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Chapter 1: Problem 66

Write the following in symbols. The product of 1 and 6 is 6

Short Answer

Expert verified
The symbolic form of the statement is \( 1 \times 6 = 6 \).

Step by step solution

01

Understanding the Statement

The problem statement is 'The product of 1 and 6 is 6.' We need to represent this sentence using mathematical symbols.
02

Identifying the Mathematical Operation

The keyword 'product' suggests that we need to find the result of multiplication, and the problem involves numbers 1 and 6.
03

Writing the Mathematical Expression

Using multiplication, we represent 'The product of 1 and 6' as the expression \( 1 \times 6 \).
04

Equating to the Result

The phrase 'is 6' denotes equivalence, meaning the expression equals 6. Therefore, we write the equation: \( 1 \times 6 = 6 \).

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Key Concepts

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

Mathematical Symbols
Mathematical symbols are vital in expressing problems and solutions in a clear and concise way. They transform lengthy sentences into simple expressions. For example, instead of saying "The product of 1 and 6 is 6," we can represent it quickly with symbols.
  • The "product" implies multiplication, which is shown as \( \times \).
  • "Is" signifies equality, represented by the symbol \( = \).
These symbols streamline communication in math, making it easier to solve and understand math problems. Learning how to use mathematical symbols correctly helps improve problem-solving skills.
Multiplication
Multiplication is one of the basic arithmetic operations, which is crucial for many areas of math. It simplifies repeated addition. For instance, saying you have six groups of one is the same as multiplying 1 by 6.To perform multiplication:
  • Identify the numbers to be multiplied (called factors).
  • Use the multiplication symbol \( \times \) to join them.
  • Calculate their product鈥攖he result of the multiplication.
In our example, multiplying 1 by 6 gives us 6. Multiplication helps us handle larger amounts or numbers efficiently, such as in calculating areas or combining quantities.
Writing Equations
Writing equations is a method to formalize relationships between numbers. It involves using mathematical symbols to express statements or conditions.Here's how you can write an equation:
  • Understand what the equation is describing (e.g., a product, a sum, a difference).
  • Use known symbols to represent operations within the sentence (like \( \times \) for product).
  • Equate the operation to the resulting number or solution using \( = \).
For the sentence "The product of 1 and 6 is 6," the equation \( 1 \times 6 = 6 \) tells us that when 1 and 6 are multiplied, their result is indeed 6. Equations play a crucial role in various fields of study, from algebra to physics, as they allow us to model and solve real-world problems reliably.

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