From Lesson 7, which of the following are examples of a Reciprocal? *
5/6 and 6/5
1 3/7 and 7/10
3/4 and 1 2/3
2 2/3 and 3 1/2
The examples of a reciprocal are:
- 5/6 and 6/5
- 3/4 and 4/3
To determine which of the given options are examples of a reciprocal, we need to understand what a reciprocal is. The reciprocal of a number is a number that, when multiplied by the original number, equals 1.
Let's break down each option:
1) 5/6 and 6/5: To check if these are reciprocals, we multiply them.
(5/6) * (6/5) = 30/30 = 1
Since the product equals 1, both 5/6 and 6/5 are reciprocals.
2) 1 3/7 and 7/10: Again, let's multiply them to check.
(1 3/7) * (7/10) = (10 + 3/7) * (7/10) = 1
Therefore, 1 3/7 and 7/10 are reciprocals.
3) 3/4 and 1 2/3: Let's multiply them.
(3/4) * (3/2) = (9/8) ≠ 1
Hence, 3/4 and 1 2/3 are not reciprocals.
4) 2 2/3 and 3 1/2: Let's multiply.
(2 2/3) * (2/7/2) = (8/3) * (2/7/2) = 16/14 ≠ 1
Thus, 2 2/3 and 3 1/2 are not reciprocals.
The options that are examples of reciprocals are:
- 5/6 and 6/5
- 1 3/7 and 7/10
To determine which examples are reciprocals, we need to understand what a reciprocal is. The reciprocal of a number is obtained by flipping the numerator and denominator of a fraction.
Let's go through each option and find their reciprocals:
1) 5/6 and 6/5: To find the reciprocal of 5/6, we flip the numerator and denominator, resulting in 6/5. In this case, both numbers are reciprocals of each other.
2) 1 3/7 and 7/10: To find the reciprocal of 1 3/7, we first convert it to an improper fraction, which would be 10/7. Flipping the numerator and denominator gives us 7/10. These two numbers are reciprocals of each other.
3) 3/4 and 1 2/3: To find the reciprocal of 3/4, we flip the numerator and denominator, resulting in 4/3. In this case, these two numbers are not reciprocals of each other.
4) 2 2/3 and 3 1/2: To find the reciprocal of 2 2/3, we convert it to an improper fraction, which would be 8/3. Flipping the numerator and denominator gives us 3/8. Similarly, the reciprocal of 3 1/2 is 2/7. Therefore, these two numbers are not reciprocals of each other.
Based on our analysis, the examples that are reciprocals are 5/6 and 6/5, as well as 1 3/7 and 7/10.