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Обучение Руководства > Prealgebra

Applications With Subtracting Integers

Learning Outcomes

  • Translate statements from words into algebraic expressions involving subtraction
  • Solve application problems involving subtraction
When we first introduced the operation symbols, we saw that the expression a−ba-b may be read in several ways as shown below. This table has six rows. The first row has a - b. The second row states a minus b. The third row states the difference of a and b. The fourth row states subtract b from a. The fifth row states b subtracted from a. The sixth row states b less than a. Be careful to get aa and bb in the right order!  

example

Translate and then simplify:
  1. The difference of 1313 and −21-21
  2. Subtract 2424 from −19-19
Solution 1. A difference means subtraction. Subtract the numbers in the order they are given.
the difference of 13 and −−21\text{the }\color{red}{difference}\text{ of }13\text{ and }--21
Translate. 13−−(−−21)13--(--21)
Simplify. 3434
2. Subtract means to take 2424 away from −19-19.
subtract24from−−19\color{red}{subtract } 24\color{red}{ from }--19
Translate. −−19−−24--19--24
Simplify. −−43--43
  Watch teh following video to see more examples of how to translate an expression in words that represents subtraction into a mathematical expression. https://youtu.be/yOeIxabFi0c

Subtract Integers in Applications

It’s hard to find something if we don’t know what we’re looking for or what to call it. So when we solve an application problem, we first need to determine what we are asked to find. Then we can write a phrase that gives the information to find it. We’ll translate the phrase into an expression and then simplify the expression to get the answer. Finally, we summarize the answer in a sentence to make sure it makes sense.

Solve Application Problems

  1. Identify what you are asked to find.
  2. Write a phrase that gives the information to find it.
  3. Translate the phrase to an expression.
  4. Simplify the expression.
  5. Answer the question with a complete sentence.
 

example

The temperature in Urbana, Illinois one morning was 1111 degrees Fahrenheit. By mid-afternoon, the temperature had dropped to −9-9 degrees Fahrenheit. What was the difference between the morning and afternoon temperatures?

Answer: Solution

Step 1. Identify what we are asked to find. the difference between the morning and afternoon temperatures
Step 2. Write a phrase that gives the information to find it. the difference of 1111 and −9-9
Step 3. Translate the phrase to an expression. The word difference indicates subtraction. 11−(−9)11-\left(-9\right)
Step 4. Simplify the expression. 2020
Step 5. Write a complete sentence that answers the question. The difference in temperature was 2020 degrees Fahrenheit.

    Geography provides another application of negative numbers with the elevations of places below sea level.  

example

Dinesh hiked from Mt. Whitney, the highest point in California, to Death Valley, the lowest point. The elevation of Mt. Whitney is 14,49714,497 feet above sea level and the elevation of Death Valley is 282282 feet below sea level. What is the difference in elevation between Mt. Whitney and Death Valley?

Answer: Solution

Step 1. What are we asked to find? The difference in elevation between Mt. Whitney and Death Valley
Step 2. Write a phrase. elevation of Mt. Whitney−elevation of Death Valley
Step 3. Translate. 14,497−(−282)14,497-\left(-282\right)
Step 4. Simplify. 14,77914,779
Step 5. Write a complete sentence that answers the question. The difference in elevation is 14,77914,779 feet.

    Managing your money can involve both positive and negative numbers. You might have overdraft protection on your checking account. This means the bank lets you write checks for more money than you have in your account (as long as they know they can get it back from you!)  

example

Leslie has $25 in her checking account and she writes a check for $8
  1. What is the balance after she writes the check?
  2. She writes a second check for $20 What is the new balance after this check?
  3. Leslie’s friend told her that she had lost a check for $10 that Leslie had given her with her birthday card. What is the balance in Leslie’s checking account now?

Answer: Solution

1.
What are we asked to find? The balance of the account
Write a phrase. $25 minus $8
Translate $25--$8
Simplify. $17
Write a sentence answer. The balance is $17 .
2.
What are we asked to find? The new balance
Write a phrase. $17 minus $20
Translate $17--$20
Simplify. --$3
Write a sentence answer. She is overdrawn by $3 .
3.
What are we asked to find? The new balance
Write a phrase. $10 more than -$3
Translate --$3+$10
Simplify. $7
Write a sentence answer. The balance is now $7 .

  Watch teh following video to see another example that uses integers to represent the balance of a checking account.  

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