Applications With Adding Integers

Learning Outcomes

  • Translate word phrases to algebraic expressions
  • Simplify algebraic expressions using the order of operations
  • Add integers in application problems

Translate Word Phrases to Algebraic Expressions

All our earlier work translating word phrases to algebra also applies to expressions that include both positive and negative numbers. Remember that the phrase the sum indicates addition.

example

Translate and simplify: the sum of [latex]-9[/latex] and [latex]5[/latex].

Solution:

The sum of [latex]−9[/latex] and [latex]5[/latex] indicates addition. the sum of [latex]-9[/latex] and [latex]5[/latex]
Translate. [latex]-9+5[/latex]
Simplify. [latex]-4[/latex]

Now you can try a similar problem.

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In the next example we add another term to the expression that is being translated. The result is an expression that contains three terms that are added or subtracted.

example

Translate and simplify: the sum of [latex]8[/latex] and [latex]-12[/latex], increased by [latex]3[/latex].

Now you can try a similar problem.

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Add 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 [latex]$5[/latex] could be represented as [latex]-$5[/latex]. 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 [latex]7[/latex] degrees below zero Fahrenheit. By noon, it had warmed up [latex]12[/latex] degrees. What was the temperature at noon?

Now you can try a similar problem.

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In the following video we show a similar example.

In the next example, a football team gaining and losing yardage can be represented with positive and negative numbers.

example

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

Now you can try a similar problem.

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The following video shows more examples of translating expressions that involve integers, and simplifying the result.