Question

Which set of rational numbers contains only numbers equivalent to 3/-5 ?

a. {-3)/5 , 6/-10 , -3/-5}
b. {-3)/-5 , 6/-10 , -3)/5}
c. {-3)/-5 , -6)/10 , 6/-10}
d. {-3)/5 , -6)/10 , 6/-10}

Answer 1

The correct set of rational numbers equivalent to 3/-5 is option d: {-3/5, -6/10, 6/-10}, as all fractions within this set simplify to the same value as 3/-5.

Step-by-step explanation:

The student is asking which set of rational numbers contains only numbers equivalent to 3/-5. Among the options provided, the set that contains numbers equivalent to 3/-5 must include fractions that simplify to 3/-5, including its negative counterpart -3/5, which is also equivalent to 3/-5.

Comparing the ratios by simplifying or cross-multiplying:

• -3/5 is equivalent to 3/-5 as they are negatives of each other, simplifying to the same value.
• 6/-10 simplifies to 3/-5 when both the numerator and the denominator are divided by 2.
• -6/10 simplifies to -3/5, which is equivalent to 3/-5.

Therefore, the correct set that contains only numbers equivalent to 3/-5 is option d. The set {
-3/5, -6/10, 6/-10} all represent the same rational number as 3/-5.