Question

Which of the following pairs of rational numbers are equivalent?

(a) 3/5, 12/14
(b) 3/2, 6/4
(c) -4/7, 8/-14

3/5 is equivalent to:

12/14
4/7
-6/10
-9/15

Answer 1

Two pairs of rational numbers are equivalent: 3/2 and 6/4, and -4/7 and 8/-14. Also, 3/5 is equivalent to -6/10. Rational numbers are equivalent if they simplify to the same value.

Step-by-step explanation:

To determine which pairs of rational numbers are equivalent, we must compare the ratios after simplifying them.

• (a) 3/5 and 12/14 are not equivalent because when you simplify 12/14, you get 6/7, which is different from 3/5.
• (b) 3/2 and 6/4 are equivalent because when you simplify 6/4, you get 3/2.
• (c) -4/7 and 8/-14 are equivalent because when you simplify 8/-14 by dividing both the numerator and the denominator by 2, you get -4/7.

Among the options given for 3/5, the equivalent rational number would be -6/10. To confirm this, we simply need to multiply both the numerator and the denominator of 3/5 by 2, which gives us 6/10. Since the sign does not affect the value of the ratio, -6/10 is still equivalent to 3/5. The other options do not simplify to 3/5.