Final answer:
When comparing two numbers a and b, it is possible for a > b and |a| < |b| to both be true if a and b have opposite signs.
Step-by-step explanation:
Comparing numbers is an important part of building a student's number sense. Number sense is the ability for a student to recognize a number, it's value and it's relationship with other numbers. It is this important last component that is built by comparing numbers.
When comparing numbers, first start with the greatest place value. Then compare the digits in the greatest place value position. If these digits are the same, continue to the next smaller place until the digits are different.
The statement a > b means that a is greater than b, while the statement |a| < |b| means that the absolute value of a is less than the absolute value of b.
Both of these statements can be true if a and b have opposite signs. For example, if a is -5 and b is 3, then a is greater than b (-5 > 3), but the absolute value of a is less than the absolute value of b (|-5| < |3|).