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Chapter 1: Problem 7

Identify each as a sum, difference, product, or quotient. 8 decreased by \(x\)

Short Answer

Expert verified
The given statement symbolizes a 'difference'.

Step by step solution

01

Identify the Action

The first step is to identify the action that is being carried out. The phrase '8 decreased by \(x\)' is implying a subtraction operation.
02

Correspond the Action to a Mathematical Operation

Next, we correspond this operation to the pertinent mathematical term. In this scenario, since 'decreased by' implies subtraction, it corresponds to a 'difference'.

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Key Concepts

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

Subtraction
Subtraction is one of the basic mathematical operations, which we often use to determine how much something is lessened or removed. In other words, subtraction helps us find out what remains when we take away a part from a whole. Consider it like taking apples away from a basket and noting how many are left.
In terms of numbers and terms, subtraction can be visually represented by the "-" symbol. For example, in the phrase "8 decreased by \(x\)", the operation is subtraction. Here, 8 is the quantity you have, and \(x\) is what you remove from it.
  • Subtraction Formula: \( a - b = c \), where \( a \) is the whole, \( b \) is the part you take away, and \( c \) is the result.
  • Performing subtraction can help solve problems in everyday life, like counting change or measuring distances reduced.
Sum
Contrary to subtraction, the sum is the result of adding numbers or quantities together. When you hear 'sum,' think about bringing things together, such as assembling ingredients in a recipe. In math, sum means putting two or more numbers together to find their total.
Although the main focus of our original problem is subtraction, understanding the sum is crucial for grasping basic algebra. This knowledge helps differentiate between operations.
  • Sum Formula: \( a + b = c \), where \( a \) and \( b \) are numbers being added, and \( c \) is their total.
  • When practicing math problems, always remember that the context will guide whether you sum or subtract values.
Difference
When we discuss the difference in math, we're referring to the result of a subtraction operation. It answers the question: how much is left after one quantity is subtracted from another?
In our exercise, and particularly the phrase "8 decreased by \(x\)," this results in a mathematical difference. In simple terms, it is what remains after taking \(x\) from 8.
  • The outcome of \( 8 - x \) is the 'difference', showing what remains.
  • Difference helps compare two numbers, revealing how one measures up against the other.
Let鈥檚 apply this: if you had 8 cookies and somebody took \(x\) of them, the cookies left with you are exactly the 'difference'.
Basic Algebra
Basic algebra is the foundational step into the world of variables and unknowns. It equips us with the tools to express situations in mathematical expressions and solve them. This exercise, involving the phrase "8 decreased by \(x\)," provides practice in translating words into algebraic terms.
In algebra, 'decreased by' typically indicates that subtraction is involved, hinting at an equation like \(8 - x\).
  • Algebra helps us form equations: Here it helps transpose a verbal sentence into \(8 - x\).
  • Understanding operations like addition and subtraction makes simplifying expressions and solving for variables easier.
By practicing basic algebra, you develop critical thinking skills useful far beyond mathematics, as it encourages logical analysis and problem-solving.

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