The reciprocal of -6/7 is -7/6. The product of two rational numbers is always a rational number. The numbers 1 and -1 are their own reciprocals. The reciprocal of 1/4 is 4. 0 is the additive identity of the rational numbers. 1 is the multiplicative identity of the rational numbers. The negative of -5 is 5. 3/5 x -4 = -12/5 x 3/5.
The Correct Answer and Explanation is:
Corrected Statements and Explanations:
- The reciprocal of -6/7 is -7/6.
✅ Correct.
The reciprocal of a number is found by flipping the numerator and denominator. The reciprocal of -6/7 is indeed -7/6. - The product of two rational numbers is always a rational number.
✅ Correct.
Multiplying any two rational numbers will always result in another rational number. This is because the product of two fractions or integers still fits the definition of a rational number. - The numbers 1 and -1 are their own reciprocals.
✅ Correct.
The reciprocal of 1 is 1. The reciprocal of -1 is -1. So this statement is true. - The reciprocal of 1/4 is 4.
✅ Correct.
Flipping 1/4 gives 4/1, which simplifies to 4. - 0 is the additive identity of the rational numbers.
✅ Correct.
Adding 0 to any rational number does not change its value. That is why 0 is called the additive identity. - 1 is the multiplicative identity of the rational numbers.
✅ Correct.
Multiplying any rational number by 1 does not change its value, so 1 is the multiplicative identity. - The negative of -5 is 5.
✅ Correct.
Taking the negative of a negative number gives a positive. So the negative of -5 is indeed 5. - 3/5 × -4 = -12/5 × 3/5.
❌ Incorrect.
Let’s compute both sides:
- Left side:
3/5 × -4 = -12/5 - Right side:
-12/5 × 3/5 = -36/25
Since -12/5 ≠ -36/25, this statement is false.
Conclusion:
All statements are true except for the last one. Rational number operations follow specific rules. Reciprocals involve flipping fractions. Identities like 0 and 1 preserve value under addition or multiplication. But you must always verify computations, as in the last case.
