Question

Frank says that 50% of a number will always be greater than 20% of any other number.

Complete one inequality to support Frank's claim and one to show that he is incorrect.

Support
50% of ___ > 20% of ____

Refute
50% of ___ < 20% of ___

Answer 1

Using examples, we showed that 50% of a number can be either greater than or less than 20% of another number, hence Frank's claim is not always true. Now the inequality 50% of 10 < 20% of 100 is correct, hence refuting Frank's claim.

Step-by-step explanation:

The claim that 50% of a number will always be greater than 20% of any other number can be evaluated using simple inequalities. To support or refute Frank's claim, we will have to create examples using arbitrary numbers.

Support

To support Frank's claim, consider 50% of 40 compared to 20% of 30:

50% of 40 = 0.50 × 40 = 20

20% of 30 = 0.20 × 30 = 6

Thus, 50% of 40 > 20% of 30 holds true in this case.

Refute

To refute the claim, let's use 50% of 10 compared to 20% of 100:

50% of 10 = 0.50 × 10 = 5

20% of 100 = 0.20 × 100 = 20

Now the inequality 50% of 10 < 20% of 100 is correct, hence refuting Frank's claim.