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Chapter 1: Problem 38

Evaluate each expression using the values provided. \(8 a-b,\) for \(a=5\) and \(b=7\)

Short Answer

Expert verified
33

Step by step solution

01

Substitute the given values

Replace the variables in the expression with the given values. Here, substitute \(a=5\) and \(b=7\) into the expression \(8a - b\). This results in \(8(5) - 7\).
02

Perform multiplication

Calculate the multiplication part first. Multiply 8 by 5 to get 40. So, the expression now becomes \(40 - 7\).
03

Perform subtraction

Subtract 7 from 40. This gives 33. Therefore, \(8a - b\) evaluates to 33 when \(a=5\) and \(b=7\).

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Key Concepts

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

Substitution
Substitution is a foundational step in evaluating algebraic expressions.
It involves replacing variables with their given numerical values.
In our example, the expression is given as \(8a - b\), and we are told that \(a=5\) and \(b=7\).
By substitution, we replace every instance of \(a\) with 5 and \(b\) with 7.
So the expression \(8a - b\) changes to \(8(5) - 7\).
This step simplifies the expression and makes it ready for further arithmetic operations.
Remember, proper substitution is crucial as it makes complex expressions easier to work with.
Order of Operations
The order of operations is essential in correctly evaluating any mathematical expression.
It dictates the sequence in which different operations must be performed to ensure consistent results.
The acronym PEMDAS helps us remember this sequence:
  • P: Parentheses
  • E: Exponents
  • M: Multiplication and D: Division (from left to right)
  • A: Addition and S: Subtraction (from left to right)

In our expression \(8(5) - 7\), according to the order of operations, we first perform the multiplication:
\(8 \times 5\) to get 40.
Once multiplication is done, we then move on to subtraction:
40 - 7.
Following the correct order allows us to simplify this to 33.
Disregarding the order of operations can lead to incorrect answers.
Arithmetic Operations
Arithmetic operations are the basic calculations involving numbers, such as addition, subtraction, multiplication, and division.
In our evaluation of \(8a - b\), all we need is multiplication and subtraction.
First, we find the product of 8 and 5:
\(8 \times 5 = 40\).
Next, we perform the subtraction by taking 7 away from 40:
40 - 7 = 33.
Simple arithmetic operations are the fundamental tools that allow us to solve more complex mathematical problems.
Understanding how these operations work and how to apply them correctly is essential for all algebra and beyond.

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Most popular questions from this chapter

Insert one pair of parentheses to convert each of the following false statements into a true statement. $$ 2 \cdot 7+3^{2} \cdot 5=104 $$

Find an equivalent expression by factoring. $$ 9 p-3 $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{W} \subseteq Z $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ \left|2^{2}-7\right|^{3}+4 $$

Find an equivalent expression by factoring. $$ 6 y-9 x-3 w $$
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