Without Using A Calculator, Evaluate The Expression $\frac{15}{x}$ For Each Value Of $x$ Given Below. You Do Not Need To Reduce Your Answers For This Exercise.$[ \begin{array}{|c|c|c|c|c|} \hline x & -30 & -15 & -5 & -3
Introduction
In this article, we will explore the process of evaluating expressions without the aid of a calculator. We will focus on the expression $\frac{15}{x}$ and evaluate it for each value of $x$ given below. This exercise will help us understand the concept of division and its application in real-world scenarios.
Understanding the Expression
The given expression is $\frac{15}{x}$. This expression represents the quotient of 15 divided by $x$. To evaluate this expression, we need to divide 15 by the value of $x$.
Evaluating the Expression for Each Value of x
We will evaluate the expression $\frac{15}{x}$ for each value of $x$ given below.
x = -30
To evaluate the expression for $x = -30$, we need to divide 15 by -30.
The value of the expression for $x = -30$ is $-\frac{1}{2}$.
x = -15
To evaluate the expression for $x = -15$, we need to divide 15 by -15.
The value of the expression for $x = -15$ is $-1$.
x = -5
To evaluate the expression for $x = -5$, we need to divide 15 by -5.
The value of the expression for $x = -5$ is $-3$.
x = -3
To evaluate the expression for $x = -3$, we need to divide 15 by -3.
The value of the expression for $x = -3$ is $-5$.
Conclusion
In this article, we evaluated the expression $\frac{15}{x}$ for each value of $x$ given below. We used the concept of division to find the value of the expression for each value of $x$. This exercise helped us understand the application of division in real-world scenarios.
Discussion
The expression $\frac{15}{x}$ can be evaluated for any value of $x$. The value of the expression will depend on the value of $x$. In this article, we evaluated the expression for four different values of $x$.
Real-World Applications
The concept of division is widely used in real-world scenarios. For example, in cooking, we use division to measure ingredients. In finance, we use division to calculate interest rates. In science, we use division to calculate the concentration of a solution.
Tips and Tricks
When evaluating expressions without a calculator, it is essential to follow the order of operations. This means that we need to perform division before multiplication and addition.
Common Mistakes
When evaluating expressions without a calculator, it is common to make mistakes. To avoid mistakes, we need to double-check our calculations.
Conclusion
Introduction
In our previous article, we explored the process of evaluating expressions without the aid of a calculator. We focused on the expression $\frac{15}{x}$ and evaluated it for each value of $x$ given below. In this article, we will answer some frequently asked questions related to evaluating expressions without a calculator.
Q&A
Q: What is the order of operations when evaluating expressions without a calculator?
A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate an expression with a negative number?
A: When evaluating an expression with a negative number, we need to remember that a negative number is the opposite of a positive number. For example, if we have the expression $\frac{15}{-30}$, we can rewrite it as $\frac{-15}{30}$.
Q: What is the difference between a fraction and a decimal?
A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. For example, $\frac{1}{2}$ is a fraction. A decimal is a way of expressing a fraction as a number with a point separating the whole number part from the fractional part. For example, $0.5$ is a decimal.
Q: How do I convert a fraction to a decimal?
A: To convert a fraction to a decimal, we can divide the numerator by the denominator. For example, to convert $\frac{1}{2}$ to a decimal, we can divide 1 by 2, which gives us 0.5.
Q: What is the difference between a variable and a constant?
A: A variable is a letter or symbol that represents a value that can change. For example, $x$ is a variable. A constant is a value that does not change. For example, 5 is a constant.
Q: How do I evaluate an expression with a variable?
A: To evaluate an expression with a variable, we need to substitute the value of the variable into the expression. For example, if we have the expression $\frac{15}{x}$ and we know that $x = 30$, we can substitute 30 into the expression to get $\frac{15}{30}$.
Q: What is the difference between a rational number and an irrational number?
A: A rational number is a number that can be expressed as a fraction. For example, $\frac{1}{2}$ is a rational number. An irrational number is a number that cannot be expressed as a fraction. For example, $\sqrt{2}$ is an irrational number.
Q: How do I evaluate an expression with a rational number?
A: To evaluate an expression with a rational number, we can simply substitute the rational number into the expression. For example, if we have the expression $\frac{15}{x}$ and we know that $x = \frac{1}{2}$, we can substitute $\frac{1}{2}$ into the expression to get $\frac{15}{\frac{1}{2}}$.
Q: What is the difference between a positive number and a negative number?
A: A positive number is a number that is greater than zero. For example, 5 is a positive number. A negative number is a number that is less than zero. For example, -5 is a negative number.
Q: How do I evaluate an expression with a positive number?
A: To evaluate an expression with a positive number, we can simply substitute the positive number into the expression. For example, if we have the expression $\frac{15}{x}$ and we know that $x = 5$, we can substitute 5 into the expression to get $\frac{15}{5}$.
Q: What is the difference between a whole number and a decimal number?
A: A whole number is a number that is not a fraction. For example, 5 is a whole number. A decimal number is a number that has a fractional part. For example, 5.5 is a decimal number.
Q: How do I evaluate an expression with a whole number?
A: To evaluate an expression with a whole number, we can simply substitute the whole number into the expression. For example, if we have the expression $\frac{15}{x}$ and we know that $x = 5$, we can substitute 5 into the expression to get $\frac{15}{5}$.
Conclusion
In this article, we answered some frequently asked questions related to evaluating expressions without a calculator. We covered topics such as the order of operations, evaluating expressions with negative numbers, fractions, and decimals, and more. We hope that this article has been helpful in answering your questions and providing you with a better understanding of evaluating expressions without a calculator.