Question

Which of the following statements is true?(1 point)
Responses

−3/4 is the reciprocal of 3/4
.
negative Start Fraction 3 over 4 End Fraction is the reciprocal of Start Fraction 3 over 4 End Fraction .

1/23 is the reciprocal of −23
.
Start Fraction 1 over 23 End Fraction is the reciprocal of negative 23 .

−5/6 is the reciprocal of −6/5
.
negative Start Fraction 5 over 6 End Fraction is the reciprocal of negative Start Fraction 6 over 5 End Fraction .

25/6
is the reciprocal of 4 1/6
.

Answer 1

To determine which statements are true, we need to define what a reciprocal is. The reciprocal of a number \( x \) is \( \frac{1}{x} \). We can evaluate each statement:

1. **−3/4 is the reciprocal of 3/4.**
- The reciprocal of \( \frac{3}{4} \) is \( \frac{4}{3} \). This statement is **false**.

2. **1/23 is the reciprocal of −23.**
- The reciprocal of \( -23 \) is \( -\frac{1}{23} \). This statement is **false**.

3. **−5/6 is the reciprocal of −6/5.**
- The reciprocal of \( -\frac{6}{5} \) is \( -\frac{5}{6} \). This statement is **true**.

4. **25/6 is the reciprocal of 4 1/6.**
- First, convert \( 4 \frac{1}{6} \) to an improper fraction: \( 4 \frac{1}{6} = \frac{25}{6} \). The reciprocal of \( \frac{25}{6} \) would be \( \frac{6}{25} \). This statement is **false**.

Thus, the only true statement is:

**−5/6 is the reciprocal of −6/5.**