Final answer:
The expression 20 x 1 1/2 is greater than 20 ÷ 1 1/2 because multiplying by a fraction greater than 1 increases a number, while dividing by such a fraction decreases it.
Step-by-step explanation:
To determine which expression is greater, 20 x 1 1/2 or 20 ÷ 1 1/2, without actual computation, we can rely on basic knowledge about multiplication and division by numbers greater than 1.
When we multiply a number by a fraction greater than 1, the result is larger than the original number.
In this case, 20 x 1 1/2 would be greater than 20 because 1 1/2 is equivalent to 1 + 1/2, which means the original 20 is increased by half of its value.
On the other hand, when we divide by a fraction greater than 1, which is the same as multiplying by its reciprocal, the result is smaller than the original number. Thus, 20 ÷ 1 1/2 is the same as 20 multiplied by the reciprocal of 1 1/2, which is 2/3, leading to a result that is smaller than 20. Consequently, the multiplication expression yields a greater value than the division one.