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Chapter 1: Problem 4

Find each product or quotient. $$5(3)(2)$$

Short Answer

Expert verified
The product of \(5 \times 3 \times 2\) is \(30\).

Step by step solution

01

Identify the Factors

The problem presents three numbers to multiply: \(5\), \(3\), and \(2\).
02

Multiply the First Two Factors

Start by multiplying the first two numbers together. This would be \(5 \times 3 = 15\).
03

Multiply the Product by the Last Factor

Next, multiply the result from the previous step by the last remaining factor. This would be \(15 \times 2 = 30\).

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Key Concepts

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

Understanding Arithmetic
Arithmetic is one of the fundamental branches of mathematics that deals with numbers and the basic operations among them, which include addition, subtraction, multiplication, and division. Each operation allows us to perform calculations that describe quantities and relationships.
  • Addition: Combining two numbers to get their total sum.
  • Subtraction: Finding the difference between two numbers by taking one away from the other.
  • Multiplication: Simplifying repeated addition, as in adding a number to itself several times.
  • Division: Distributing a number into equal parts or groups.

In addition to just understanding these operations, arithmetic allows us to solve many everyday problems, whether buying groceries, planning a budget, or figuring out how much paint is needed for a room. In this exercise, we focused on multiplication, specifically multiplying multiple numbers together to get a product.
Mastering Order of Operations
The order of operations is a fundamental concept that helps ensure consistent and accurate results when performing mathematical calculations. It is like a set of rules to follow when working with multiple operations in the same expression. The acronym PEMDAS helps remember the sequence:
  • P: Parentheses - Do computations within parentheses first.
  • E: Exponents - Solve exponents or powers next.
  • M/D: Multiplication and Division - Work these from left to right as they appear.
  • A/S: Addition and Subtraction - Finally, perform these from left to right.

In our exercise, following the order of operations perfectly aligns with multiplications as we proceed from left to right, like multiplying \(5 \times 3\), then \(15 \times 2\). Misunderstanding this order can lead to incorrect results, but sticking to PEMDAS helps avoid confusion.
Basics of Algebra
Basic algebra extends arithmetic by using symbols like letters to represent numbers in equations and expressions. This allows us to generalize mathematical concepts and solve for unknown values. Understanding basic algebra is critical for more advanced mathematical topics.
  • Variables: Symbols (like \(x\) or \(y\)) that stand in for unknown numbers.
  • Coefficients: Numbers that multiply the variables.
  • Constants: Numbers on their own without variables.

In basic algebra, we're often tasked with simplifying expressions or solving equations. Although our exercise doesn't include variables, the concept of multiplication is vital in algebra for simplifying expressions like \(5x \times 3x = 15x^2\). Understanding multiplication in arithmetic paves the way for handling complex expressions in algebra.

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