Problem 85 - Intermediate Algebra

Question

In the following exercises, simplify each expression. $$ \text { (a) } 44-28 \text { (B) } 44+(-28) $$

Step-by-Step Solution

Answer

The simplified expressions are both 16.

Step 1: Simplify part (a)

Start by simplifying the expression in part (a), which is \(44 - 28\). Subtract 28 from 44: \[44 - 28 = 16\].

Step 2: Simplify part (b)

Now move on to part (b), which is \(44 + (-28)\). Adding a negative number is the same as subtraction: \[44 + (-28) = 44 - 28\]. This gives us the same result as in part (a): \[44 + (-28) = 16\].

Step 3: Combine the results

Both parts (a) and (b) simplify to the same value: \(16\).

Key Concepts

Subtraction

Subtraction is a fundamental arithmetic operation. It involves taking one number away from another. In algebra, subtraction can be applied to both positive and negative numbers. For instance, in the exercise where we have \(44 - 28\), we simply take 28 away from 44. This gives us 16.
When subtracting, always start by aligning numbers by their place value.

• First, subtract the digits in the one's place.
• Next, move to the ten's place and so on.

Be careful with borrowing if necessary. In this case, no borrowing is required.

Adding Negative Numbers

Adding negative numbers might seem a bit tricky, but it's actually straightforward when you get the hang of it. Essentially, adding a negative number is the same as subtracting its positive counterpart.
For example, in our exercise, \(44 + (-28)\), we treat it like \(44 - 28\).
This means:

• Think of the negative sign as an instruction to subtract.
• Proceed as usual with the subtraction operation.

This method simplifies work with negative numbers and prevents errors.

Integer Operations

Integer operations include addition, subtraction, multiplication, and division with whole numbers. Let's break down how integers work:

• Positive integers are numbers greater than zero.
• Negative integers are numbers less than zero and include a negative sign.

When performing operations with integers:

• Adding two positive integers: Add the numbers normally.
• Adding two negative integers: Treat it like regular addition and add the negative sign to the result.
• Subtracting an integer: Turn the subtraction into adding the opposite (negative sign).

Remember, understanding integer operations are crucial for simplifying algebraic expressions effortlessly.