Problem 97 - Elementary Algebra

Question

Fill in the blank with \(<,=\), or \(>\). 13 _____ \(-(-12)\)

Step-by-Step Solution

Answer

13 > 12

Step 1: Simplify the expression on the right

The expression on the right is \[ -(-12) \]To solve this, recall that two negatives make a positive. Thus, \[ -(-12) = 12. \]

Step 2: Compare the numbers

Now we need to compare the two numbers: 13 and 12. Since 13 is greater than 12, we use the greater than symbol (>).

Step 3: Fill in the blank

Based on the comparison from the previous step, you can fill in the blank with \[ 13 > 12 \] which means we place '>' in the blank.

Key Concepts

Comparison of Numbers

Comparison of numbers is a basic yet crucial mathematical skill used to determine the relationship between two numbers. This skill involves assessing whether one number is greater than, less than, or equal to another number. Here’s how you can easily compare numbers:

• Align the numbers by their place value, starting from the leftmost digit.
• If the digits are the same, move to the next digit on the right until there is a difference.
• The number with the greater digit in the place with the first difference is the larger number.

In the problem, we compared 13 and 12. By aligning these numbers, we observes that 3 is greater than 2 in the units place.
This allows you to conclude that 13 is greater than 12.

Negative Numbers

Negative numbers are numbers less than zero, and they are crucial in mathematics when talking about quantities below a reference point. They typically denote a loss, decrease, or drop from a positive condition. A clear understanding of negative numbers helps in solving many types of equations and expressions.
For instance, consider the expression \[ -(-12) \]
This essentially means removing a negative sign from a negative quantity, which results in a positive number. Therefore, \[ -(-12) = 12 \].
It's essential to remember the rule "two negatives make a positive," especially with number operations. This principle applied helps you simplify expressions involving negative numbers effectively.

Greater Than Symbol

The greater than symbol (>) is a fundamental part of expressing inequality in mathematics. When comparing two values, this symbol indicates that the value on the left side is larger than the value on the right.
In our exercise, we had to decide between "greater than" ( > ), "less than" ( < ), and "equal to" ( = ). By determining that 13 is larger than 12, we use the greater than symbol to express this relationship: \[ 13 > 12 \].
Understanding the correct use of this symbol is key for comparing values correctly, ensuring your mathematical expressions accurately reflect the relationship between numbers.