# Reciprocals

Reciprocal of the fraction is fraction that is turned "upside down", i.e. reciprocal of the fraction color(green)(a/b) is color(red)(b/a).

There is very nice fact about reciprocals.

Fact. Product of fraction and its reciprocal always equals 1.

Indeed, a/b*b/a=(ab)/(ab)=1.

If we take fraction 3/4 then its reciprocal is 4/3. Now, reciprocal of 4/3 is 3/4, i.e. initial fraction.

Fact. Reciprocal of reciprocal of the number a is number a.

Example 1. Find reciprocal of 5/7.

We just turn fraction "upside down": 7/5.

Answer: 7/5=1 2/5.

Next example.

Example 2. Find reciprocal of 4.

Recall that each integer can be represented as fraction: 4=4/1.

Now turn fraction "upside down": 1/4.

Answer: 1/4.

Next example.

Example 3. Find reciprocal of -2 1/7.

Convert mixed number to improper fraction: -2 1/7=-15/7.

Now turn fraction "upside down": -7/15.

Answer: -7/15.

Now, do a couple of exercises.

Exercise 1. Find reciprocal of 7/11.

Answer: 11/7=1 4/7.

Next exercise.

Exercise 2. Find reciprocal of -5.

Answer: -1/5.

Next exercise.

Exercise 3. Find reciprocal of 1/4.

Next exercise.

Exercise 4. Find reciprocal of 2 8/9.

Answer: 9/26.

Next exercise.

Exercise 5. Find reciprocal of 1/(5/8).

Answer: 5/8. Hint: reciprocal of 1/a is a. Here, a is 5/8.

Next exercise.

Exercise 6. Find reciprocal of reciprocal of -3.

Answer: -3. Hint: reciprocal of -3 is -1/3, reciprocal of -1/3 is again -3.