Question

By what number should $4\frac{1}{2}$be divided to get $\frac{3}{2}$ ?

• A. $3$
• B. $4\frac{1}{4}$
• C. $1\frac{1}{4}$
• D. $4$

Answer 1

The correct option is A

$3$

Let the required number be $x$

According to the question, $4\frac{1}{2}÷x=\frac{3}{2}$

$$\begin{gathered} \Rightarrow \left(\frac{4\times 2+1}{2}\right)÷x=\frac{3}{2} \\ \Rightarrow \left(\frac{8+1}{2}\right)÷x=\frac{3}{2} \\ \Rightarrow \frac{9}{2}÷x=\frac{3}{2} \\ \Rightarrow \frac{9}{2}\times \frac{1}{x}=\frac{3}{2} \\ \Rightarrow \frac{9}{2x}=\frac{3}{2} \\ \Rightarrow 2x\times 3=9\times 2 \\ \Rightarrow 6x=18 \\ \Rightarrow x=\frac{18}{6} \\ \Rightarrow x=3 \end{gathered}$$

So, the number that divides $4\frac{1}{2}$ to get $\frac{3}{2}$ is $3$.

Hence, the correct answer is option A.