Question

Which pairs of rational numbers are equivalent? Select all that apply.

Options:
a. 3/5 and 6/10
b. 1/4 and 2/6
c. 4/3 and 8/6
d. 5/6 and 10/12

Answer 1

The equivalent pairs of rational numbers are 3/5 and 6/10, 4/3 and 8/6, and 5/6 and 10/12, as they all simplify to the same value.

Step-by-step explanation:

To determine which pairs of rational numbers are equivalent, we can simplify or multiply the fractions to see if they produce the same value. Equivalent fractions have the same value when expressed in simplest form.

1. 3/5 and 6/10: We can simplify 6/10 by dividing both the numerator and the denominator by 2, which gives us 3/5. Therefore, these fractions are equivalent.
2. 1/4 and 2/6: Simplifying 2/6 by dividing both the numerator and the denominator by 2 gives us 1/3, which is not equivalent to 1/4. These fractions are not equivalent.
3. 4/3 and 8/6: Simplify 8/6 by dividing both the numerator and the denominator by 2 gives us 4/3. Thus, these fractions are equivalent.
4. 5/6 and 10/12: Simplify 10/12 by dividing both the numerator and the denominator by 2 gives us 5/6. Hence, these fractions are equivalent.

In conclusion, the pairs of rational numbers that are equivalent are 3/5 and 6/10, 4/3 and 8/6, and 5/6 and 10/12.