State whether the following statements are true or false. Give reasons in support of your answer: a) The rational number 17/5 lies to the left of zero on the number line. b) The rational number -7/5 lies to the left of zero on the number line. c) The rational number -17/5 lies to the right of zero on the number line. d) The rational numbers -17/5 and 7/-5 lie to the right of zero on the number line. e) The rational numbers -17/5 and 17/-5 lie on opposite sides of zero on the number line.
The Correct Answer and Explanation is:
Let’s evaluate each of the given statements one by one:
a) The rational number 17/5 lies to the left of zero on the number line.
False.
Reason: 17/5 is a positive rational number, and all positive numbers are located to the right of zero on the number line. Since 17 divided by 5 equals 3.4, which is greater than zero, it lies to the right of zero.
b) The rational number -7/5 lies to the left of zero on the number line.
True.
Reason: -7/5 is a negative rational number, and all negative numbers lie to the left of zero on the number line. Since -7 divided by 5 equals -1.4, it is less than zero.
c) The rational number -17/5 lies to the right of zero on the number line.
False.
Reason: -17/5 is a negative rational number. Any number with a negative sign lies to the left of zero. Since -17 divided by 5 is -3.4, it is clearly on the left side of zero.
d) The rational numbers -17/5 and 7/-5 lie to the right of zero on the number line.
False.
Reason: Both -17/5 and 7/-5 are negative rational numbers. The expression 7/-5 is equivalent to -7/5. Since both numbers are negative, they lie to the left of zero, not the right.
e) The rational numbers -17/5 and 17/-5 lie on opposite sides of zero on the number line.
False.
Reason: Both -17/5 and 17/-5 represent the same number. The negative sign can be placed on the numerator or the denominator without changing the value. Both are equal to -3.4. Since they are equal, they lie on the same side of zero.
Conclusion:
Only statement b is true. The rest of the statements are false because they misinterpret the signs and locations of rational numbers on the number line. A rational number’s sign determines which side of zero it lies on.
