The length of a paper clip chain is directly proportional to the number of paper clips. if a chain with 65 paper clips has a length of 97.5 inches, how long is a chain with 14 paper clips?

The length of a paper clip chain is directly proportional to the number of paper clips. If a chain with 65 paper clips has a length of 97.5 inches then the length of chain with 14 paper clips is 21 inches.

Solution:

Given that the length of a paper clip chain is directly proportional to the number of paper clips. Directly propotional means when the length of paper clip increases, then the number of paper clips also increases in same ratio.

Hence, by above definition, we get  

 ------- eqn 1

From question, for a chain with 65 paper clips has a length of 97.5 inches, we get  

Similarly, for a chain with 14 paper clips with length to be found, we get  

Now by using eqn 1, we can calculate the length of 14 paper clips  is,

Rearranging the terms we get,

Hence the length of chain with 14 paper clips is 21 inches.

b)

Step-by-step explanation:

The given expression  :

First we convert the mixed fraction into the improper fraction :

Now, the expression becomes :

Now, we find a common denominator by finding the LCM of both denominators.

LCM (5,3)=

Now, expression becomes :