Problem 57 - Elementary and Intermediate Algebra

Question

Subtract. $$ -7-4 $$

Step-by-Step Solution

Answer

-11

Step 1: Identify the Terms

Observe the expression -7 - 4 which has two terms: -7 and 4.

Step 2: Rewrite the Expression

Rewrite the subtraction as an addition problem: -7 - 4 = -7 + (-4)

Step 3: Add the Numbers

Combine the two numbers. Since both are negative, add their absolute values: |-7| + |-4| = 7 + 4 = 11. The sum is -11 because both original numbers were negative.

Key Concepts

Integer Subtraction

Subtracting integers can seem tricky at first, but it becomes easier once you understand the rules. When you subtract a number, you are essentially adding its opposite. For example, subtracting 4 is the same as adding -4:

• Original: -7 - 4

Convert the subtraction into an addition of a negative number:

• Converted: -7 + (-4)

Now, you can add the numbers together following the rules for adding negative numbers. This might make it easier to solve the problem accurately every time. Feel free to always change subtraction problems involving integers into addition problems for better clarity.

Absolute Value

Understanding absolute value is crucial when adding and subtracting integers. The absolute value of a number is its distance from zero on the number line, without considering its direction.
For example:

• The absolute value of -7 is 7.
• The absolute value of -4 is 4.

This means when you add or subtract negative numbers, you can calculate the absolute values and then add them together as if they were positive. Converting negative numbers to their absolute values allows you to focus on combining the quantities, rather than worrying about the signs until the final step.

Addition of Negative Numbers

Adding negative numbers can be thought of as combining debts or losses. When you add two negative numbers, you effectively combine their absolute values and then attach a minus sign to the result. For instance: Given the problem -7 + (-4), convert to absolute values:

• |-7| = 7
• |-4| = 4

Combine these values:

• 7 + 4 = 11

The result is 11, and since you were adding two negative numbers, the final result is negative:

• -7 + (-4) = -11

Always remember that adding more negative numbers increases the total negative value, just like combining more losses or debts would increase your total debt. Understanding this can help you solve integer subtraction and negative addition problems with confidence.