Problem 31 - Fundamentals of Mathematics

Question

For the following 18 problems, perform each subtraction. Use a calcula tor to cherk each result. $$ 0-(-10) $$

Step-by-Step Solution

Answer

0 - (-10) equals 10.

Step 1: Understand the Problem

We need to subtract \(-10\) from 0, which is written as \(0 - (-10)\). This is a subtraction operation involving a negative number.

Step 2: Simplify the Subtraction

Subtracting a negative number is the same as adding its positive value. Therefore, \(0 - (-10)\) simplifies to \(0 + 10\).

Step 3: Perform the Addition

Calculate the result of the addition: \(0 + 10 = 10\).

Step 4: Verify with a Calculator

Use a calculator to enter \(0 - (-10)\) and check that the result is indeed 10.

Key Concepts

Subtraction

Subtraction is one of the four basic arithmetic operations. It involves finding the difference between two numbers. In simple terms, subtraction is what we use to take away one number from another. We represent subtraction using the minus sign "-". It's helpful to think of subtraction as counting backward or removing items from a group.

For instance, if you have 15 apples and you subtract 5, you're left with 10 apples. The operation can be written as:
\[ 15 - 5 = 10 \]

• The number from which we subtract is called the minuend.
• The number that is being subtracted is the subtrahend.
• The answer we get is the difference.

In the exercise example, subtraction was used with a twist: subtracting a negative number, which we'll explore next.

Negative Numbers

Negative numbers are like the opposites of positive numbers and are often used to represent values below zero. When we see a number with a minus sign in front, like \(-5\),it is a negative number. These numbers are useful for expressing debts or temperatures below freezing, among other things.

A unique property of negative numbers is their behavior in subtraction. Subtracting a negative number is similar to adding its positive counterpart. This can be seen in the exercise:
\[ 0 - (-10) \]
Here, subtracting \(-10\)actually turns into adding \(+10\),resulting in \(0 + 10 = 10\). This is a key rule to remember when dealing with negative numbers in subtraction.

• They extend to both directions on the number line, with negatives to the left of zero.
• Arithmetic rules change slightly when incorporating negative numbers.

Using a Calculator

Calculators are incredibly helpful tools in arithmetic, especially when performing more complex calculations or checking your work. Using a calculator for operations like subtraction involves simply entering the numbers in the order of the operation and pressing the corresponding function key.

In the exercise, we used a calculator to verify our manual subtraction process:
\[ 0 - (-10) \]
We entered these using the "-" key for subtraction and the "(-)" key to indicate a negative number. Calculators then convert \(0 - (-10)\) to the addition problem\(0 + 10\).

• Ensure the calculator is in standard mode to avoid errors in simple arithmetic calculations.
• Double-check entries to ensure that negative signs are correctly placed.
• Useful in quickly verifying arithmetic by giving instant results.

By mastering calculator use, students can prevent errors and gain confidence in their calculation ability.