Question

Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three? Hello my child needs help with this question could someone help

Answer 1

We want to get why

`\frac{3}{\text{ \lparen1/5\rparen}}\text{ is different from }\frac{\text{ \lparen1/5\rparen}}{3}`

Reason 1: Commutation Law Does Not Hold For Division (or quotient)

Generally,

`(a)/(b)\\e(b)/(a)`

Reason 2: Actual Computation

First

`\begin{gathered} \frac{3}{\text{ \lparen1/5\rparen}}=3/(1)/(5) \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=3*(5)/(1) \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=15 \end{gathered}`

Secondly

`\begin{gathered} \frac{\text{ \lparen1/5\rparen}}{3}=(1)/(5)/3 \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=(1)/(5)*(1)/(3) \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=(1)/(15) \end{gathered}`

It is now obvious that

`\frac{3}{\text{ \lparen1/5\rparen}}\\e\frac{\text{ \lparen1/5\rparen}}{3}`