Subscribe to our βΆοΈ YouTube channel π΄ for the latest videos, updates, and tips.
Home | About Us | Contact Us | Privacy | Math Blog
We will learn about the equality of rational numbers using cross multiplication.
How to determine whether the two given rational numbers are equal or not using cross multiplication?
We know there are many methods to determine the equality of two rational numbers but here we will learn the method of equality of two rational numbers using cross multiplication.
In this method, to determine the equality of two rational numbers a/b and c/d, we use the following result:
ab = cd
β a Γ d = b Γ c
β Numerator of first Γ Denominator of second = Denominator of first Γ Numerator of second
Solved
examples on equality of rational numbers using
cross multiplication:
1. Which of the following pairs of
rational numbers are equal?
(i) β832 and 6β24
(ii) β4β18 and 824
Solution:
(i) The given rational numbers are β832 and 6β24
Numerator of first Γ Denominator of second = (-8) Γ (-24) = 192 and, Denominator of first Γ Numerator of second = 32 Γ 6 = 192.
Clearly,
Numerator of first Γ Denominator of second = Denominator
of first Γ Numerator of second
Hence, β832 = 6β24
Therefore, the given rational numbers β832 and 6β24 are equal.
(ii) The given rational numbers are β4β18 and 824
Numerator of first Γ Denominator of second = -4 Γ 24 = -96 and, Denominator of first Γ Numerator of second = (-18)
Γ 8 = -144
Clearly,
Numerator of first Γ Denominator of second β Denominator of first Γ Numerator of second
Hence, β4β18 β 824.
Therefore, the given rational numbers β4β18 and 824 are not equal.
2. If β68 = k64, find the value of k.
Solution :
We know that ab = cd if ad = bc
Therefore, β68 = k64
β -6 Γ 64 = 8 Γ k, [Numerator of first Γ Denominator of second = Denominator of first Γ Numerator of second]
β -384 = 8k
β 8k = -384
β 8k8 = β3848, [Dividing both sides by 8]
β k = -48
Therefore, the value of k = -48
3. If 7m = 4963, find the value of m.
Solution:
In order to write 4963 as a rational number with numerator 7, we first find a number which when divided 49 gives 7.
Clearly, such a number is 49 Γ· 7 = 7.
Dividing the numerator and denominator of 49/63 by 7, we have
4963 = 49Γ·763Γ·7 = 79
Therefore, 7m = 4963
β 7m = 79
β m = 9
4. Fill in the blank: β715 = .....135
Solution:
In order to fill the required blank, we have to express -7 as a rational number with denominator 135. For this, we first find an integer which when multiplied with 15 gives us 135.
Clearly,
such an integer is 135 Γ· 15 = 9
Multiplying the numerator and denominator of β715 by 9, we get
β715 = (β7)Γ915Γ9 = β63135
Therefore, the required
number is -63.
β 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 Equality of Rational Numbers using Cross Multiplication 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.
Jul 25, 25 12:21 PM
Jul 25, 25 03:15 AM
Jul 24, 25 03:46 PM
Jul 23, 25 11:37 AM
Jul 20, 25 10:22 AM
β 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.