Problem 75 - Elementary and Intermediate Algebra

Question

Perform the operations. $$ 8-9-10 $$

Step-by-Step Solution

Answer

-11

Step 1: Evaluate the First Operation

The expression to solve is \( 8 - 9 - 10 \). Let's start by performing the first operation, which is \( 8 - 9 \). Subtract 9 from 8, which gives us \(-1\).

Step 2: Evaluate the Second Operation

Now we have the result from the first step, \(-1\). We need to subtract 10 from \(-1\). Calculate \(-1 - 10\), which results in \(-11\).

Key Concepts

Subtraction

Subtraction is one of the most fundamental arithmetic operations. In subtraction, you take one number away from another. It's often represented by the minus sign (-). Let's break it down further.

• Minuend: The number from which you subtract. In the expression, it's the number on the left.
• Subtrahend: The number you subtract from the minuend. It's the number on the right.
• Difference: The result you get after subtraction.

For example, in the expression \(8 - 9\), 8 is the minuend, 9 is the subtrahend, and the difference is -1.

Subtraction allows us to find out how much more one quantity is compared to another or by how much one quantity exceeds the other.

Negative Numbers

Negative numbers are numbers less than zero, represented with a minus sign (-). They can be a bit tricky, especially in subtraction, so let's look at them more closely.

Negative numbers are used to describe values below zero, often seen in temperatures, bank accounts, and elevation levels.

• For example, \(-1\) is one unit below zero on the number line.
• When you subtract a larger number from a smaller one, your result is a negative number.

Let's consider the operation \(-1 - 10\). Beginning at \(-1\) on the number line, move 10 units left, landing at \(-11\). The concept of negative numbers is critical for understanding shifts on the number line and managing them correctly in arithmetic operations.

Order of Operations

The order of operations is a rule used to clarify which procedures to perform first in a mathematical expression. This concept ensures everyone solves expressions in the same way, avoiding different answers to the same problem.

Remember the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). However, in straightforward expressions like \(8 - 9 - 10\), the order is simpler:

Subtraction and addition proceed from left to right, as they appear in the expression.

• First, perform \(8 - 9\), resulting in \(-1\).
• Next, calculate \(-1 - 10\), yielding \(-11\).

Understanding and correctly applying *order of operations* is vital in getting accurate results in math calculations.