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Chapter 1: Problem 62

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

Short Answer

Expert verified
8

Step by step solution

01

Simplify inside the parentheses

First, simplify each expression inside the parentheses. For the first parentheses: \(8 - 9 = -1\) For the second parentheses: \(4 - 12 = -8\)
02

Perform the multiplication

Now multiply the results from Step 1. \((-1) \times (-8) = 8\)

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Key Concepts

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

Simplifying Expressions
In algebra, simplifying expressions is a crucial skill. It allows you to break down complex problems into manageable parts.
This means combining like terms and reducing equations to their simplest form.

The exercise starts with the expression \( (8-9)(4-12) \). Let's break it down step-by-step:

First, look inside the parentheses:
  • For \( 8 - 9 \), subtract 9 from 8, which equals \( -1 \).
  • For \( 4 - 12 \), subtract 12 from 4, which equals \( -8 \).
By simplifying each part, the expression becomes \( (-1)(-8) \).
Take your time with each step to ensure accuracy.
Multiplication of Integers
Multiplying integers, especially with negative numbers, follows specific rules that can make calculations straightforward.

When you multiply two numbers, consider the signs:
  • If both numbers have the same sign (both positive or both negative), the result is positive.
    Example: \( (-1) \times (-8) = 8 \)
  • If the numbers have different signs (one positive and one negative), the result is negative.
    Example: \( (-1) \times 8 = -8 \)
In this case, since both \( -1 \) and \( -8 \) are negative, their product is positive.

So, \( (-1) \times (-8) \) equals \( 8 \).

Always remember these rules when dealing with multiplication in algebra.
Negative Numbers
Understanding negative numbers is essential in algebra. Negative numbers can change the direction or value of an equation.

When you see a negative sign, it means the number is less than zero.

Rules for working with negative numbers:
  • Adding a negative number is the same as subtracting the positive version.
    Example: \( 4 + (-3) \) equals \( 4 - 3 = 1 \).
  • Subtracting a negative number is the same as adding the positive version.
    Example: \( 4 - (-3) = 4 + 3 = 7 \).
  • When multiplying or dividing two negatives, the result is positive.
    Example: \( (-2) \times (-3) = 6 \).
Negative numbers might seem tricky at first, but with practice, they will become more intuitive.

In our exercise, \( 8 - 9 \) results in \( -1 \) and \( 4 - 12 \) gives \( -8 \). Understanding these basics helps a lot in solving algebra problems easily.

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Most popular questions from this chapter

Nadine Blackwood enjoys playing Triominoes every Wednesday night. Last Wednesday, on four successive turns, her scores were \(-19,28,-5,\) and \(13 .\) What was her final score for the four turns?

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ 5 x-4 a^{2} $$

Write a numerical expression for each phrase and simplify. The product of \(-\frac{2}{3}\) and \(-\frac{1}{5},\) divided by \(\frac{1}{7}\)

Write a numerical expression for each phrase and simplify. See Examples 8 and \(9 .\) The difference between 7 and \(-14\)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ 6 x-5 y+4 a $$
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