Mathematics Form 1-4 : CHAPTER TWENTY FIVE – RECIPROCALS

Specific Objectives

By the end of the topic the learner should be able to:

1. Find reciprocals of numbers by division.
2. Find reciprocals of numbers from tables.
3. Use reciprocals of numbers in computation.

Content

1. Reciprocals of numbers by division.
2. Reciprocals of numbers from tables.
3. Computation using reciprocals.

Introduction

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

x × (reciprocal of x) = 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⁄_decimal, which can then be converted to a decimal.

Example

For 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 verify that the product is 1.

Reciprocal of Numbers from Tables

Reciprocals 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 – 0.0010 = 0.4072.

Example

Find the reciprocal of 45.8.

Solution

You first write 45.8 in standard form which is 4.58 × 10¹.

Then, using reciprocal tables:

Reciprocal of 4.58 ≈ 0.2183

Reciprocal of 10¹ = 10^-1 = 0.1

Therefore, reciprocal of 45.8 = 0.2183 × 0.1 = 0.02183.

Example

Find the reciprocal of 0.0236.

Solution

Change 0.0236 into standard form which is 2.36 × 10^-2.

Reciprocal of 2.36 ≈ 0.4237

Reciprocal of 10^-2 = 10² = 100

Therefore, reciprocal of 0.0236 = 0.4237 × 100 = 42.37.

Example

Use reciprocal tables to solve the following:

Solution

Multiply the numerators by the reciprocal of denominators, then add them:

1 × (reciprocal of 0.0125) + 1 × (reciprocal of 12.5)

Using tables find the reciprocals:

= 1 × 80 + 1 × 0.08

= 80.08

Example

Solution

= 4 × (reciprocal of 0.375) – 3 × (reciprocal of 37.5)

= (4 × 2.667) – (3 × 0.026667)

= 10.59

End of topic