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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

Sagot :

Solution

We want to get why

[tex]\frac{3}{\text{ \lparen1/5\rparen}}\text{ is different from }\frac{\text{ \lparen1/5\rparen}}{3}[/tex]

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

Generally,

[tex]\frac{a}{b}\ne\frac{b}{a}[/tex]

Reason 2: Actual Computation

First

[tex]\begin{gathered} \frac{3}{\text{ \lparen1/5\rparen}}=3\div\frac{1}{5} \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=3\times\frac{5}{1} \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=15 \end{gathered}[/tex]

Secondly

[tex]\begin{gathered} \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{5}\div3 \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{5}\times\frac{1}{3} \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{15} \end{gathered}[/tex]

It is now obvious that

[tex]\frac{3}{\text{ \lparen1/5\rparen}}\ne\frac{\text{ \lparen1/5\rparen}}{3}[/tex]

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