Problem 134 - Beginning and Intermediate Algebra

Question

Write each of the following as an expression and evaluate. 7 subtracted from the quotient of 0 and 5

Step-by-Step Solution

Answer

The result is -7.

Step 1: Understand the Problem Statement

We need to find the expression for '7 subtracted from the quotient of 0 and 5'. Here, quotient signifies division. So, first, we need to divide 0 by 5.

Step 2: Calculate the Quotient

Now, let's find the quotient. 0 divided by 5 is expressed as \( \frac{0}{5} \). This division evaluates to 0 because dividing zero by any nonzero number results in zero.

Step 3: Form the Expression for Subtraction

The problem asks to subtract 7 from the quotient we found. The quotient is 0, so the expression becomes \( 0 - 7 \).

Step 4: Evaluate the Expression

Perform the subtraction: \( 0 - 7 = -7 \). Thus, after evaluating the expression, we get -7.

Key Concepts

Understanding Division

Division is a fundamental math operation where you split a number (the dividend) into equal parts, according to another number (the divisor). To divide means to determine how many units of the divisor fit into the dividend. This operation is essential and widely used in various mathematical contexts.

• When the dividend is zero, as in \( \frac{0}{5} \), the result is always zero. That's because zero "fit" into any number of parts without remainder.
• However, dividing by zero is undefined. It can never be done as there's no sensible way to distribute parts into zero groups.

Understanding these rules is important when working with algebraic expressions, ensuring division is only performed where it makes sense.

The Process of Subtraction

Subtraction is another basic arithmetic operation. It involves taking one number away from another, which helps determine the difference between them. The expression "7 subtracted from the quotient of 0 and 5" involves subtraction after evaluating the initial operation (division).

• To subtract one number from another means to determine what remains when the first number is removed from the second.
• For example, in \(0 - 7\), you need to understand that you're effectively shifting to the left on a number line, ending up at -7.
• This action reduces your total, moving into negative numbers if the number being subtracted is larger.

Subtraction, when correctly understood, is important in calculating differences, such as in financial contexts or measurement.

Evaluating Expressions

Evaluating expressions involves performing the operations defined within to achieve a specific outcome or solution. When given tasks like "7 subtracted from the quotient of 0 and 5," you follow a clear path to reach the result.

Steps in Evaluation

• First, identify the operations involved. In this case, both division and subtraction.
• Next, compute each operation step-by-step. Begin with division as prioritized here before moving to subtraction.
• Finally, execute the subtraction based on the quotient obtained. For the expression \(0 - 7\), the result is -7.

Evaluating expressions accurately helps in problem-solving across various real-life scenarios, ensuring the right results through correct procedures.