Final answer:
Equivalent ratios to 16:4 can be found by dividing both terms by the same number, such as 4, which simplifies to 4:1. Ratios and proportions are fundamental in determining actual dimensions from scale models or drawings using a given unit scale.
Step-by-step explanation:
Ratios are a way to compare two quantities, which can be written in different forms such as fractions, with a colon, or with the word "to". For example, 2/3, 2:3, and "2 to 3" all represent the same ratio. A proportion is created when two ratios are found to be equivalent or equal, indicating that the relationship between quantities is the same in both ratios.
When working with scale models or drawings, you often use a unit scale, which is a ratio that compares the dimensions of an actual object to the dimensions that a scale model or drawing represents of the actual object. Let's consider the ratio 16:4. To find ratios equivalent to 16:4, you divide both terms by the same non-zero number. For example, dividing both terms by 4 yields the ratio 4:1.
Now let's use scale factors to solve problems:
1. If you have a proportion like 1/48=w/16, you can solve for w by cross-multiplication.
2. For example, given a scale factor of 1:4, a scale dimension of 4 can be represented in a proportion like 1:2=4:x, where x can be solved to find the actual dimension.