Problem 117 - Algebra A Combined Function

Question

Translate each phrase to an expression. Use \(x\) to represent "a number." The product of -71 and a number

Step-by-Step Solution

Answer

The expression is \(-71x\).

Step 1: Understand the Meaning of 'Product'

In mathematics, the word 'product' refers to the result of multiplying two or more numbers together. In this problem, we need to find the product of -71 and a number.

Step 2: Identify the Number Representation

In this problem, we're asked to represent 'a number' using a variable. We use the variable \(x\) to stand for 'a number.'

Step 3: Write the Expression

Since we want the product of -71 and a number \(x\), we multiply them together to get the expression \(-71x\).

Key Concepts

Product in Mathematics

When we talk about the "product" in mathematics, we're diving into the realm of multiplication. The product is the outcome of multiplying two numbers together. It's a key part of many math problems and isn't just limited to whole numbers.
For example:

• The product of 3 and 4 is 12, as 3 times 4 equals 12.
• For our exercise, the product is between -71 and another number, which means we multiply -71 by that number to find the product.

Remember, when multiplying a negative number with a positive, the result is negative. So, the product of -71 and any number is -71 times that number.

Variable Representation

Variables in math are symbols or letters that stand in for unknown values, like a mystery placeholder! The most common letter used is "x," but they can be any letter. Variables make it easier to work with algebraic expressions without knowing all the details upfront.
In the exercise, we use:

• "x" to represent "a number," which means that "x" can be any number you choose or as determined by context in a problem.
• This allows algebraic expressions to be flexible and adaptable to different scenarios.

Think of variables as helpful tools for creating and understanding expressions about many potential numbers at once.

Translating Word Phrases to Algebra

Turning word phrases into algebra involves identifying key terms and understanding their mathematical meaning. It's like translating a story into numbers and symbols.
Here's a simple guide:

• Find operation words: "Product" means multiplication.
• Identify the numbers involved: -71 in this instance and our mystery number "x."
• Write it out as an algebraic expression: In this case, the phrase "the product of -71 and a number" becomes the expression \(-71x\).

Using this method helps you convert real-world situations into math problems you can solve. Always ensure each word matches a part of your expression – this accuracy is key to successful algebra translation.