Adding Integers in Applications

Adding Integers in Applications

Recall that we were introduced to some situations in everyday life that use positive and negative numbers, such as temperatures, banking, and sports. For example, a debt of \(\text{\$5}\) could be represented as \(\text{−\$5.}\) Let’s practice translating and solving a few applications.

Solving applications is easy if we have a plan. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question.

Example

The temperature in Buffalo, NY, one morning started at \(7\phantom{\rule{0.2em}{0ex}}\text{degrees}\) below zero Fahrenheit. By noon, it had warmed up \(12\phantom{\rule{0.2em}{0ex}}\text{degrees}.\) What was the temperature at noon?

Solution

We are asked to find the temperature at noon.

Write a phrase for the temperature.The temperature warmed up 12 degrees from 7 degrees below zero.
Translate to math notation.−7 + 12
Simplify.5
Write a sentence to answer the question.The temperature at noon was 5 degrees Fahrenheit.

Example

A football team took possession of the football on their \(\text{42-yard line.}\) In the next three plays, they lost \(\text{6 yards,}\) gained \(\text{4 yards,}\) and then lost \(\text{8 yards.}\) On what yard line was the ball at the end of those three plays?

Solution

We are asked to find the yard line the ball was on at the end of three plays.

Write a word phrase for the position of the ball.Start at 42, then lose 6, gain 4, lose 8.
Translate to math notation.42 − 6 + 4 − 8
Simplify.32
Write a sentence to answer the question.At the end of the three plays, the ball is on the 32-yard line.

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This is a lesson from the tutorial, Introducing Integers and you are encouraged to log in or register, so that you can track your progress.

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