The expression which is equivalent to [tex]36\div 4[/tex] is [tex](36\times\frac{1}{4})[/tex] i.e., [tex]\fbox{\begin\\\ \bf option D\\\end{minispace}}[/tex].
Further explanation:
The given expression is [tex]36\div 4[/tex].
The symbol [tex](\div)[/tex] used in the given expression is a symbol of division.
The given expression is also expressed as [tex]\dfrac{36}{4}[/tex].
Solve the given expression as follows:
[tex]\begin{aligned}\dfrac{36}{4}&=\dfrac{4\times9}{4}\\&=9\end{aligned}[/tex]
Therefore, the value of expression [tex]36\div 4[/tex] is [tex]\fbox{\begin\\\ 9\\\end{minispace}}[/tex].
Option A:
The expression given in option A is [tex]\dfrac{4}{36}[/tex].
Evaluate the expression [tex]\dfrac{4}{36}[/tex] as follows:
[tex]\begin{aligned}\dfrac{4}{36}&=\dfrac{4}{4\times 9}\\&=\dfrac{1}{9}\end{aligned}[/tex]
Therefore, the value of expression [tex]\dfrac{4}{36}[/tex] is [tex]\fbox{\begin\\\ \dfrac{1}{9}\\\end{minispace}}[/tex].
Since, the value of expression [tex]\dfrac{4}{36}[/tex] is not equal to the value of the expression [tex]36\div 4[/tex] so, the option A is incorrect.
Option B:
The expression given in option B is [tex]\left(\dfrac{36}{(\frac{1}{4})}\right)[/tex].
Evaluate the expression [tex]\left(\dfrac{36}{(\frac{1}{4})}\right)[/tex] as follows:
[tex]\begin{aligned}\dfrac{36}{(\frac{1}{4})}&=36\times\dfrac{4}{1}\\ &=144\end{aligned}[/tex]
Therefore, the value of expression [tex]\left(\dfrac{36}{(\frac{1}{4})}\right)[/tex] is [tex]\fbox{\begin\\\ 144\\\end{minispace}}[/tex].
Since, the value of expression [tex]\left(\dfrac{36}{(\frac{1}{4})}\right)[/tex] is not equal to the value of the expression [tex]36\div 4[/tex] so, the option B is incorrect.
Option C:
The expression given in option C is [tex]\dfrac{1}{36}\times\dfrac{1}{4}[/tex].
Evaluate the expression [tex]\dfrac{1}{36}\times\dfrac{1}{4}[/tex] as follows:
[tex]\dfrac{1}{36}\times\dfrac{1}{4}=\dfrac{1}{144}[/tex]
Therefore, the value of expression [tex]\dfrac{1}{36}\times\dfrac{1}{4}[/tex] is [tex]\fbox{\begin\\\ \dfrac{1}{144}\\\end{minispace}}[/tex].
Since, the value of expression [tex]\dfrac{1}{36}\times\dfrac{1}{4}[/tex] is not equal to the value of the expression [tex]36\div 4[/tex] so, the option C is incorrect.
Option D:
The expression given in option D is [tex]36\times \dfrac{1}{4}[/tex].
Evaluate the expression [tex]36\times \dfrac{1}{4}[/tex] as follows:
[tex]\begin{aligned}36\times \dfrac{1}{4}&=4\times9\times\dfrac{1}{4}\\&=9\end{aligned}[/tex]
Therefore, the value of expression [tex]36\times \dfrac{1}{4}[/tex] is [tex]\fboc{\begin\\\ 9\\\end{minispace}}[/tex].
Since, the value of expression [tex]36\times \dfrac{1}{4}[/tex] is equal to the value of the expression [tex]36\div 4[/tex] so, the option D is correct.
The value of the expression [tex]36\times \dfrac{1}{4}[/tex] is same as the value of the expression [tex]36\div 4[/tex] so it can be said that both the expression are equivalent.
Therefore, option D is correct.
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Answer details
Grade: Middle school
Subject: Mathematics
Chapter: Simplification
Keywords: Simplification, expression, algebra, algebraic expression, equivalent, division, multiplication, 36/4, evaluate, simplified.
