Final answer:
To create three ratios equivalent to 16:12, we can reduce the original ratio by dividing both numbers by their greatest common divisor, or multiply both by the same number. Examples include the ratios 4:3, 32:24, and 48:36.
Step-by-step explanation:
To find three ratios that are equivalent to 16:12, we need to find multiples or divisors of both numbers that give us the same proportion. Here are the steps:
- Divide both terms in the ratio by their greatest common divisor, which is 4. So, 16 ÷ 4 = 4 and 12 ÷ 4 = 3, giving us the equivalent ratio of 4:3.
- Multiply both terms of the original ratio by the same number, for example by 2. Thus, 16 × 2 = 32 and 12 × 2 = 24, resulting in the equivalent ratio of 32:24.
- Again, multiply both terms by a different number, such as 3. We get 16 × 3 = 48 and 12 × 3 = 36, yielding the equivalent ratio of 48:36.
When setting these ratios equal to the unit scale to form two proportions, one for length and one for width, we could follow examples like:
- For length proportion using the scale 1 inch = 2000 miles: 1 inch / 2000 miles = 3 inches / x miles, solve for x.
- For width proportion with feet as the unit: 1/48 = w/16, solve for w.