If [tex]\frac{j}{k}=\frac{4}{5}[/tex], which of the following correctly expresses [tex]k[/tex] in terms of [tex]j[/tex]?

Choose 1 answer:

A. [tex]k=\frac{4}{5j}[/tex]
B. [tex]k=\frac{5}{4j}[/tex]
C. [tex]k=\frac{4j}{5}[/tex]
D. [tex]k=\frac{5j}{4}[/tex]



Answer :

To determine which of the given options correctly expresses [tex]\( k \)[/tex] in terms of [tex]\( j \)[/tex] when [tex]\(\frac{j}{k} = \frac{4}{5}\)[/tex], follow these steps:

1. We start with the given equation:
[tex]\[ \frac{j}{k} = \frac{4}{5} \][/tex]

2. To isolate [tex]\( k \)[/tex], multiply both sides of the equation by [tex]\( k \)[/tex]:
[tex]\[ j = \frac{4}{5}k \][/tex]

3. Now, to solve for [tex]\( k \)[/tex], we need to get [tex]\( k \)[/tex] by itself. We do this by dividing both sides by [tex]\(\frac{4}{5}\)[/tex]:
[tex]\[ k = \frac{j}{\frac{4}{5}} \][/tex]

4. Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(\frac{4}{5}\)[/tex] is [tex]\(\frac{5}{4}\)[/tex]:
[tex]\[ k = j \times \frac{5}{4} \][/tex]

5. Therefore, [tex]\( k \)[/tex] in terms of [tex]\( j \)[/tex] is:
[tex]\[ k = \frac{5j}{4} \][/tex]

Given the options:
- (A) [tex]\( k = \frac{4}{5 j} \)[/tex]
- (B) [tex]\( k = \frac{5}{4 j} \)[/tex]
- (C) [tex]\( k = \frac{4 j}{5} \)[/tex]
- (D) [tex]\( k = \frac{5 j}{4} \)[/tex]

The correct answer is [tex]\( k = \frac{5 j}{4} \)[/tex], which corresponds to option (D).