Problem 57 - Beginning and Intermediate Algebra

Question

Find each difference. $$ -7-1 $$

Step-by-Step Solution

Answer

-8

Step 1: Identify the Math Operation

The problem involves subtraction: -7 - 1

Step 2: Rewrite as Addition

Subtracting a number is the same as adding its negative. Rewrite -7 - 1 as: -7 + (-1)

Step 3: Combine the Numbers

Now, add the two negative numbers together: -7 + (-1) . When you add two negative numbers, the result is also negative. Calculate: -7 + (-1) = -8

Key Concepts

Integer Operations

Understanding how to perform operations with integers is crucial for solving many mathematical problems. In arithmetic, integers are whole numbers that can be positive, negative, or zero. The four basic operations with integers are addition, subtraction, multiplication, and division. To handle these operations efficiently, remember:

• Adding two positive integers always gives a positive result.
• Adding two negative integers always gives a negative result.
• Subtracting an integer is like adding its opposite.
• When multiplying or dividing two integers with the same sign, the result is positive.
• When multiplying or dividing two integers with different signs, the result is negative.

For example, in the problem -7 - 1, we use subtraction. But we can transform this into an addition problem to make it easier to solve.

Negative Numbers

Negative numbers can be tricky but are easy to understand with practice. A negative number is any number less than zero, represented with a minus sign (-). Here are some key points to remember:

• A negative number plus another negative number always results in a more negative number. For example, -7 + (-1) = -8.
• Negative numbers are less than zero and appear to the left of zero on the number line, indicating their smaller value compared to positive numbers.
• When you subtract a number, you move leftward on the number line.

In our problem -7 - 1, converting it to -7 + (-1) helps by making the operation straightforward: combining two negative numbers into a more negative result.

Addition of Integers

Adding integers, whether they are positive or negative, follows specific rules. Knowing these rules helps in efficiently combining numbers:

• When you add two positive integers, the result is positive. For example, 5 + 3 = 8.
• When you add two negative integers, you get a more negative integer. For example, -4 + (-6) results in -10.
• When you add a positive integer and a negative integer, the result depends on which number has the greater absolute value. For example, 7 + (-5) equals 2, since 7 is greater.

In the given exercise -7 - 1, converting to -7 + (-1) illustrates this. Since both numbers are negative, they combine to give -8. This method simplifies the calculation by using consistent addition rules.