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Chapter 1: Problem 63

Evaluate each expression if \(a=5, b=1,\) and \(c=3\) $$\frac{65}{a}$$

Short Answer

Expert verified
The value of the expression is 13.

Step by step solution

01

Identify the Expression

The expression given to us is \( \frac{65}{a} \). Our goal is to evaluate this expression by substituting the value of \(a\).
02

Substitute the Given Value

Substitute the given value of \(a\), which is 5, into the expression: \( \frac{65}{5} \).
03

Perform the Division

Divide 65 by 5. Calculate \( 65 \div 5 \) to get 13.

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Key Concepts

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

Basic Arithmetic
Basic arithmetic involves understanding the four fundamental operations: addition, subtraction, multiplication, and division. These operations form the foundation of all mathematics.
In this exercise, the focus is on division, which is used to split a quantity into equal parts. When we talk about division, we deal with a dividend (the number to be divided) and a divisor (the number by which we divide).
Understanding basic arithmetic is essential because it not only helps in solving simple problems but also lays the groundwork for tackling more complex algebraic equations.
Substitution
Substitution is a method used in mathematics to replace variables with known values. This is particularly useful when dealing with algebraic expressions, as it allows us to evaluate these expressions with actual numbers.
In this context, the given expression is \( \frac{65}{a} \). Since we know that \(a\) equals 5, substitution allows us to replace \(a\) with 5, turning the expression into \( \frac{65}{5} \).
This step is crucial, as it simplifies the problem-solving process, making it possible to compute a specific numerical result.
Division
Division is one of the core operations in basic arithmetic, instrumental for evaluating expressions like \( \frac{65}{a} \).
After substitution, we convert the original expression to \( \frac{65}{5} \). Now, division comes into play. To divide, we determine how many times the divisor (5 in this case) fits into the dividend (65).
To perform the division:
  • First, identify how many times 5 divides into 65.
  • This results in a quotient of 13, as 5 goes into 65 exactly 13 times without any remainder.
Dividing numbers accurately is key to solving many mathematical problems, allowing us to calculate precise results.
Evaluate Expressions
Evaluating expressions involves determining the value of an algebraic expression by performing operations and applying given values to variables.
In this exercise, evaluating the expression \( \frac{65}{a} \) means calculating its value for a specific value of \(a\).
Through substitution and basic arithmetic operations, we simplify the expression to \( \frac{65}{5} \) and then further to 13.
To evaluate expressions effectively:
  • Ensure that you substitute variables with their assigned values accurately.
  • Perform arithmetic operations methodically to avoid errors.
This approach ensures that mathematical expressions are evaluated accurately, contributing to a better understanding of problem-solving techniques in algebra.

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