In maths, the easiest method to solve fractions without calculating LCM or GCD is the cross multiplication method.
In this method, we directly multiply the number in numerator of one fraction with the number in denominator of the second fraction.
Similarly, we also multiply number in denominator of first fraction with the number in numerator of the second fraction.
Thus, by equating them we can solve the multiplication of two or more fractions.
: Let us consider the fractions a/b and c/d.
If we have to find, a/b*c/d
Then we use cross multiplication method directly as follows.
This is method of cross multiplication.
Here, b and d are denominator and b,d is not equal to zero always.
And a,c are the numerators.
To understand the cross multiplication in more detail see following examples:
1.) If 12 bananas are of cost 36 Rs. Then what is the cost of 18 banana.
Here, cost of 12 bananas is 30. Hence, cost of single banana will be 30/12.
Now, let us consider x be the cost of 18 bananas then cost of single banana will be x/18.
Thus, we can equate the cost of single banana from both the conditions.
Hence, we write as
Now we take cross multiplication,
Thus, x= 540/12= 270/6 = 135/3= 45
Thus, without finding the cost of single banana, here we have found the cost of 18 banana which is 45 Rs.
: 2.) If a car travels 120 km in 3 hrs then how much time in hour is needed to cover the distance 250 km by the same car.
Given that, a car covers 120 km in 3 hrs, hence the distance covered in 1hr will be 120/3.
Let, x be the time in hours required to cover distance 240 km by the same car. Then the distance covered in one hr will be 240/x.
Hence, we can equate the both the fractions,
Thus, x= 720/120= 6 hrs
Thus, the time required to cover the distance 240 km is 6 hrs
3.) Let, the cost of 6 apples is 70 rs then what is the cost of 2 apples.
Given that, the cost of 6 apples is 70. Then the cost of single apple will be 70/6.
Let us consider, the cost of 2 apples will be x.
Then the cost of single apple will be x/2.
Now, we equate both the fractions,
Now, we take cross multiplication as
Thus, x= 140/6= 23.33
In this way, we can find the cost of 2 apples as 23.33rs without finding the cost of single apple.
4.) Reema buy 6 pencils for 40rs. And her friend Heena wants to buy the same pencils but she want to buy 12 pencils. Then what should be Heena will pays to shopkeeper for 12 pencils.
Given that, Reema buy 6 pencils for 40 rs.
Hence, the cost of single pencil will be 40/6.
Let us suppose, x be the cost of 12 pencils which want to buy Heena.
Then cost of single pencil will be x/12.
Thus, we can equate both the fractions as,
Now, we take cross multiplication,
Thus, x= 480/6= 80
Thus, the cost of 12 pencils will be 80 rs.
In this way, we can find directly the cost of no. of pencils without finding the cost of single pencil, with the help of cross multiplication of fractions.
In this way, the cross multiplication of fractions sometimes makes easier to solve the numericals also.