Question

Which of the following mathematical statements are true?

$StatementA:\frac{2}{15}\times \frac{120}{120}=\frac{2}{15}$

$StatementB:\frac{5}{7}\times \frac{1}{120}<\frac{5}{7}$

$StatementC:\frac{4}{5}\times \frac{1}{120}=\frac{4}{5}$

• A. Both B and C
• B. Only statement A
• C. Both A and B
• D. Only statement B

Answer 1

The correct option is C Both A and B

$Rule1:$
$\text{When a fraction is multiplied by a fraction}\text{of the type}\frac{n}{n}\text{, then the resulting product}\text{will be the}same\text{as the original fraction.}$

$Rule2:$
$\text{When a fraction is multiplied by a fraction}\text{less than 1, then the resulting product will}\text{be}less\text{than the original fraction}$

$\text{For statement A, we have:}$

$LeftHandSide:\frac{2}{15}\times \frac{120}{120}=\frac{2\times 120}{15\times 120}=\frac{240}{1800}=\frac{2}{15}$

$RightHandSide:\frac{2}{15}$

$⟹LeftHandSide=RightHandSide$

$\therefore StatementA\text{is true.}$

$\text{For statement B, we have:}$

$LeftHandSide:\frac{5}{7}\times \frac{1}{120}=\frac{5\times 1}{7\times 120}=\frac{5}{840}$

$RightHandSide:\frac{5}{7}=\frac{5\times 120}{7\times 120}=\frac{600}{840}$

$\frac{5}{840}<\frac{600}{840}$

$⟹LeftHandSide<RightHandSide$

$\therefore StatementB\text{is true.}$

$\text{For statement C, we have:}$

$LeftHandSide:\frac{4}{5}\times \frac{1}{120}=\frac{4\times 1}{5\times 120}=\frac{4}{600}$

$RightHandSide:\frac{4}{5}$

$\frac{4}{600}\ne \frac{4}{5}$

$⟹LeftHandSide\ne RightHandSide$

$\therefore StatementC\text{is false.}$