Problem 85 - Elementary Algebra

Question

For exercises \(85-108\), write \(>\) or \(<\) between the numbers to make a true statement. $$ 12 \quad 5 $$

Step-by-Step Solution

Answer

12 > 5

Step 1: Understand the Symbols

The symbols '>' and '<' are used to compare two numbers. '>' means greater than, and '<' means less than.

Step 2: Compare the Values

Compare the two given numbers, 12 and 5. Determine which number is larger or smaller.

Step 3: Insert the Correct Symbol

Since 12 is greater than 5, we use the '>' symbol. The correct statement is 12 > 5.

Key Concepts

greater than

The 'greater than' symbol (>) is used to compare two numbers and shows that the number on the left is larger. For instance, in the given exercise, we have the numbers 12 and 5. When we compare them, we see that 12 is larger than 5. Therefore, we use the 'greater than' symbol to write the statement: 12 > 5.
It's quite straightforward!
Just remember:

• The 'greater than' symbol always points to the smaller number.

This can be visualized by imagining the symbol as a hungry crocodile that always wants to eat the larger number.

less than

The 'less than' symbol (<) works similarly to the 'greater than' symbol but in the opposite way. It indicates that the number on the left is smaller than the number on the right. Using the same exercise numbers with the 'less than' symbol, we would compare 5 and 12 and write 5 < 12 because 5 is smaller than 12.
To easily remember this, note that:

• The 'less than' symbol always points to the smaller number.

This can be remembered by thinking of the symbol as an arrow that points towards the smaller value, showing the direction.

number comparison

Number comparison is a fundamental concept in mathematics where we decide if one number is greater than, less than, or equal to another number. In the given example with 12 and 5, we compare both numbers to find out which is larger or smaller. By comparing:

• We determine that 12 is greater than 5, hence we use the 'greater than' symbol to write 12 > 5.
• If the order was reversed, and we were comparing 5 and 12, we would write 5 < 12.

A helpful tip for number comparison is to always start by checking each digit from left to right, especially with larger numbers. If the digits differ at any position, the number with the higher digit at that position is the greater number.