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Chapter 5: Problem 7

Perform the indicated operations. $$-4.67-(-3.914)$$

Short Answer

Expert verified
-0.756

Step by step solution

01

Understand the operation

The expression involves the subtraction of a negative number from a negative number: -4.67 - (-3.914)
02

Apply the rule of subtraction with negative numbers

Remember that subtracting a negative number is the same as adding the positive of that number. Therefore, -4.67 - (-3.914) becomes -4.67 + 3.914
03

Perform the addition

To perform the addition of -4.67 and 3.914, note that they have different signs. Subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value: -4.67 + 3.914 = -0.756

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

negative number operations
When dealing with negative numbers, getting the signs right is crucial. A negative number is any number less than zero, represented with a minus sign (e.g., -1, -2.5, -100).

  • Adding a negative number is like subtraction. For example, 5 + (-3) is the same as 5 - 3.
  • Subtracting a negative number is like addition. For example, 5 - (-3) is the same as 5 + 3.

In the exercise, we subtracted -3.914 from -4.67. By understanding negative number operations, you can transform these types of problems into simpler addition problems. This simplifies the process and reduces errors.
subtraction rules
Subtraction can be tricky, especially with negative numbers. One key rule to remember is that subtracting a negative number is equivalent to adding the positive version of that number.

Let's go through some key points:
  • When you see subtraction with a negative number, change the minus and the negative into a plus. For example, -4.67 - (-3.914) becomes -4.67 + 3.914.
  • This rule simplifies subtraction because switching to addition makes it easier to combine the numbers.

In the provided example, we took the expression -4.67 - (-3.914) and applied this rule. We changed it to -4.67 + 3.914 to make the next step, addition, more straightforward.
absolute value difference
To simplify operations with negative numbers, it's important to understand absolute values.

  • The absolute value of a number is its distance from zero, regardless of its sign. It is always positive.
  • For example, the absolute values of -4.67 and 3.914 are simply 4.67 and 3.914, respectively.

When combining numbers with different signs, subtract the smaller absolute value from the larger absolute value.

  • In our exercise, -4.67 (absolute value 4.67) and 3.914 (absolute value 3.914) are combined by subtracting the smaller from the larger: |4.67| - |3.914| = 4.67 - 3.914 = 0.756.
  • Since the absolute value of -4.67 was larger, the result keeps the negative sign, giving us -0.756.

Understanding absolute values in this context means you can simplify and accurately solve subtraction problems with negative numbers by focusing on their distances from zero.

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Most popular questions from this chapter

Solve the application. Check to see if your answers are reasonable. Ty Cobb was at bat 11,434 times and had 4189 hits, giving him the all-time best batting average. Find his average. Round to the thousandths place.

For Exercises 67鈥�75, divide. Round the answer to the indicated place value. Use the rounded quotient to check. $$1.8 \div7 \text { hundredths }$$

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For Exercises 80鈥�88, solve the application. Check to see if your answers are reasonable. Brooke owes \(39,628.68 on the mortgage for her house. If her monthly payment is \)695.24, how many months does she still need to pay? How many years is this?
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