Problem 25 - Prealgebra

Question

Subtract. $$156-(-243)$$

Step-by-Step Solution

Answer

The result of the subtraction is 399.

Step 1: Understand the Subtraction of Negative Numbers

When we subtract a negative number from another number, we can think of it as adding the positive equivalent of that number. This means we change the subtraction of a negative number to addition. For this exercise, instead of subtracting \(-243\), we will add \(+243\).

Step 2: Rewrite the Expression

Rewrite the given expression by changing the subtraction of a negative to addition:\[156 - (-243) = 156 + 243\]

Step 3: Perform the Addition

Now add the two numbers together. Start by lining up the numbers vertically by their place value and add:\(156 + 243\):1. Add the ones place: \(6 + 3 = 9\).2. Add the tens place: \(5 + 4 = 9\).3. Add the hundreds place: \(1 + 2 = 3\).This gives us the sum of 399.

Key Concepts

Negative Numbers

Negative numbers can be a bit tricky when you first encounter them, but they're really just like any other numbers. They simply represent values less than zero, meaning they are on the left side of the number line. To visualize this, think of a thermometer: temperatures below zero degrees are considered negative.

Negative numbers are shown with a minus sign in front of them. So, -5 would mean five units below zero. When dealing with negative numbers, it's important to differentiate between the minus sign used for operations and the negative sign indicating a negative number.

Why Are They Important?
Knowing how to work with negative numbers is crucial as they appear frequently in real-world contexts such as temperatures, elevation below sea level, bank transactions when withdrawing money, and more.

• They help in understanding debts when talking about finances.
• They allow for temperature readings below zero.
• They are used in scientific and mathematical computations on continuous scales.

Addition of Integers

Adding integers may sound complicated, but it follows simple rules. An integer is any whole number, including both positive and negative numbers as well as zero. So when we talk about adding integers, we're thinking about combining these numbers into a single sum.

• Addition of positive numbers is straightforward and works the same way you're already familiar with.
• For adding a positive integer to a negative integer, imagine moving on a number line. You move to the right for a positive number and to the left for a negative. For example, if you add 10 to -3, you start at -3 and move 10 steps to the right, landing on 7.
• When adding two negative integers, you're simply moving further into the negatives. For instance, -5 plus -3 is -8.

Subtraction Rules

Subtraction can seem a bit more complex when dealing with negative numbers, but they can become quite manageable with practice. In math, subtraction is essentially the opposite of addition. The key rule to remember is when you subtract a negative number, you are actually adding its positive equivalent.

Here's How It Works

For any subtraction expression, like 10 - (-4), transform it into an addition statement like 10 + 4, which equals 14.

This transformation is based on the rule that subtracting a negative is the same as adding a positive.

Visualize it on a number line — moving to the right when adding, and reversing when subtracting a negative, thus moving to the right again.

By keeping these rules in mind, you'll find the operations involving integers to be less daunting. Subtraction, just like addition, can be mastered with a little practice and understanding of these simple rules. Remember, practice makes perfect!