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Chapter 1: Problem 66

Perform each indicated operation. \((8-9)(4-12)\)

Short Answer

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Step by step solution

01

- Simplify Each Parenthesis

Begin by simplifying the expressions inside each parenthesis. Compute the values for \(8 - 9\) and \(4 - 12\).
02

- Calculate the Values

For \(8 - 9\), subtract 9 from 8: \(8 - 9 = -1\). For \(4 - 12\), subtract 12 from 4: \(4 - 12 = -8\).
03

- Multiply the Results

Now multiply the results from Step 2: \(-1 \times -8\). The product of two negative numbers is positive, so \(-1 \times -8 = 8\).

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Key Concepts

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

Simplifying Expressions
Before you can solve any algebraic expression, it's crucial to simplify it first. Simplifying means making the expression as easy to work with as possible.
For example, let's look at \( (8-9)(4-12) \). We start by simplifying the expressions inside each parenthesis.
The first parenthesis: \(8 - 9 = -1\)
The second parenthesis: \(4 - 12 = -8\)
So, the simplified expression is \((-1)(-8)\).
Once each part is simplified, you can then carry out further operations like addition, subtraction, multiplication, or even more complex algebraic operations. This step-by-step simplification is critical for avoiding mistakes later on.
Negative Numbers
Understanding how to work with negative numbers is an essential part of basic algebra.
Negative numbers are those less than zero and are often used to represent loss or decrease. For example, when you subtract a larger number from a smaller one: \(8 - 9 = -1\)
Here are some common points to remember about negative numbers:
  • Negative numbers have a minus sign (-) before them.
  • When subtracting larger numbers from smaller ones, the result is negative.
So, when handling expressions with negative numbers, always pay close attention to the signs to avoid mistakes.
Multiplication of Negatives
The multiplication of negative numbers can sometimes be tricky, but with practice, it becomes simpler.
A fundamental rule is:
  • The product of two negative numbers is a positive number.
  • The product of one positive and one negative number is a negative number.
Let's take \(-1 \times -8\) as an example. According to the rule, the product of these two negatives is \(+8\).
Conversely, if we had \(-1 \times 8\), the result would be \(-8\).
Remembering these rules can simplify many algebra problems and help you get the right answer more consistently.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 3 if the sum of its digits is divisible by \(3,\) and not otherwise. (a) Is 4,799,232 divisible by \(3 ?\) (b) Is 2,443,871 divisible by \(3 ?\)

Solve each problem. The lowest temperature ever recorded in Illinois was \(-36^{\circ} \mathrm{F}\) on January \(5,1999 .\) The lowest temperature ever recorded in Utah was on February \(1,1985,\) and was \(33^{\circ} \mathrm{F}\) lower than Illinois's record low. What is the record low temperature for Utah? (Data from National Climatic Data Center.)

Solve each problem. In \(2000,\) the U.S. federal budget had a surplus of \(\$ 236\) billion. In \(2016,\) the federal budget had a deficit of \(\$ 616\) billion. Express the difference between these amounts as a positive number. (Data from U.S. Office of Management and Budget.)

Write a numerical expression for each phrase, and simplify the expression. 9 less than -13

Solve each problem. Marcial owes \(\$ 679.00\) on his Visa account. He returns three items costing \(\$ 36.89, \$ 29.40\), and \(\$ 113.55\) and receives credit for these on the account. Next, he makes purchases of \(\$ 135.78\) and \(\$ 412.88\) and two purchases of \(\$ 20.00\) each. He makes a payment of \(\$ 400\). He then incurs a finance charge of \(\$ 24.57 .\) How much does he still owe?
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