Worksheet on Equality of Rational Numbers

Practice the questions given in the worksheet on equality of rational numbers. We know a rational number remains unchanged if we multiply or divide its numerator and denominator by the same non- zero integer. It follows from this that a rational number can be written in several equivalent forms. Two rational numbers are said to be equivalent if one can be obtained from the other either by multiplying or by dividing its numerator and denominator by the same non-zero integer.

The questions are related to check whether the two given rational numbers are equal or not using three different methods i.e. equality of rational numbers using standard form, equality of rational numbers with common denominator and equality of rational numbers using cross multiplication.

1. Which of the following rational numbers are equal?

(i) -15/27 and 6/-18       

(ii) -18/24 and 15/-20      

(iii) -12/32 and 27/-72     

(iv) -6/-18 and 11/19 

2. If each of the following pairs represents a pair of equivalent rational numbers, find the values of x.

(i) 3/4 and 7/x      

(ii) -5/6 and x/7         

(iii) 5/7 and x/-14     

(iv) 12/5 and -60/x

3. Fill in the blanks so as to make the statement true:

(i) A number which can be expressed in the form m/n, where m and n are integers and n is not equal to zero, is called a ________.

(ii) If the integers m and n have no common divisor other than 1 and n is positive, then the rational number m/n is said to be in the ________.

(iii) Two rational numbers are said to be equal, if they have the same ________ form.

(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/______

(v) lf p and q are positive integers , then m/n is a ________ rational number and m/-n is a ________ rational number.

(vi) The standard form of -1 is ________.

(vii) If m/n is a rational number, then n cannot be ________

(viii) Two rational numbers with different numerators are equal, if their numerators are in the same  ________ as their denominators.

4. Write whether the statement is true or false:

(i) Every integer is a rational number.

(ii) Every rational number is a fraction.

(iii) The quotient of two integers is always an integer.

(iv) Every fraction is a rational number.

(v) Every rational number is an integer.

(vi) Two rational numbers with different numerators cannot be equal.

(vii) 10 can be written as a rational number with any integer as numerator.

(viii) If m/n is a rational number and k any integer, then m/n = (m × k)/(n × k)

(ix) -16/40 is equal to 14/-35

(x) 100 can be written as a rational number with any integer as denominator. 

Answers for the worksheet on equality of rational numbers are given below to check the exact answers of the above questions on whether the two given rational numbers are equal or not.

Answers:

1. (ii), (iii)                

2. 28/3                     

(ii) -35/6      

(iii) -10

(iv) -25

3. (i) rational number

(ii) standard form     

(iii) standard    

(iv) y ÷ k

(v) positive, negative

(vi) -1/1           

(vii) zero        

(viii) ratio   

4. (i) true

(ii) false 

(iii) false       

(iv) true

(v) false

(vi) false

(vii) false

(viii) false

(ix) true

(x) false

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