Final answer:
This Mathematics problem involves understanding and completing a ratio table, writing proportions by setting ratios equal to one another, and understanding how to set ratios equal to unit scale for scaling problems.
Step-by-step explanation:
The subject of this question is Mathematics, specifically involving the concept of ratios and proportions. To complete the ratio table, we need to understand that a ratio compares two quantities, showing the relative size of one compared to the other. Ratios can be written in different forms such as 'a to b', 'a:b', or as a fraction 'a/b'.
For the given ratios:
- a) 1 : 1 indicates that for every 1 unit of the first quantity, there is 1 unit of the second quantity. This is an example of a perfect equality in ratios.
- b) 43 : 28 shows that for every 43 units of the first quantity, there are 28 units of the second quantity. This is an example of a ratio where the first quantity is larger than the second.
- c) 43 : 50 tells us that for every 43 units of the first quantity, there are 50 units of the second quantity. Unlike the previous example, the second quantity is larger here.
- d) 73 : 73, similarly to the first ratio, shows perfect equality, but with 73 units of each quantity.
To write a proportion like '1/48=w/16', we cross-multiply to find the value of 'w', which gives us 'w = (16*1)/48'.
Setting ratios equal to unit scale involves taking a ratio like '14/1=1/10', meaning 1 unit of the first quantity corresponds to 1/10 of the unit on the unit scale. It is common in scaling problems.