College

Determine if each pair of ratios or rates is equivalent. Show all your work.

1. 15 out of 20 students own hand-held games.
2. 105 out of 160 students own hand-held games.

Are these ratios equivalent?

Answer :

Final answer:

The ratios 15 out of 20 students and 105 out of 160 students owning hand-held games are not equivalent when simplified and converted to decimals, 0.75 and approximately 0.65625 respectively.

Explanation:

To determine if the two ratios, 15 out of 20 students owning hand-held games and 105 out of 160 students owning hand-held games, are equivalent, we can simplify the ratios or convert them into fractions and then decimals or percentages for comparison.

First, let's simplify the ratios:

  • 15 out of 20 can be simplified by dividing both the numerator (15) and the denominator (20) by their greatest common divisor, which is 5, thus we get 3 out of 4.
  • 105 out of 160 can be simplified by dividing both numbers by their greatest common divisor, which is 5, getting 21 out of 32.

Second, let's convert these simplified ratios to decimals:
3 divided by 4 equals 0.75.
21 divided by 32 equals approximately 0.65625.

Since 0.75 does not equal approximately 0.65625, the two ratios are not equivalent.

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