Lesson 8.2 ­ Reciprocals
Example 1
Ruby is 42. Her daughter Jeanette is 18.
a. Use a ratio to compare Ruby's age to Jeanette's age.
b. Use a ratio to compare Jeanette's age to Ruby's age.
Example 2
In both of the problems above, multiply your answers from part a and b. What do you notice? We get 1.
Reciprocals ­ two numbers with a product of 1.
What is the reciprocal of...
1. 3
20
1. Get the number to fraction form.
2. Flip the fraction to get it's reciprocal.
2. ­2 = 3. 4. What number has no reciprocal? Zero.
Why did we get a product of 1 when we multiplied the two ratios from example 1? example 2?
Look at the first example...
a. 42
b. 18
18
42
These two ratios are reciprocals of one another, so their product is 1.
What about the reciprocal of 0.625?
If it were a fraction it would be easier. Write the reciprocal of 0.625 as a fraction, decimal and percent.
Steps:
1. Write the reciprocal of 0.625 as a fraction
625
1000
2. Write the result as a simple fraction.
1000 8
625 5
3. Write the result as a decimal.
1000 625 = 1.6
4. Write the result as a percent.
1.6 100 = 160%
West to East is 5.5 times greater.
I need East to West. times greater.