Reciprocal of a Rational Number
We will learn the reciprocal of a rational number.
For every non-zero rational number a/b there exists a rational number b/a such that
a/b × b/a = 1 = b/a × a/b
The rational number b/a is called the multiplicative inverse or reciprocal of a/b and is denoted by (a/b)-1.
The reciprocal of 12 is 1/12
The reciprocal of 5/16 is 16/5.
The reciprocal of 3/4 is 4/3 i.e., (3/4)^-1 = 4/3.
The reciprocal of -5/12 is 12/-5 i.e., (-5/12)^-1 = 12/-5.
The reciprocal of (-14)/17 is 17/-14 i.e., (-17)/14.
The reciprocal of -8 is 1/-8 i.e., (-1)/8.
The reciprocal of -5 is 1/-5, since -5 × 1/-5 = -5/1 × 1/-5 = -5 × 1/-5 × 1 = 1.
Note: The reciprocal of 1 is 1 and the reciprocal of -1 is -1. 1
and -1 are the only rational numbers which are their own reciprocals. No other
rational number is its own reciprocal.
We know that there is no rational number which when multiplied with 0, gives 1. Therefore, rational number 0 has no reciprocal or multiplicative inverse.
Solved example on reciprocal of a rational number:
1. Write the reciprocal of each of the following rational numbers:
(i) 5
(ii) -15
(iii) 7/8
(iv) -9/13
(v) 11/-19
Solution:
(i) The reciprocal of 5 is 1/5 i.e., (5)^-1 = 1/5.
(ii) The reciprocal of -15 is 1/-15 i.e., (-15)^-1 = 1/-15.
(iii) The reciprocal of 7/8 is 8/7 i.e., (7/8)^-1 = 8/7.
(iv) The reciprocal of -9/13 is 13/-9 i.e., (-9/13)^-1 = 13/-9.
(v) The reciprocal of 11/-19 is -19/11 i.e., (11/-19)^-1 = -19/11.
2. Find the reciprocal of 3/7 × 2/11.
Solution:
3/7 × 2/11
= (3 × 2)/(7 × 11)
= 6/77
Therefore, the reciprocal of 3/7 × 2/11 = Reciprocal of 6/77 = 77/6.
3. Find the reciprocal of -4/5 × 6/-7.
Solution:
-4/5 × 6/-7
= (-4 × 6)/(5 × -7)
= -24/-35
= 24/35
Therefore, the reciprocal of -4/5 × 6/-7 = Reciprocal of 24/35 = 35/24.
● Rational Numbers
Introduction of Rational Numbers
Is Every Rational Number a Natural Number?
Is Every Rational Number an Integer?
Is Every Rational Number a Fraction?
Equivalent form of Rational Numbers
Rational Number in Different Forms
Properties of Rational Numbers
Lowest form of a Rational Number
Standard form of a Rational Number
Equality of Rational Numbers using Standard Form
Equality of Rational Numbers with Common Denominator
Equality of Rational Numbers using Cross Multiplication
Comparison of Rational Numbers
Rational Numbers in Ascending Order
Rational Numbers in Descending Order
Representation of Rational Numbers on the Number Line
Rational Numbers on the Number Line
Addition of Rational Number with Same Denominator
Addition of Rational Number with Different Denominator
Properties of Addition of Rational Numbers
Subtraction of Rational Number with Same Denominator
Subtraction of Rational Number with Different Denominator
Subtraction of Rational Numbers
Properties of Subtraction of Rational Numbers
Rational Expressions Involving Addition and Subtraction
Simplify Rational Expressions Involving the Sum or Difference
Multiplication of Rational Numbers
Properties of Multiplication of Rational Numbers
Rational Expressions Involving Addition, Subtraction and Multiplication
Reciprocal of a Rational Number
Rational Expressions Involving Division
Properties of Division of Rational Numbers
Rational Numbers between Two Rational Numbers
8th Grade Math Practice
From Reciprocal of a Rational Number to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Properties of Division | Division of Property Overview|Math Properties
Jan 22, 25 01:30 AM
The properties of division are discussed here: 1. If we divide a number by 1 the quotient is the number itself. In other words, when any number is divided by 1, we always get the number itself as the… -
Terms Used in Division | Dividend | Divisor | Quotient | Remainder
Jan 22, 25 12:54 AM
The terms used in division are dividend, divisor, quotient and remainder. Division is repeated subtraction. For example: 24 ÷ 6 How many times would you subtract 6 from 24 to reach 0? -
Divide on a Number Line | Various Division Problems | Solved Examples
Jan 22, 25 12:41 AM
How to divide on a number line? Learn to divide using number line to find the quotient. Solved examples to show divide on a number line: 1. Solve 14 ÷ 7 Solution: 7 is subtracted repeatedly -
Divide by Repeated Subtraction | Division as Repeated Subtraction
Jan 22, 25 12:18 AM
How to divide by repeated subtraction? We will learn how to find the quotient and remainder by the method of repeated subtraction a division problem may be solved. -
Division Sharing and Grouping | Facts about Division | Basic Division
Jan 21, 25 08:06 AM
We will learn division sharing and grouping. Share eight strawberries between four children. Let us distribute strawberries equally to all the four children one by one.
● Rational Numbers - Worksheets
Worksheet on Equivalent Rational Numbers
Worksheet on Lowest form of a Rational Number
Worksheet on Standard form of a Rational Number
Worksheet on Equality of Rational Numbers
Worksheet on Comparison of Rational Numbers
Worksheet on Representation of Rational Number on a Number Line
Worksheet on Adding Rational Numbers
Worksheet on Properties of Addition of Rational Numbers
Worksheet on Subtracting Rational Numbers
Worksheet on Addition and
Subtraction of Rational Number
Worksheet on Rational Expressions Involving Sum and Difference
Worksheet on Multiplication of Rational Number
Worksheet on Properties of Multiplication of Rational Numbers
Worksheet on Division of Rational Numbers
Worksheet on Properties of Division of Rational Numbers
Worksheet on Finding Rational Numbers between Two Rational Numbers
Worksheet on Word Problems on Rational Numbers
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.