Problem 42 - Prealgebra

Question

Simplify as much as possible by first changing all subtractions to addition of the opposite and then adding left to right. $$44-(-11)+55$$

Step-by-Step Solution

Answer

The expression simplifies to 110.

Step 1: Convert Subtraction into Addition

Let's start by changing the expression's subtraction to addition of the opposite. The original expression is \(44 - (-11) + 55\). By changing subtraction to addition, we use the rule that subtracting a negative is the same as adding its opposite. Therefore, \(44 - (-11)\) can be rewritten as \(44 + 11\). Now, the expression becomes \(44 + 11 + 55\).

Step 2: Add Numbers from Left to Right

Now, we'll add the numbers from left to right. Start with the first two numbers: \(44 + 11\). Adding these gives \(55\). Now, we update the expression to \(55 + 55\).

Step 3: Complete the Addition

Finally, perform the addition for the remaining terms: \(55 + 55\) equals \(110\). Therefore, the simplified expression is \(110\).

Key Concepts

Addition

Addition is one of the fundamental operations in mathematics. It's the process of bringing two or more numbers together to get a total sum.

• When you add numbers, you are combining them into a larger value.
• Addition is represented by the plus sign "+".
• The order of the numbers being added does not change the result. This is known as the commutative property of addition.

For example, when you add 44 and 11, you are essentially putting together these quantities: \[44 + 11 = 55\]This operation is intuitive and helps in building a strong foundational understanding for more complex arithmetic operations.

Subtraction to Addition

Switching subtraction to addition can sometimes make math problems easier to solve. Particularly when dealing with negative numbers, this method simplifies the process.
This technique involves changing a subtraction operation into an addition by adding the opposite of the number you're subtracting.

• For example, if you have \(44 - (-11)\), you change the subtraction of \(-11\) to the addition of its opposite: 11.
• This means subtracting a negative is the same as adding a positive.

By converting subtraction into addition and using opposite numbers, calculations become more straightforward and errors are minimized.

Opposite Numbers

Opposite numbers are essentially numbers that are the same distance from zero on the number line but in opposite directions.

• If a number is positive, its opposite will be negative, and vice versa.
• Adding a number and its opposite will always result in zero. For example, \(5 + (-5) = 0\).

This concept helps in simplifying expressions where subtraction of negative numbers is involved because subtracting a negative is akin to adding its opposite positive value.
For example, the subtraction \(44 - (-11)\) becomes addition: \[44 + 11\]This transformation is a handy trick in prealgebra, simplifying what might initially seem like more complex problems.