Is each statement true or false? Explain your reasoning.

45/100⋅72=45/72⋅100

16% of 250 is equal to 250% of 16

Answers

Answer 1

Statement 1 - [tex]\frac{45}{100} *72=\frac{45}{72} *100[/tex] - false

Statement 2 - [tex]16\%\, of\, 250= 250\%\, of\, 16[/tex] - true

Percentage

Percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the example: [tex]\frac{1}{100} =1%[/tex].

Statement 1 - [tex]\frac{45}{100} *72=\frac{45}{72} *100[/tex]

       Solving each side of the expression:

               [tex]\frac{45}{100} *72=\frac{3240}{100} =\frac{3240\div 20}{100\div 20} =\frac{162}{5} \\ \\ and\\ \\ \frac{45}{72} *100=\frac{4500}{72} =\frac{4500\div 36}{72\div 36} =\frac{125}{2}[/tex]

Therefore,  [tex]\frac{45}{100} *72\neq \frac{45}{72} *100[/tex] and the statement is false.

Statement 2 - 16% of 250 = 250% of 16

       Solving each side of the expression:

               [tex]16\%\, of\, 250= \frac{16*250}{100}=\frac{4000}{100}=40 \\ \\ and\\ \\ 250\%\, of\, 16= \frac{250*16}{100}=\frac{4000}{100}=40[/tex]

Therefore,  [tex]16\%\, of\, 250= 250\%\, of\, 16[/tex] and the statement is true.

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