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Chapter 1: Problem 55

Select the lesser of the two given numbers. $$ -7,-6 $$

Short Answer

Expert verified
-7

Step by step solution

01

- Understanding the numbers

Identify the two given numbers: -7 and -6.
02

- Comparing the numbers

Compare -7 and -6. In a number line, -7 is located to the left of -6. Since the number line increases from left to right, -7 is less than -6.
03

- Selecting the lesser number

Based on the comparison, -7 is lesser than -6.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

number line
When learning about comparing integers, a number line can be very helpful. A number line is a straight line where every point represents a number. It usually has zero in the center, positive numbers to the right, and negative numbers to the left.

Here are a few basic facts about a number line:
  • Numbers increase as you move to the right.
  • Numbers decrease as you move to the left.
  • Every number to the left of zero is a negative number, and every number to the right of zero is a positive number.
To visualize the exercise, place -7 and -6 on a number line. -7 will be further to the left than -6 as it is more negative. Hence, -7 is lesser than -6.
negative numbers
Negative numbers are simply numbers less than zero. They are represented with a minus sign (-) in front. Understanding negative numbers is crucial when comparing integers.

Here are a few key points on negative numbers:
  • Negative numbers are always on the left side of zero on a number line.
  • The more negative a number, the smaller its value.
  • When comparing negative numbers, the number with the greater absolute value is considered smaller. For example, -7 is less than -6 because 7 is greater than 6 in absolute terms.
When working with negative numbers, always remember: the greater the magnitude, the smaller the number.
number comparison
Comparing numbers, especially negatives, can be tricky without a solid understanding of how a number line works. When comparing two numbers, you can use the number line to see their positions relative to each other.
If you have to compare -7 and -6, position them on the number line and see which one is further left.

Use these simple rules for number comparison:
  • On a number line, the number to the left is always smaller.
  • Among negative numbers, the one with the higher absolute value is smaller.
  • Zero is always greater than any negative number.
For the given exercise, -7 is clearly less than -6 because it lies further left on the number line. This methodical approach will guide you in comparing any integers confidently.

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