Problem 2 - Algebra 1

Question

Consider the verbal phrase: the difference of 7 and a number \(\boldsymbol{n}\). Translate the verbal phrase into an algebraic expression.

Step-by-Step Solution

Answer

The algebraic expression for 'the difference of 7 and a number n' is \(7 - n\).

Step 1: Identify the Operation

The word 'difference' means that you are subtracting one thing from another. So, you are dealing with a subtraction operation in this exercise.

Step 2: Identify the Numbers

In the phrase 'the difference of 7 and a number n', 7 and n are the numbers being considered.

Step 3: Identify the Order of Subtraction

In the English language, the number that comes after 'the difference of' is the one that is being subtracted from, not the one being subtracted. Thus, it is 'n' that is being subtracted from '7'.

Step 4: Translate into an Algebraic Expression

Now that you know the operation is subtraction and that 'n' is subtracted from '7', you can write the algebraic expression, which is \(7 - n\).

Key Concepts

Verbal Phrases

When working with algebra, verbal phrases describe mathematical operations in words. Comprehending these phrases is crucial for translating them into algebraic expressions. In this exercise, the phrase is "the difference of 7 and a number \(n\)." Here, the word "difference" clues us into the operation involved, which is subtraction. Verbal phrases are used in everyday language to describe operations, so recognizing them becomes easier with practice.

• The word "sum" typically refers to addition.
• "Product" indicates multiplication.
• "Quotient" suggests division.
• And as we've seen, "difference" means subtraction.

Understanding these phrases helps one make the correct translation between words and mathematical symbols, a vital skill in algebra.

Subtraction

Subtraction is one of the four basic arithmetic operations. In this context, it involves finding the difference between two numbers. When you see the term "difference," it's indicating a subtraction problem. To subtract, you take one value away from another.
Think of subtraction as asking, "How much remains if we take away?"
It's important to identify the correct order, as subtraction is not commutative.

• For example, \(7 - 3\) gives a different result than \(3 - 7\).

Therefore, the phrase "the difference of 7 and a number \(n\)" translates to subtracting \(n\) from 7, not the other way around.

Translation to Algebraic Expressions

Translating verbal phrases into algebraic expressions involves converting words into mathematical symbols and operations. This skill is essential for solving algebra problems efficiently and accurately.
Start by carefully reading the entire verbal phrase. Identify keywords like "difference," "sum," or "product" that signify specific operations. Locate the numbers or variables you'll be working with.
For our exercise, "the difference of 7 and a number \(n\)" is translated to the algebraic expression \(7 - n\).

• The number 7 is the minuend, or what you're subtracting from.
• The unknown number \(n\) is the subtrahend, which is being subtracted.

With practice, you'll grow more confident in converting complex verbal descriptions into precise algebraic expressions efficiently.