Question

Which fraction goes in to the bank to make the sentence true?

Answer 1

Answer: 3/4 ( Option D )

Explanations:

The given expression is:

`(2)/(3)<\text{ }☐`

To know which fraction will go into the blank, we consider the options one by one, and which ever is true is the correct choice.

Find the LCM so that both fractions have a common denominator and see if what happens at the numerator is true

Option A is 1/8, therefore lets see if 2/3 is truly less that 1/8

`\begin{gathered} (2)/(3)\text{ < }(1)/(8) \\ \text{The LCM of 3 and 8 is 24. Therefore:} \\ \frac{16\text{ < 3}}{24} \\ 16\text{ < 3 is false, therefore option A is wrong} \end{gathered}`

Option B is 3/6. Let us see if 2/3 is truly less than 3/6

`\begin{gathered} (2)/(3)\text{ < }(3)/(6) \\ \text{The LCM of 3 and 6 is 6} \\ (4<3)/(6) \\ 4\text{ < 3 is false, therefore option B is wrong} \end{gathered}`

Option C is 3/5. Let us see if 2/3 is truly less than 3/5

`\begin{gathered} (2)/(3)<(3)/(5) \\ \text{The LCM of 3 and 5 is 15} \\ (10<9)/(15) \\ 10\text{ < 9 is false, therefore option C is wrong} \end{gathered}`

Option C is 3/4. Let us see if 2/3 is truly less than 3/4

`\begin{gathered} (2)/(3)<(3)/(4) \\ \frac{8<\text{ 9}}{12} \\ 8\text{ < 9 is true, therefore Option D is correct} \end{gathered}`

2/3 < 3/4 is the correct expression. Therefore, option D is the right choice