Question

Evaluate the expression for the given value of the variable. (Review 1.1) \(9 d\) when \(d=0.5\)

Short answer

The evaluated expression \(9d\) when \(d=0.5\) is \(4.5\).

Step-by-step solution

Understanding the given problem

The given expression is \(9d\) and it's given that \(d=0.5\). We have to find the value of the given expression by substituting the value of \(d\).

Substituting the value of d

Replace \(d\) with \(0.5\) in the expression \(9d\). So it becomes \(9*0.5\).

Performing multiplication

Now, by performing the multiplication operation, the result would be \(4.5\).

Key concepts

Substitution Method

The substitution method is a foundational technique used in algebra to evaluate expressions. This method involves replacing variables in an algebraic expression with their numerical values. It's like giving your friends nicknames and then using those nicknames to refer to them; you're substituting one thing for another. For instance, if you're given the expression \(9d\) and you know that the value of \(d\) is 0.5, you essentially plug in 0.5 wherever you see \(d\), turning \(9d\) into \(9 \times 0.5\).

It's imperative to replace the variable with the given value accurately and then proceed with the arithmetic. This two-step process simplifies the expression and makes it ready for evaluation. For learners, it's as straightforward as finding 'X' marks the spot on a treasure map - the X being the variable and the spot being the value you're substituting.

Algebraic Expressions

Algebraic expressions are like sentences that contain numbers, variables (which are symbols representing numbers), and operations (add, subtract, multiply, divide). These expressions are the building blocks of algebra and form the language through which we can describe patterns, relationships, and changes in quantities. They can range from the simple, such as \(3x + 2\), to the complex, like \(4x^2 - 3xy + 6\).

Understanding algebraic expressions is key in mathematics because it allows you to create general solutions that work for many different values, not just one specific case. It’s like cooking with a recipe that tells you to 'add sugar to taste' rather than saying 'add exactly one spoonful of sugar'—it’s a flexible guideline rather than a rigid instruction.

Multiplication Operation

The multiplication operation is a cornerstone of mathematics, often visualized as repeated addition. For example, when we multiply 9 by 0.5, it's the same as adding 0.5 to itself 9 times. In the context of our previous example, the expression \(9d\) with \(d = 0.5\) would translate to multiplying 9 by 0.5. This operation is fundamental as it allows us to scale numbers and figure out total amounts when we have several groups of items.

When you're just starting out with multiplication, it may seem like a lot of memorization. But with practice, recognizing patterns and understanding the principles behind it can make it much easier. Typically, multiplication problems like these are the first step in developing more advanced problem-solving skills in algebra.