Constructing Ratios to Express Comparison of Two Quantities
Note there are three different ways to write a ratio, which is a comparison of two numbers that can be written as: [latex]a[/latex] to [latex]b[/latex] OR [latex]a:b[/latex] OR the fraction [latex]a/b[/latex]. Which method you use often depends upon the situation. For the most part, we will want to write our ratios using the fraction notation. Note that, while all ratios are fractions, not all fractions are ratios. Ratios make part to part, part to whole, and whole to part comparisons. Fractions make part to whole comparisons only.
Example 2.3
Expressing the Relationship between Two Currencies as a Ratio
The Euro (€) is the most common currency used in Europe. Twenty-two nations, including Italy, France, Germany, Spain, Portugal, and the Netherlands use it. On June 9, 2021, [latex]1[/latex] U.S. dollar was worth [latex]0.82[/latex] Euros. Write this comparison as a ratio.
Solution
Using the definition of ratio, let [latex]a=1[/latex] U.S. dollar and let [latex]b=0.82[/latex] Euros. Then the ratio can be written as either [latex]1[/latex] to [latex]0.82[/latex]; or [latex]1:0.82[/latex]; or [latex]\frac{1}{0.82}[/latex].
Exercise 2.3
Solution
[latex]a = 1[/latex] U.S. dollar, and [latex]b = 1.21[/latex] Canadian dollars, the ratio is [latex]1[/latex] to [latex]1.21[/latex]; or [latex]1:1.21[/latex]; or [latex]\frac{1}{1.21}[/latex].