Problem 18 - Prealgebra

Question

Subtract. $$20-32$$

Step-by-Step Solution

Answer

The result of subtracting 32 from 20 is -12.

Step 1: Identify the Operation

The task requires us to subtract one number from another, specifically to subtract 32 from 20.

Step 2: Perform the Subtraction

Since 20 is smaller than 32, this operation will result in a negative number. We calculate the difference by thinking of it as 32 minus 20, which equals 12. Since we subtracted a larger number from a smaller one, the result is negative: -12.

Key Concepts

Understanding Negative Numbers

Negative numbers can seem a bit tricky at first, but they add a whole new dimension to mathematics. A negative number is any number less than zero, represented with a minus sign (−) in front of it.
For example, −5 is five less than zero. These numbers often represent values like debts, temperatures below freezing, or directions going backward.

• Negative numbers appear on the left side of zero on a number line.
• When adding a negative number, you are essentially subtracting its absolute value.

In subtraction, if the result is negative, it means the subtracted number is larger than the number from which you are subtracting. Practicing with negative numbers helps develop a strong understanding of integer operations.

Diving into Integer Operations

Integer operations are the basic arithmetic operations that involve whole numbers, both positive and negative. These include addition, subtraction, multiplication, and division.
Mastering how to operate with integers is crucial in math, as they form the foundation for algebra and later math studies.

• Addition: When adding numbers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the "larger" number (in terms of absolute value).
• Subtraction: When subtracting, change the sign of the number being subtracted and add. For example, subtracting 5 from 3 means you calculate 3 + (−5), yielding −2.
• Multiplication and Division: The product or the quotient of numbers with different signs is negative, while it is positive if both numbers have the same sign.

The ability to accurately perform these operations is essential for solving real-world problems and advanced math equations.

The Importance of a Number Line

A number line is a visual tool used to represent numbers and perform operations such as addition and subtraction. It’s a straight, horizontal line where numbers are placed at equal intervals.
This tool is particularly useful in understanding concepts involving negative numbers and integer operations.

• The number line extends infinitely in both positive and negative directions.
• Zero is typically placed in the center, with positive numbers to the right and negative numbers to the left.

When subtracting 32 from 20, you start at 20 on the number line and move 32 steps to the left, landing on −12.
This movement not only visualizes subtraction but also shows how larger values can lead to negative results when subtracted from smaller ones. Using a number line helps students better grasp distance and direction in math.