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Chapter 1: Problem 287

Simplify each expression. $$ (8-11)(9-12) $$

Short Answer

Expert verified
9

Step by step solution

01

Simplify inside the parentheses

First, simplify the expressions inside the parentheses. For the first set of parentheses: \(8 - 11 = -3\) For the second set of parentheses: \(9 - 12 = -3\)
02

Multiply the simplified results

Now multiply the results from step 1. \((-3) \times (-3)\)
03

Solve the multiplication

Multiply the values to get the final result. \((-3) \times (-3) = 9\)

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Key Concepts

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

Order of Operations
The order of operations is a fundamental concept in mathematics. It helps us understand the correct sequence to evaluate an expression.
The acronym PEMDAS is often used to remember the order:
  • P: Parentheses
  • E: Exponents
  • M: Multiplication
  • D: Division
  • A: Addition
  • S: Subtraction
Always start with operations inside parentheses.
This way, you simplify complex expressions step by step. In our exercise, we first tackled the expression inside each set of parentheses. We simplified \(8 - 11\) to \(-3\) and \(9 - 12\) to \(-3\).
Only after we simplified inside the parentheses, did we move to the next operation, which was multiplication.

Sticking to this order ensured that we didn't miscalculate along the way.
Multiplication
Multiplication is one of the basic arithmetic operations and is essential when simplifying expressions.
In our exercise, after simplifying the expressions inside the parentheses, we applied multiplication.
We had \((-3) \times (-3)\).
Multiplication involves combining equal groups. Here, we multiplied negative numbers, which we will explore more deeply shortly. Multiplying two negative numbers follows specific rules, but always remember the core idea that we combine quantities in groups.
Getting comfortable with multiplication helps across various math problems.
Practice it frequently to build a solid foundation for more complex operations.
Negative Numbers
Understanding negative numbers is crucial in mathematics, especially when working with expressions.
Negative numbers are values less than zero and can sometimes be tricky. In our exercise, we simplified \(8 - 11\) to \(-3\) and \(9 - 12\) to \(-3\).
Then, we multiplied these results together: \(-3 \times -3\).
When multiplying negative numbers, an important rule is:
  • Negative multiplied by Negative: The product is positive.
    So, \(-3 \times -3 = 9\).
  • Negative multiplied by Positive: The product is negative.
  • Positive multiplied by Positive: The product is positive.
Grasping these rules will help you handle operations involving negative numbers with confidence.
They are applied frequently in various branches of mathematics, from algebra to calculus.
Always refer back to these rules if you get stuck on similar problems.

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