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Chapter 1: Problem 40

Evaluate the expression for the given values of the variables. $$7 a, \text { for } a=465$$

Short Answer

Expert verified
The value of the expression '7a' for a as 465 is 3255.

Step by step solution

01

Understand the expression

The expression given is '7a'. This means 7 times the variable a.
02

Substitute the given value for variable 'a'

Now substitute the value given for 'a', which is 465, into the expression. This gives: 7(465).
03

Evaluate the expression

To find the value of the expression now, we carry out the multiplication: 7 times 465 equals 3255.

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Key Concepts

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

Variable Substitution
When tackling arithmetic expressions, the first step is often to perform variable substitution. This is how we replace variables in an expression with their given numerical values, so we can simplify the expression into a straightforward arithmetic calculation.
Imagine an expression like \(7a\), where 'a' represents a certain number. If you know that \(a = 465\), you can substitute 465 for 'a' in the expression.
This substitution transforms the expression from a variable format \(7a\) into a numerical one: \(7 \times 465\).

Some points to remember:
  • First, identify each variable in the expression and what value it represents.
  • Be sure to replace these variables correctly; each instance of the variable must be substituted unless otherwise specified.
  • Once substitution is complete, the expression will only contain numbers and operations, ready for further calculations like multiplication.
Proper variable substitution simplifies complex expressions and enables you to move confidently into solving them.
Multiplication
After substituting variables, the next mathematical operation to tackle in an expression like \(7 \times 465\) is multiplication. The goal here is to simplify the expression by applying basic multiplication rules.

Let's dive into how multiplication works:
When you multiply two numbers, you are essentially adding one of the numbers to itself repeatedly, as many times as dictated by the other number. For example, \(7 \times 465\) means adding 465 together seven times.

  • Multiplication is commutative, meaning that \(a \times b = b \times a\), making it possible to rearrange numbers for easier calculation if needed.
  • It is often helpful to break down larger numbers into smaller parts to simplify the calculation, but remember that singular direct multiplication is efficient for most homework problems.
  • Always double-check your arithmetic to prevent minor mistakes from leading to incorrect results.
Applying multiplication will bring you to the final numerical answer of the expression.
Evaluating Expressions
Evaluating expressions is the final step after substituting variables and performing necessary operations. It involves calculating the final result based on the numerical expression derived from earlier steps.
In our example, after substituting and multiplying, the expression \(7 \times 465\) simplifies to a straightforward arithmetic problem, yielding \(3255\).

Here's how evaluating expressions fits in:
  • Ensure all substitutions and calculations leading up to this step are accurate.
  • In expressions with multiple operations, follow the proper order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right) 鈥� abbreviated as PEMDAS.
  • The goal is to simplify the expression step by step, ensuring clarity and correctness.
Evaluating expressions is the culmination of the process, where the complete solution to the problem is achieved.

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Most popular questions from this chapter

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