Problem 22 - Elementary Algebra

Question

For the following exercises, perform the indicated operations. $$ 1-7 $$

Step-by-Step Solution

Answer

Answer: The result of 1 - 7 is -6.

Step 1: Understand the operation

The given operation is subtraction, which means we need to find the difference between two numbers, 1 and 7. We need to find the result of 1 subtracted by 7 (1 - 7).

Step 2: Perform the subtraction

To subtract 7 from 1, recall that we can think of subtraction as finding the difference between two numbers on a number line. Locate 1 on the number line, and move 7 units to the left, since we are subtracting a positive number. The number we arrive at is -6. Therefore, the result of the subtraction is \(-6\).

Key Concepts

Understanding Subtraction

Subtraction is one of the basic arithmetic operations that allows us to find the difference between two numbers. Subtraction is often described as "taking away" a number from another, or finding how much something has reduced or decreased. It's a fundamental concept in mathematics which serves as the opposite of addition.

When we subtract, we start with a *minuend*, which is the initial amount, and we subtract a *subtrahend* from it. The result is known as an *difference*. For example, in the equation \(1 - 7\), *1* is the minuend, *7* is the subtrahend, and \(-6\) is the difference.

• Minuend: the number you start with.
• Subtrahend: the number you subtract.
• Difference: the result of subtraction.

Subtraction can also be visualized on a number line, which helps in understanding the direction and magnitude of the operation.

Exploring Negative Numbers

Negative numbers are numbers less than zero, and play a key role in subtraction, especially when the result is a decrease below zero. They can often be thought of as debts, losses, or temperatures below freezing.

When subtracting a larger number from a smaller one, the result is a negative number. It's like moving backwards on the number line. For instance, subtracting 7 from 1 results in \(-6\), indicating we've moved 6 steps left past zero into the negative side.

• Negative numbers indicate values less than zero.
• Represent situations like being in debt or below zero temperatures.
• Subtraction across zero results in negative numbers.

Getting comfortable with these concepts can make understanding and working with negative numbers much easier.

Using a Number Line for Subtraction

A number line is a visual tool used to represent numbers by marking them as points along a line. It's extremely useful in understanding subtraction as it provides a clear picture of how numbers relate to each other.

Imagine the number line as a horizontal line with zero in the center. Positive numbers move to the right, while negative numbers extend to the left. To subtract using a number line, you start at the number you're subtracting from, and move left by the amount you're subtracting.

In the case of \(1 - 7\):

• Start at 1 on the number line.
• Move 7 spaces to the left because you're subtracting 7.
• Land on -6 as a result.

This technique helps visualize and better understand the results of subtraction, including when crossing into negative numbers.