Problem 25 - Fundamentals of Mathematics

Question

How should each number be read? $$ -(-1) $$

Step-by-Step Solution

Answer

The expression \(-(-1)\) is read as 'one.'

Step 1: Identify the Expression

The expression given is \(-(-1)\). It's a negative sign applied to another negative number.

Step 2: Apply the Negative Sign

When we have a negative sign before a negative number, it changes the negative to a positive. Mathematically, \(-(-1) = 1\). This is because two negatives cancel each other out.

Step 3: Read the Number

Now that we know \(-(-1) = 1\), the number is read as 'one.'

Key Concepts

Negative Numbers

Negative numbers might seem tricky at first, but they are simply numbers less than zero, often used to represent the opposite of positive quantities. They are commonly used in everyday contexts like temperatures below freezing or debts below a zero balance.

• Negative numbers are represented with a minus sign (-) before them, such as -3 or -45.
• In mathematics, a negative number indicates an opposite position on the number line from zero.
• If you have two negative signs together, as in -(-1), this can be understood as a reversal of opposition, turning the result into a positive.

Understanding how negative numbers interact is key to solving many problems in algebra!

Mathematical Operations

Mathematical operations are the building blocks of algebra. They include addition, subtraction, multiplication, and division. With negative numbers, these operations can introduce unique challenges.

• Adding and subtracting negatives can be thought of as moving left and right on the number line.
• For instance, subtracting a negative number is the same as adding the positive equivalent.
• Multiplying and dividing with negative numbers follows specific rules. If one number is negative and the other is positive, the result is negative. If both numbers are negative, the result is positive, as in our example: -(-1) = 1.

Recognizing these patterns helps simplify the operations and solve problems efficiently.

Number Reading

Understanding how to read numbers correctly is essential in algebra. It ensures clarity and precision in every mathematical communication.

• The number \(-(-1)\) is calculated to be positive one, as two negatives make a positive in multiplication or division contexts.
• Integers, like the result we found (1), are read simply as you would naturally say them — in this case, 'one.'
• In more complex expressions, focus on reading symbols and numbers accurately to avoid errors.

Practicing the reading of numbers within expressions helps reinforce understanding and fluency in mathematical language.