3.3 Subtract integers  (Page 5/6)

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!)

Leslie has $\text{\$25}$ in her checking account and she writes a check for $\text{\$8.}$

1. ⓐ What is the balance after she writes the check?
2. ⓑ She writes a second check for $\text{\$20.}$ What is the new balance after this check?
3. ⓒ Leslie’s friend told her that she had lost a check for $\text{\$10}$ that Leslie had given her with her birthday card. What is the balance in Leslie’s checking account now?

Solution

ⓐ
What are we asked to find?	The balance of the account
Write a phrase.	$\$25$ minus $\$8$
Translate
Simplify.
Write a sentence answer.	The balance is $\$17$ .

ⓑ
What are we asked to find?	The new balance
Write a phrase.	$\$17$ minus $\$20$
Translate
Simplify.
Write a sentence answer.	She is overdrawn by $\$3$ .

ⓒ
What are we asked to find?	The new balance
Write a phrase.	$\$10$ more than $-\$3$
Translate
Simplify.
Write a sentence answer.	The balance is now $\$7$ .

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Key concepts

• Subtraction of Integers

  5 – 3	–5 – (–3)
  2	–2
  2 positives	2 negatives
  When there would be enough counters of the color to take away, subtract.
  –5 – 3	5 – (–3)
  –8	8
  5 negatives, want to subtract 3 positives	5 positives, want to subtract 3 negatives
  need neutral pairs	need neutral pairs

• Subtraction Property
  • $a-b=a+(\mathit{\text{−b}})$
  • $a-\left(\mathrm{-b}\right)=a+b$
• Solve Application Problems
  • Step 1. Identify what you are asked to find.
  • Step 2. Write a phrase that gives the information to find it.
  • Step 3. Translate the phrase to an expression.
  • Step 4. Simplify the expression.
  • Step 5. Answer the question with a complete sentence.

Practice makes perfect

Model Subtraction of Integers

In the following exercises, model each expression and simplify.