Reciprocals
Reciprocal of the fraction is fraction that is turned "upside down", i.e. reciprocal of the fraction is .
There is very nice fact about reciprocals.
Fact. Product of fraction and its reciprocal always equals 1.
Indeed, .
If we take fraction then its reciprocal is . Now, reciprocal of is , i.e. initial fraction.
Fact. Reciprocal of reciprocal of the number is number .
Example 1. Find reciprocal of .
We just turn fraction "upside down": .
Answer: .
Next example.
Example 2. Find reciprocal of 4.
Recall that each integer can be represented as fraction: .
Now turn fraction "upside down": .
Answer: .
Next example.
Example 3. Find reciprocal of .
Convert mixed number to improper fraction: .
Now turn fraction "upside down": .
Answer: .
Now, do a couple of exercises.
Exercise 1. Find reciprocal of .
Answer: .
Next exercise.
Exercise 2. Find reciprocal of -5.
Answer: .
Next exercise.
Exercise 3. Find reciprocal of .
Answer: 4.
Next exercise.
Exercise 4. Find reciprocal of .
Answer: .
Next exercise.
Exercise 5. Find reciprocal of .
Answer: . Hint: reciprocal of is . Here, is .
Next exercise.
Exercise 6. Find reciprocal of reciprocal of -3.
Answer: -3. Hint: reciprocal of -3 is , reciprocal of is again -3.