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Chapter 1: Problem 61

Perform each indicated operation. $$ (12-14)(1-4) $$

Short Answer

Expert verified
6

Step by step solution

01

Simplify Inside Parentheses

First, simplify each expression inside the parentheses. For the first set, calculate the result of \(12 - 14\). For the second set, calculate the result of \(1 - 4\).
02

Perform the Subtractions

Calculate \(12 - 14 = -2\) and \(1 - 4 = -3\).
03

Multiply the Results

Multiply the two results obtained from the subtraction: \(-2\) and \(-3\). So, \(-2 \times -3 = 6\).

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Key Concepts

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

simplify expressions
Simplifying expressions is all about making a mathematical statement as simple as it can be. It typically involves combining like terms and performing basic arithmetic operations. In our exercise, we simplify the expressions inside the parentheses first. Here, we have \(12 - 14\) and \(1 - 4\). By calculating these, we reduce the complexity of the problem before moving to multiplication. Simplifying expressions helps in solving algebra problems easily and quickly.
operations with integers
Operations with integers include addition, subtraction, multiplication, and division involving whole numbers, both positive and negative. In our exercise, we performed subtraction within the parentheses. To break it down:
  • \(12 - 14 = -2\)
  • \(1 - 4 = -3\)

It鈥檚 important to understand the rules for these operations, especially when working with negative numbers. For subtraction, think of it as adding a negative number. Multiplying two negative numbers, as shown by \(-2 \times -3 = 6\), will give a positive product.
parentheses in algebra
Parentheses in algebra indicate which operations should be performed first. This is part of the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In our exercise, the parentheses told us to solve \(12 - 14\) and \(1 - 4\) first before multiplying the results together.

Parentheses help organize complex expressions and ensure we get the correct result. Always simplify expressions inside parentheses first to follow the correct order of operations in algebra.

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Most popular questions from this chapter

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