Problem 21 - Prealgebra

Question

Subtract. $$-30-20$$

Step-by-Step Solution

Answer

The result of -30 - 20 is -50.

Step 1: Identify the Operation

First, identify that you need to perform a subtraction operation with the numbers inside the expression. The expression given is \[-30 - 20\] which involves subtracting 20 from -30.

Step 2: Apply the Negative Subtraction Rule

When subtracting a positive number from a negative number, you move further left on the number line. Subtracting 20 from -30: \[-30 - 20 = -30 + (-20)\].

Step 3: Combine the Numbers

Add the two negative numbers together by combining their absolute values and retaining the negative sign: \[-30 + (-20) = -50\].

Key Concepts

Negative Numbers

Negative numbers are values less than zero. In mathematical terms, they are represented with a minus sign (-) before the number. These numbers are crucial in mathematics as they help in understanding and describing values below zero. A negative number often represents a deficit or something owed, such as temperatures below freezing, or a debt.

• Simplifying expressions with negative numbers requires careful application of arithmetic rules, such as adding and subtracting while considering their signs.


• For instance, when subtracting a positive number from a negative one, like \(-30 - 20\), it's equivalent to adding the negative of the number being subtracted, turning it into \(-30 + (-20)\)


• This results in a deeper negative outcome as the overall position on the number line moves left.

Understanding and manipulating negative numbers is essential for solving problems in arithmetic, particularly when calculations involve conditions below the neutral point of zero.

Number Line

A number line is a visual representation of numbers on a straight line. It extends in both directions infinitely, with zero placed generally at the center. You can mark both positive and negative numbers on this line, making it a great tool for understanding basic operations, especially involving direction and movement.

• To perform subtraction using a number line, start at the first number, and move to the left to subtract.


• For example, with \(-30 - 20\)
, start at -30. From -30, move 20 steps to the left, which results in -50.

• This visualizes the concept of subtraction as moving left for negative impact.

Using a number line helps students visualize how numbers interact with each other, particularly negative numbers, enhancing comprehension and problem-solving accuracy.

Prealgebra

Prealgebra is a branch of mathematics that lays the groundwork for algebra. It covers basic arithmetic operations and introduces concepts such as integers, fractions, decimals, and basic geometry. This field of math also emphasizes understanding of numerical concepts and the relationships between numbers.

• When encountering expressions like \(-30 - 20\), prealgebra foundations encourage examination of both individual terms and the collective interactions between them.


• The expression involves understanding how to deal with negatives and compute step-by-step the correct outcome.


• Learning prealgebra ensures students grasp fundamental operations before delving into more abstract algebraic concepts.

By mastering prealgebra, students prepare themselves for the challenges of algebraic thinking and advanced mathematical concepts, ensuring a solid mathematical base.