Problem 31 - Fundamentals of Mathematics

Question

Find the sums in the following 27 problems. If possible, use a calculator to check each result. $$ 0+(-12) $$

Step-by-Step Solution

Answer

The sum is -12.

Step 1: Identify the Numbers in the Problem

The problem involves two numbers: 0 and -12. We need to find their sum.

Step 2: Understand the Concept of Addition with Zero

When you add 0 to any number, the sum is the other number. Adding zero does not change the value of the number being added.

Step 3: Perform the Addition

Since 0 added to -12 does not change the value, the result is simply -12.

Step 4: Check Using a Calculator

Enter the expression 0 + (-12) into a calculator to verify the result. You should see -12 as the output.

Key Concepts

Adding Integers

When it comes to adding integers, it's essential to understand that integers are whole numbers which can be positive, negative, or zero. Adding integers combines these numbers into a single value or sum.

• Positive Integers: Adding two positive numbers is like moving forward on a number line. The total gets bigger.
• Negative Integers: Adding two negative numbers is like moving backward, making the total more negative.
• Mixed Numbers:- When you have one positive and one negative number, imagine it like a tug of war. The final sum depends on which number is farther from zero. If the numbers have the same magnitude but different signs, they cancel each other out, resulting in zero.

To add integers, just count forwards or backwards on the number line. This way, you can visualize the sum better.

Addition with Zero

Zero is a unique integer because it acts as an identity element for addition. This means adding zero to any number doesn’t change that number.

• '0’ Virtue: Zero by itself doesn't add any value. It's almost like doing nothing in the number world. If you start with any number and add 0, you get back the same number.
• Practical Understanding: Think about having a balance at $50 in your bank account. If you neither deposit nor withdraw anything (adding zero), it is still $50.

In our exercise, adding 0 to -12 means the result remains -12 because zero does not affect other numbers during addition.

Negative Numbers

Negative numbers represent values less than zero, like depths below sea level or temperatures below freezing. Understanding how they interact with other values, especially when adding, is vital.

• Adding Negative Numbers: When you add negative numbers, think of it as owing more. If you have -5 and add -3, it’s like owing 5, then owing 3 more, which results in -8.
• Visualize with a Number Line: On a number line, negative numbers are to the left of zero. Adding a bigger negative number means moving further left, making the sum more negative.
• Practical Scenario: If you have a debt of 12 units and add no further amount (0), your debt remains -12.

Comprehending negative numbers helps when solving real-world problems involving balances or temperatures.