Ratio Values and Simplifying Ratios

The relation between two quantities is caught in the form of a ratio. Three kinds, dividing the front figure by the back one to give the value of the ratio, dividing both by the greatest common divisor to reach the simplest ratio, and turning a ratio holding decimals or fractions into a whole-number ratio, are traced first as calculation and then a second time in word-problem form.

Finding the value of the ratio, papers line up that divided the back figure by the front one and inverted the value. Where the front figure is the larger, the value of the ratio must come out above 1. Which side of 1 the written figure falls on brings a wrong direction of division into the open.

What gets arranged here goes only as far as reducing a pair of figures to a simple form. In Equal Ratios and Their Uses that pair is kept matched and carried into scenes that find actual amounts.