Problem 23 - Prealgebra

Question

Subtract. $$-79-21$$

Step-by-Step Solution

Answer

-100

Step 1: Understand the Expression

We have the expression \(-79-21\), which requires subtraction of 21 from -79. This can also be viewed as adding a negative number to -79.

Step 2: Rewrite as Addition of Negatives

Instead of subtracting 21, think of this as adding the negative of 21. So the expression is equivalent to \(-79 + (-21)\).

Step 3: Combine the Numbers

Both numbers are negative, so add their absolute values and keep the negative sign. Calculate \(79 + 21 = 100\). Thus, \(-79 + (-21) = -100\).

Key Concepts

Integer Arithmetic

Understanding integer arithmetic is key when working with positive and negative numbers. There are different operations in arithmetic, such as addition, subtraction, multiplication, and division, and they are applied in specific ways to integers.
When you perform subtraction with integers, you may actually be performing addition in disguise. For example, when you subtract a number, you are in essence adding its negative counterpart. This is a crucial concept to grasp, particularly with negative numbers.
Remembering to transform subtraction into addition of negatives helps in simplifying problems. It aligns with the rule that - subtracting a positive number is the same as adding a negative. This clarification ensures clarity when solving equations involving negative numbers.

Negative Numbers

Negative numbers are values less than zero. They are represented with a minus sign (-). Using negative numbers becomes particularly important when representing something that has been withdrawn, missing, or reduced.
When dealing with negative numbers:

• They are located to the left of zero on a number line.
• They follow specific rules, such as two negative signs create a positive when multiplied or divided.
• Operations on negative numbers can be visualized as moving left (subtracting) or right (adding) on a number line.

This spatial representation simplifies understanding, as one can literally 'see' the math in action.

Addition of Negatives

When you add two negative numbers, you follow a simple process. You add their absolute values and then attach a negative sign to the result. Absolute values ignore the negative sign, focusing on the distance from zero.
For instance, adding degative transformations can be clarified with examples: - If we add degative 5 ( -5) and degative 3 ( -3), we calculate 5 + 3 = 8, and then keep the negative sign to get -8. Translating - arithmetic operations into steps like this simplifies calculations and decreases mistakes. These clear-cut steps aid in grasping the addition of negatives more easily, turning confusion into confidence.