Question

Sarah said that when you multiply two fractions that are both less than 1, you may sometimes get a product equal to or greater than 1.

is sarah's statement true why or why not? please use some fractions to prove or disprove sarah's statement

Answer 1

Sarah's statement is false.

Explanation:

If a fraction is less than 1, it means that its numerator is less than its denominator.

So, if we multiply two fractions both are less than 1, then, numerators of both the fractions are less than their denominators.

Hence, in the resultant fraction, the numerator is less than the denominator and hence its value is less than 1.

Answer 2

Sarah's statement is not true and it is explained with the help of counter example.

Explanation:

Sarah gave a statement that the product of two fraction whose value is smaller than 1 gives a product of 1 or greater than 1.

No, this may not always be true. In fact product of two fractions whose value are less than 1 is always smaller than 1.

This can be explained with the help of a counter example:

1)

`\displaystyle(1)/(2) < 1\\\\\displaystyle(1)/(2)* \displaystyle(1)/(2) = \displaystyle(1)/(4) < 1`

2)

`\displaystyle(3)/(4), \displaystyle(2)/(4) < 1\\\\\displaystyle(3)/(4)* \displaystyle(2)/(4) = \displaystyle(6)/(16) < 1`

3)

`\displaystyle(3)/(4), \displaystyle(4)/(7) < 1\\\\\displaystyle(3)/(4)* \displaystyle(4)/(7) = \displaystyle(3)/(7) < 1`