determine with and without computation whether a quantity is increased or increased when multiplied by a fraction

Question

Which value of r in 6r makes expression equal a number greater than 6

Answer 1

6r > 6

r > 1

Answer 2

6 times itself is 6.  So 6 times any number greater than itself is larger than 6.

 

r > 6

 

 

If you multiply any number by a fraction, you decrease the value.  This is because multiplying by a fraction is the same as dividing by the reciprocal of that fraction.  For example, multiplying by 1/3 is the same dividing by 3.  Division makes a value smaller.