Problem 52 - Elementary Algebra

Question

Rewrite the problem in a simpler form. $$ 31-(-1) $$

Step-by-Step Solution

Answer

Answer: The simplified expression is 32.

Step 1: Identify the problem

We are asked to simplify the expression: $$ 31-(-1) $$

Step 2: Apply the rule for subtracting a negative number

When subtracting a negative number, we can remember the rule "minus a negative is the same as plus a positive." So, we can rewrite the expression as: $$ 31+1 $$

Step 3: Perform the addition

Now, we simply need to add the numbers together: $$ 31+1=32 $$ The simplified expression is 32.

Key Concepts

Subtracting Negative Numbers

Handling negative numbers can sometimes be tricky, but there's a simple rule that can help make things easier: subtracting a negative number is like adding a positive number! This means if you see a math problem like \(31 - (-1)\), you can change the subtraction to addition. Remember, when you have two negative signs next to each other, they turn into a positive sign. This is because you're essentially removing a negative, which is akin to gaining a positive.

• Example: \(31 - (-1) = 31 + 1\)
• Double negatives cancel out to become positive.

So, whenever you see subtraction involved with a negative number, flip those settings around, and think of it as a normal addition.

Addition

Adding numbers might be one of the first things you learned in math. It's about combining numbers to get a total. After understanding the rules around negative numbers, the next step is straightforward addition. Consider the problem once it's rewritten to \(31 + 1\). Here, you simply add these numbers together to find their total.

• Start with the larger number (31 in this case).
• Count up the additional amount (1 in this example).
• Add these together: \(31 + 1 = 32\).

Addition might seem basic, but it becomes much easier when you follow simple steps. Always align numbers properly and maintain focus on small increments for accurate results.

Mathematical Rules

Mathematical rules act as guidelines to simplify expressions and solve problems effectively. By understanding these rules, you make math problems more approachable. Some basics include handling negatives, regular addition, subtraction, multiplication, and division.

• Subtracting Negatives: This flips the operation to addition.
• Addition: Combine numbers to get a sum.
• Always simplify as much as possible before solving.

Mathematics doesn't have to be confusing. By following structured rules, expressions become manageable. These rules are like a roadmap, directing you through the jungle of numbers, ensuring you reach a correct solution smoothly.