RECIPROCALS - Mathematics Form 2 Notes

• Introduction
• Finding the Reciprocal of Decimals

Introduction

The reciprocal of a number is simply the number put in fraction form and turned upside down

Example

Find the reciprocal of 2.

Solution:

Change 2 into fraction form which is ²/₁
Then turn it upside down and get ¹/₂

Note:

When you multiply a number by its reciprocal you get 1 ,
²/₁ x ¹/₂ =1

Finding the Reciprocal of Decimals

• Finding the reciprocal of a decimal can be done in a number of ways.
  
  Change the decimal to a fraction first.
  
  Example.
  0.25 is ²⁵/₁₀₀ and is equivalent to the fraction ¹/₄. Therefore its reciprocal would be ⁴/₁ or 4.
  
  Keep the decimal and form the fraction 1/?? Which can then be or converted to a decimal.
  
  Example
  0.75 The reciprocal is 1/0.75. Using a calculator, the decimal form can be found by performing the operation: 1 divided by 0.75. The decimal reciprocal in this case is a repeating decimal, 1 .33333....
  After finding a reciprocal of a number, perform a quick check by multiplying your original number and the reciprocal to determine that the product.
  
  Reciprocal of Numbers from Tables.
  Reciprocal of numbers can be found using tables.
  
  Example
  Find the reciprocal of 2.456 using the reciprocal tables.
  
  Solution.
  Using reciprocal tables, the reciprocal of 2.456 is 0.4082 - 0.001 0 = 0.4072
  
  Example
  Find the reciprocal of 45.8.
  
  Solution
  You first write 45.8 in standard form which is 4.58 x 10¹.
  Then   1    =       1      
           45.8   4.58 x10¹
  =¹/₁₀ x ¹/_4.58
  = ¹/₁₀ x 0.2183
  = 0.02183
  
  Example
  Find the reciprocal of 0.0236
  
  Solution
  Change 0.0236 in standard form which is 2.36 x 10⁻²
  =     1      =       1        
     0.0236     2.36 x 10⁻²
  =  1    x   1  
    10⁻²   2.36
  = 10² x 0.4237
  = 42.37
  
  Example
  Use reciprocal tables to solve the following:
      1      +   1  
  0.0125     12.5
  
  Solution
  Multiply the numerators by the reciprocal of denominators, then add them
  1 (reciprocal 0.01 25) + 1 (reciprocal 12.5)
  Using tables find the reciprocals,
  = 1 (80) +1 (0.08)
  = 80.08
  
  Example
     4     −   3  
  0.375     37.5
  
  Solution
  = 4 (rec0.375) – 3(37.5)
  = (4 x2.667) – (3x0.026667)
  = 10.59