Let us learn about Equality of Rational Numbers using Cross Multiplication in detail here. Check out the Procedure to determine whether Rational Numbers are Equal or not using the Cross Multiplication Technique. Have a glance at the solved examples explaining the concept in detail so that you can solve related problems.
How to determine Equality of Rational Numbers using Cross Multiplication?
There are numerous methods to check the equality of rational numbers. But here we are using the Cross Multiplication Method to check whether the given rational numbers are equal or not. Follow the guidelines to check the equality of rational numbers.
Let us consider two rational numbers a/b, c/d
a/b = c/d
⇔ a × d = b × c
⇔ The Numerator of First × The Denominator of Second = The Denominator of First × The Numerator of the Second
Solved Examples
1. Determine whether the following pair of Rational Numbers are Equal or Not?
8/4 and 6/3
Given Rational Numbers are 8/4 and 6/3
⇔ We know a × d = b × c
Multiplying Numerator of First × The Denominator of Second = The Denominator of First × The Numerator of the Second we get
8*3 = 6*4
24 = 24
Therefore, the given rational numbers 8/4 and 6/3 are equal.
2. If -8/6 = k/30, find the value of k?
Solution:
-8/6 = k/30
Cross multiplying we get
-8*30 = k*6
Performing basic math we get the value of k
(-8*30)/6 =k
k=-40
Therefore, the value of k is -40.
3. If 5/m = 40/16 determine the value of m?
Solution:
5/m = 40/16
Cross multiplying we get 5*16 = m*40
Separating m to get the value of it.
m= (5*16)/40
= 80/40
= 2
Therefore, the value of m is 2.
4. Fill in the Blank -7/10 = …/120?
Solution:
In order to express -7 as a denominator with 120, we first need to find out the number which when multiplied by 10 gives 120.
Thus, the integer is 120÷ 10 = 12
Multiplying the numerator and denominator of a given rational number with 12 we get
-7/10 = (-7*12)/(10*12)
= -84/120
Thus, the required number is -84/120.