which type of questions do we have to apply HCF N LCM operations in?

Question

 I am unable to identify where to apply HCF n LCM to find the solution for a questions?

 

Answer 1

You apply the LCM when simplifying combining expressions and solving equations that consist of fractions with different denominators.  This is because we cannot combine fractions with different denominators.  It is only easier to combine fractions that have the same whole.  For example,

 

(1 / 2)x + (2 / 3)x = 5

 

This equation has different denominators: 2 and 3 (left side), and 1 (right side).  The 1 comes from (5 / 1) which is 5.

 

The lowest multiple the denominators have in common is 6.   This equation now becomes

 

(3 / 6)x + (4 / 6)x = 30 / 6

 

Notice that if we reduce each term in the equation, we get the original equation.  On the left side of the equation, we can add the terms.

 

(7 / 6)x = 30 / 6

 

 

Noticing that the denominators on each side of the equation are the same, we can just equate the numerators.

 

7x = 30

 

 

Divide 7 on both sides of the equation.

 

x = 30/7

 

 

If we plug x into the equation

 

(7 / 6)(30 / 7) = 30 / 6

 

30 / 6 = 30 / 6

 

5 = 5

 

This statement is true.

 

Now you know how to apply the LCM to problems like these.

 

 

You apply the HCF when reducing fractions in simplest form.  For example,

 

5/10

 

 

The highest factor that 5 and 10 have in common is 5.  Divide the numerator and denominator by this HCF.

 

(5 / 10) ÷ (5 / 5)   is the same as dividing by 1, which does not change the original fraction.  As a result, we have

 

1 / 2.

 

This fraction can no longer be simplified because it is in simplest terms.