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Chapter 0: Problem 1

Fill in the most appropriate symbol \(<, \leq\), \(>\) or \(\geq\) in place of \(\square\) for the following: a \(17 \square-17\) b \(-17 \square 17\) c \(-2 \square-1\) d \(-5 \square-5\) e \(-2 \square 0\)

Short Answer

Expert verified
a: >, b: <, c: <, d: =, e: <

Step by step solution

01

- Compare 17 and -17

To compare 17 and -17, note that any positive number is greater than any negative number. Therefore, 17 is greater than -17.
02

- Compare -17 and 17

Any negative number is less than any positive number. Thus, -17 is less than 17.
03

- Compare -2 and -1

When comparing negative numbers, the number with the smaller absolute value is greater. Since -2 has a greater absolute value than -1, -2 is less than -1.
04

- Compare -5 and -5

Comparing any number to itself, they are always equal. Hence, -5 is equal to -5.
05

- Compare -2 and 0

Any negative number is less than zero. Therefore, -2 is less than 0.

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Key Concepts

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

Inequalities
To compare any two numbers, we use symbols like \(<, \leq, \gt\) and \(\geq\). These symbols are called inequalities.

  • \(<\) means 'less than'
  • \(\leq\) means 'less than or equal to'
  • \(\gt\) means 'greater than'
  • \(\geq\) means 'greater than or equal to'


For example, if we compare 5 and 3, we write \(5 \gt 3\), because 5 is greater than 3. Now, knowing how to use these symbols will help us understand the relationships between different numbers.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It's always a positive number or zero.

We use vertical bars to represent the absolute value. For example, \(|3| = 3\) and \(|-3| = 3\).

When comparing negative numbers, their absolute values can help us understand their order. For instance, \(-2\) vs. \(-1\). The absolute value of \(-2\) is 2, and the absolute value of \(-1\) is 1. Since 2 \(>\) 1, we know that \(-2 \lt -1\).
Positive and Negative Numbers
Positive numbers are greater than zero and negative numbers are less than zero.

When comparing numbers, always remember these rules:
  • Any positive number is greater than any negative number. For example, \(5 \gt -3\).
  • Zero is greater than any negative number and less than any positive number. For example, \(-2 \lt 0\), but \(0 \lt 2\).
  • When comparing two negative numbers, the one with a smaller absolute value is greater.


Using these principles, comparing any numbers becomes much easier. For example, based on this, \(-5 \eq -5\) because any number is equal to itself.

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Most popular questions from this chapter

Evaluate the following: a \(7-12\) b \(-3+1\) c \(-3-(-1)\) ] d \(-11+(-11)\) e \(-11-(-11)\)

Compute the following and write your final answers in their simplest form: a \(\frac{1}{2} \times \frac{1}{3}\) b \(\frac{17}{12} \times \frac{84}{60}\) c \(\frac{235}{19} \times \frac{38}{5}\)

Express the following numbers as mixed fractions: $$ \frac{355}{113}, \frac{213}{71}, \frac{878}{323}, \frac{577}{408}, \frac{64}{7} $$

Evaluate a \(\frac{1}{2}-\frac{1}{3}\) b \(\frac{22}{7}-\frac{16}{9}\) c \(\frac{41}{29}-\frac{204}{145}\) d \(\frac{3}{31}-\frac{2}{41}\)

Write the following fractions in their simplest form: a \(\frac{7}{21}\) b \(\frac{8}{20}\) c \(\frac{72}{100}\) d \(\frac{56}{75}\) e \(\frac{272}{272}\)
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