with that multiplier.

What gets compared turns from quantities to figures in Enlargement and Reduction, which follows. In scenes weighing the side lengths of two drawings against each other, the view of ratio matched here goes straight to work.