Problem 34 - Elementary Algebra

Question

Translate each sentence to a mathematical statement and then simplify. Subtract -3 from 27

Step-by-Step Solution

Answer

The answer is 30.

Step 1: Understand the Problem

The sentence given is "Subtract -3 from 27". We need to translate this sentence into a mathematical expression which involves subtraction of a negative number from a positive number.

Step 2: Translate to Mathematical Expression

The phrase "Subtract -3 from 27" translates to the mathematical expression: \( 27 - (-3) \). Subtracting a negative is the same as adding the positive of that number.

Step 3: Simplify the Expression

To simplify the expression \( 27 - (-3) \), we know that subtracting a negative number is equivalent to addition. Therefore, \( 27 - (-3) \) simplifies to \( 27 + 3 \).

Step 4: Calculate the Result

Now, add the numbers: \( 27 + 3 = 30 \). Therefore, the simplified result of the expression is 30.

Key Concepts

Subtracting Negative Numbers

Subtracting a negative number might initially seem confusing, but it's actually a straightforward concept once you grasp the rules. When you see a subtraction operation involving a negative, like in the expression "Subtract -3 from 27," you are actually adding. This is because subtracting a negative is equivalent to adding its positive counterpart.
To visualize it, consider a number line:

• Start at 27.
• From 27, move in the positive direction by 3 units.

This movement brings you to 30, confirming the idea that subtracting a negative number results in an addition operation. Understanding this concept is key to tackling more complex equations and expressions involving negatives.

Simplifying Expressions

To simplify expressions, you need to perform mathematical operations in a way that makes a problem easier to solve. Simplifying does not change the result; it merely presents it more clearly. Let's look at the expression from our exercise:

• The initial expression is: \( 27 - (-3) \).
• The simplification step involves recognizing that \(-(-3)\) turns into \(+3\), since the two negative signs cancel each other.
• This simplifies the expression to \( 27 + 3 \).

By simplifying, you streamline calculations and minimize errors. It's much easier to work with a simple addition than to tackle both a subtraction and a negative sign in one operation.

Addition in Mathematics

Addition is one of the fundamental operations in mathematics. It involves combining numbers to find their total sum. In our example, after transforming the subtraction of a negative number into an addition, we perform the operation \( 27 + 3 \).
This operation is basic but crucial. Here's a quick breakdown:

• Identify the numbers involved: 27 and 3.
• Add them together: \( 27 + 3 = 30 \).

Addition is used in everyday life, from calculating totals in shopping to summing up scores in games. Grasping how and when to use addition lays the foundation for more advanced arithmetic operations. In the context of our exercise, understanding addition helps resolve expressions involving negative numbers.