Question

Which of the following best describes the expression \(7(y-1)\) ? A. sum B. difference C. product D. quotient

Short answer

C. product

Step-by-step solution

Understand the Given Expression

The given expression is 7(y-1). It consists of a constant (7) multiplied by another expression (y-1).

Identify the Operations

Within the parentheses, y-1 represents a subtraction operation, creating a difference. However, the entire expression involves multiplying 7 by (y-1).

Classify the Main Operation

The outermost operation in the expression is multiplication. Regardless of the operations inside the parentheses, the expression as a whole is multiplied by 7.

Match with Given Options

Among the options provided (sum, difference, product, quotient), the term that best describes an expression involving multiplication is 'product'.

Key concepts

mathematical operations

Mathematical operations are the basic building blocks of math. They include addition, subtraction, multiplication, and division. They allow us to manipulate numbers and expressions in various ways. In the exercise, we deal with two main operations: subtraction and multiplication.

• Addition: Combining two numbers to get a sum.
• Subtraction: Taking one number away from another to get a difference.
• Multiplication: Scaling one number by another to get a product.
• Division: Splitting one number into parts defined by another to get a quotient.

By identifying these operations, we can better understand how to solve expressions and equations.

algebraic expressions

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. In our problem, the expression is \(7(y-1)\).

Here's how to break it down:

A variable is a symbol (often a letter) that represents an unknown value. In our expression, 'y' is the variable.

Constants are fixed values like '7' in our expression.

Parentheses are used to group parts of an expression to show that operations inside them should be performed first. For example, in \(y-1\), we perform the subtraction before multiplication.

By understanding these parts, navigating any algebraic expression becomes much easier!

multiplication

Multiplication is one of the core arithmetic operations and is often used in algebraic expressions. It involves scaling one number by another. In the exercise, we have \(7(y-1)\), where 7 multiplies the entire \(y-1\) expression.

Here's how to understand it:

When you see a number and parentheses, like 7(y-1), it means you multiply 7 by each term inside the parentheses.

Performing the operations in the correct order is crucial: First, do the subtraction inside the parentheses (y-1), then multiply the result by 7.

Remember, the overall result of this operation is called the product. That's why the answer to the exercise is 'product'.

Mastering multiplication and understanding how it combines with other operations will make solving algebraic expressions much smoother!