Which context describes a difference of rational numbers?
The team’s score did not change during the game.
A football player loses yards on a play.
A football player gains yards on a play.
The team’s score increased when scoring.
A football player loses yards on a play.
The context that describes a difference of rational numbers is when a football player loses yards on a play.
To understand why, let's break it down:
Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, rational numbers can be written as a fraction in the form a/b, where a and b are integers.
In the given options, the only context that involves a change of value that can be expressed as a fraction is when a football player loses yards on a play. When a player loses yards, the distance he moves backwards can be represented as a negative value, such as -10, -5, etc. These negative values can be expressed as fractions, for example, -10/-1 or -5/1, which are rational numbers.
The other options, such as the team's score not changing, a football player gaining yards, or the team's score increasing when scoring, do not involve a change that can be expressed as a difference of rational numbers. The team's score could stay the same as a whole number (e.g., 0, 10, etc.), a football player can gain yards that are whole numbers (e.g., 5, 10, etc.), and the team's score increasing when scoring is not a difference but rather an addition, which does not relate to rational numbers specifically.
Therefore, the context that describes a difference of rational numbers is when a football player loses yards on a play.