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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● 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
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