Problem 23 - Fundamentals of Mathematics

Question

For the following 18 problems, perform each subtraction. Use a calcula tor to cherk each result. $$ 14-30 $$

Step-by-Step Solution

Answer

The result of 14 - 30 is -16.

Step 1: Understand the Problem

We need to subtract the number 30 from 14. In mathematical terms, we need to find out what 14 minus 30 equals to.

Step 2: Perform the Subtraction

To subtract 30 from 14, we can rearrange this to be 14 - 30 which is dissimilar from 30 - 14 and usually results in a negative number because the second number is larger than the first. Perform the subtraction: \[14 - 30 = -16\]

Step 3: Verify with a Calculator

Use a calculator to double-check the result of 14 - 30. Enter '14', press the subtraction sign '-', enter '30', and press 'equals' '='. The calculator should display '-16', confirming our calculation.

Key Concepts

Negative Numbers

Understanding negative numbers is crucial in arithmetic, especially when dealing with subtraction. Negative numbers are values less than zero, often represented with a minus sign (-). They appear on the left side of the number line. For instance, when you subtract a larger number from a smaller one, the result is a negative number. Let’s take the exercise where you are asked to subtract 30 from 14. Since 30 is larger than 14, the difference is negative, specifically -16.

Here's how you might visualize it: imagine having 14 apples, and if 30 apples were taken away (even though impossible to do physically), the concept of negative numbers helps illustrate the resulting shortage, represented by -16 apples. Understanding these numbers helps in various scenarios, from calculating temperatures below zero to managing debts.

Using a Calculator for Verification

Calculators are essential tools when confirming arithmetic operations. They can quickly verify the results of mathematical problems, ensuring accuracy, especially when dealing with subtraction involving negative numbers.

To double-check the previous example, input the problem into a calculator like this:

• Press '1' and '4' to input the number 14.
• Press the subtraction key '-'.
• Press '3' and '0' to input the number 30.
• Press the equal sign '='.

The display should show -16, confirming the manual calculation result. Calculators are especially useful when learning basic arithmetic, offering quick confirmation to ensure the understanding of negative numbers is on point.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. Each operation has its own rules and sub-categories. Subtraction, for example, can lead to negative results when dealing with unequal numbers. Imagine subtracting 30 from 14, where subtraction means taking away parts from a whole.

Let’s break it down:

• Identify the numbers involved: 14 (minuend) and 30 (subtrahend).
• Perform the subtraction: \[14 - 30 = -16\]
• The negative sign indicates the result is below zero.

Understanding these operations is foundational in mathematics. It paves the way for tackling more complex problems involving financial transactions, measurements, and data analysis. Practicing these basics builds confidence and improves problem-solving skills.