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Chapter 1: Problem 63

Write the following in symbols. The product of 6 and 7 is 42

Short Answer

Expert verified
The symbolic expression is \( 6 \times 7 = 42 \).

Step by step solution

01

Identify the Elements of the Phrase

The phrase "The product of 6 and 7 is 42" contains three main elements: the numbers 6 and 7, the mathematical operation 'product', and the result 42.
02

Understand the Operation

The term 'product' in mathematics refers to the result of multiplying two or more numbers together. Here, it indicates that we need to multiply the numbers 6 and 7.
03

Translate the Operation into Symbols

The operation of multiplication between two numbers, 6 and 7, is represented in symbols as \( 6 \times 7 \).
04

Write the Complete Equation

The phrase states that the product of 6 and 7 'is' 42. In mathematics, 'is' is represented by the equals sign (=). Combining this with our multiplication, the complete equation in symbols is \( 6 \times 7 = 42 \).

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Key Concepts

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

Product
In mathematics, the term 'product' refers to the result obtained when two or more numbers are multiplied together. Think of it like multiplying numbers in order to find a total. For example, if you multiply 6 and 7, the resulting product is 42. This is because multiplying 6 by 7 (i.e., adds 7, six times), gives you 42.
Understanding the term 'product' is crucial for various mathematical operations.
  • It helps in recognizing multiplication problems.
  • It allows identification of scenarios where multiplication is needed.
This concept is fundamental in not only simple arithmetic but also in complex algebraic expressions. Therefore, understanding products lays a strong foundation for more advanced mathematics.
Multiplication
Multiplication is one of the basic operations in arithmetic. It combines groups of equal sizes into one whole. In simpler terms, if you were to "combine" something repeatedly, that's what multiplication does. For instance, multiplying 6 by 7 is like adding 7 to itself six times (7 + 7 + 7 + 7 + 7 + 7).
When performing multiplication, keep in mind:
  • The numbers you multiply are called "factors." In the example 6 and 7 are factors.
  • The result is the "product." Here, it is 42.
Use the multiplication symbol (脳) to show this operation. For 6 times 7, write it as 6 脳 7. Mastering multiplication helps in solving various math problems efficiently and quickly.
Equation Writing
Equation writing is the process of converting textual statements into mathematical symbols. This skill is essential in math because it allows you to express problems and solutions in a universal language.
Consider "The product of 6 and 7 is 42". Each word or phrase has a specific mathematical symbol:
  • 'The product of' means you will multiply.
  • 'Is' translates to an equals sign (=).
By using these translations, you can express the sentence as an equation: 6 脳 7 = 42. Writing equations is key to solving mathematical problems as it allows for clear and concise representation of relationships between numbers. Practicing this skill will enhance your ability to approach and solve a wide range of math problems.

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Most popular questions from this chapter

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{l} 4,963 \\ 5,428 \\ \hline \end{array}$$

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{r} 638 \\ 191 \\ \hline \end{array}$$

Divide. You shouldn't have any wrong answers because you can always check your results with multiplication. $$1,440\div32$$

Find a solution for each equation. $$n+8=13$$

The application problems that follow may involve more than merely division. Some may require addition, subtraction, or multiplication, whereas others may use a combination of two or more operations. Hourly Wages If a man works an 8 -hour shift and is paid \(\$ 96,\) how much does he make for 1 hour?
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