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Chapter 1: Problem 1

Write each of the following in symbols. The quotient of 6 and 3

Short Answer

Expert verified
The symbolic form is \( 6 \, \div \, 3 \) or \( \frac{6}{3} \).

Step by step solution

01

Identify the Operation

The word 'quotient' refers to the result of division. In mathematical symbols, division is represented by the division symbol (梅) or a forward slash (/) in some contexts.
02

Identify the Numbers

The problem mentions the 'quotient of 6 and 3', which means you are dividing 6 by 3.
03

Write in Symbolic Form

Now that we know the operation is division and the numbers are 6 and 3, we can express this in symbols as \( 6 \, \div \, 3 \) or \( \frac{6}{3} \).

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Key Concepts

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

Understanding the Quotient
The term "quotient" is essential in mathematics. It refers to the result of a division problem. When you divide one number by another, the answer you get is called the quotient.
For example, if you divide 15 by 3, the quotient is 5. This simply means that 3 fits into 15 exactly five times. Quotients can be whole numbers or include decimals. If a number doesn't divide evenly, you might end up with a decimal quotient.
  • Example: The quotient of 7 divided by 2 is 3.5.
  • Example: The quotient of 10 divided by 2 is 5.
Exploring the concept of quotients helps to build a solid foundation in arithmetic operations. Recognizing what a quotient is helps you understand what division accomplishes.
Using Mathematical Symbols
Mathematical symbols are shorthand representations used to express operations and relationships between numbers. These symbols make it quicker and easier to work with mathematical problems.
For division, the most commonly used symbols are the division sign (梅) and the forward slash (/). Both denote the same operation but may be used in different contexts.
  • The division sign (梅) is often used in simple arithmetic or elementary mathematics.
  • The forward slash (/) is more common in algebraic expressions or computer-based contexts.
Other symbols you might encounter in math include:
  • Plus sign (+) for addition
  • Minus sign (鈭�) for subtraction
  • Multiplication sign (脳 or 路)
  • Equals sign (=)
Mastering these symbols is crucial as they are the building blocks of mathematical language.
Basic Arithmetic Operations
Arithmetic is a fundamental aspect of mathematics, focusing on basic operations like addition, subtraction, multiplication, and division. These operations form the backbone of most mathematical concepts.
Let's take a closer look at each:
  • Addition joins two or more numbers to get a sum. For example, 2 + 3 equals 5.
  • Subtraction determines the difference between numbers. For example, 5 - 2 equals 3.
  • Multiplication is repeated addition. For example, 4 脳 3 equals 12, or 4 added three times.
  • Division finds out how many times one number is contained within another. For example, dividing 9 by 3 yields a quotient of 3.
Understanding these operations is critical because they are used in everyday calculations and more complex problem-solving.

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Most popular questions from this chapter

Mentally give a one-digit estimate for each of the following quotients. That is, for each quotient, mentally estimate the answer using one of the digits \(1,2,3,4,5,6,7,8,\) or 9 $$673\div109$$

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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. Milligrams of Calcium Suppose one egg contains 25 milligrams of calcium, a piece of toast contains 40 milligrams of calcium, and a glass of milk contains 215 milligrams of calcium. How many milligrams of calcium are contained in a breakfast that consists of three eggs, two glasses of milk, and four pieces of toast?

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. cost of a Dress A dress shop orders 45 dresses for a total of \(\$ 2,205 .\) If they paid the same amount for each dress, how much was each dress?

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. Price per Pound If 6 pounds of a certain kind of fruit cost \(\$ 4.74,\) how much does 1 pound cost?
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