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Write three ratios that are equivalent to [16:12].

User DrGriff
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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.
User Harmlezz
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