Final answer:
The ratio 16:8 is equivalent to 2:1 because both numbers in the ratio can be divided by 8. This is similar to how 22:11:22 simplifies to 2:1:2. To find unknown actual sizes from scale models, we set up proportions and solve for the unknown variables.
Step-by-step explanation:
The question asks if the ratio 16:8 is equivalent to 2:1. To determine this, we can simplify the first ratio by dividing both parts by 8, which gives us 2:1, confirming that 16:8 is indeed equivalent to 2:1. Similarly, 22:11:22 simplifies to 2:1:2 because each term in the ratio can be divided by 11.
To explore the concept further with larger numbers, we use proportion. For example, if we had a scale model with a scale length (Length-scale) of 8 units and wanted to find the actual length (w) of the display, given that scale/actual is 1/160, we would set up the proportion 8/w = 1/160 and solve for w. Similarly, if the ratio of the width's scale to actual size is 4 to 1, we would have Width-scale/actual = 4/1.
To solve this, we write another proportion. If the only unit given is feet, our proportion might look like 1/48 = w/16, which we can solve to find the unknown width w in feet.