Question

which of the following pairs represent equivalent rational numbers? I) 7/12 and 28/48 2) -2/-3 and -16 / 24
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Answer 1

Answer:

I) To determine if 7/12 and 28/48 are equivalent rational numbers, we can simplify both fractions to their lowest terms and compare them.

- To simplify 7/12, we can divide both the numerator and denominator by their greatest common factor, which is 1. So, 7/12 is already in its lowest terms.

- To simplify 28/48, we can divide both the numerator and denominator by their greatest common factor, which is 4. So, 28/48 simplifies to 7/12.

Since both fractions simplify to 7/12, they are equivalent rational numbers.

II) To determine if -2/-3 and -16/24 are equivalent rational numbers, we can simplify both fractions to their lowest terms and compare them.

- To simplify -2/-3, we can divide both the numerator and denominator by their greatest common factor, which is 1. So, -2/-3 is equivalent to 2/3.

- To simplify -16/24, we can divide both the numerator and denominator by their greatest common factor, which is 8. So, -16/24 simplifies to -2/3.

Since -2/-3 is equivalent to 2/3, and -2/3 is not equivalent to -2/3, these fractions are not equivalent rational numbers.

Therefore, the answer is I) 7/12 and 28/48 represent equivalent rational numbers.