Introduction

Let's consider the number -1. We can plot it on a number line, as follows:

All of the numbers to the left of -1 are less than -1.

On the other hand, any number to the right of -1 is greater than -1.

The same idea is true for all numbers. For any given number:

  • all numbers to the left on a number line are smaller

  • all numbers to the right on a number line are larger

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Example: Comparing a Positive and Negative Number

Which symbols could replace the empty box below to make the statement true? 1 \,\,\square\,\, -2

EXPLANATION

First, we plot both numbers on a number line.

We see that 1 is to the right of -2. Therefore, 1 is greater than -2.

So, the correct statement must be: 1 > -2

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Practice: Comparing a Positive and Negative Number

Which symbols could replace the empty box below to make the statement true?

\[ -1 \,\,\square\,\, 3 \]

  1. $>$
  2. $< $
  3. $=$
a
 I and II only
b
 I only
c
 III only
d
 II only
e
 II and III only
Practice: Comparing a Positive and Negative Number

Which symbols could replace the empty box below to make the statement true?

\[ -6 \,\,\square\,\, 2 \]

  1. $>$
  2. $< $
  3. $=$
a
 II only
b
 II and III only
c
 III only
d
 I and II only
e
 I only
Example: Comparing a Negative Number and Zero

Which symbols could replace the empty box below to make the statement true? -6 \,\,\square\,\, 0

EXPLANATION

First, we plot both numbers on a number line.

We see that -6 is to the left of 0. Therefore, -6 is less than 0.

So, the correct statement must be: -6 < 0

FLAG
Practice: Comparing a Negative Number and Zero

Which symbols could replace the empty box below to make the statement true?

\[ -1 \,\,\square\,\, 0 \]

  1. $>$
  2. $< $
  3. $=$
a
 I and III only
b
 I only
c
 III only
d
 II and III only
e
 II only
Practice: Comparing a Negative Number and Zero

Which symbols could replace the empty box below to make the statement true?

\[ -5 \,\,\square\,\, 0 \]

  1. $>$
  2. $< $
  3. $=$
a
 III only
b
 I only
c
 I and II only
d
 II only
e
 II and III only
Example: Comparing Two Negative Numbers

Which symbols could replace the empty box below to make the statement true? -5 \,\,\,\,\square\,\,\, {-2}

EXPLANATION

First, we plot both numbers on a number line.

We see that -5 is to the left of -2. Therefore, -5 is less than -2.

So, the correct statement must be: -5 < - 2

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Practice: Comparing Two Negative Numbers

Which symbols could replace the empty box below to make the statement true?

\[ -8 \,\,\,\,\square\, -2 \]

  1. $>$
  2. $< $
  3. $=$
a
 II and III only
b
 I only
c
 III only
d
 I and II only
e
 II only
Practice: Comparing Two Negative Numbers

Which symbols could replace the empty box below to make the statement true?

\[ -4 \,\,\,\,\square\, -9 \]

  1. $>$
  2. $< $
  3. $=$
a
 III only
b
 I and III only
c
 II only
d
 I only
e
 II and III only
Example: Comparing Two Points on a Number Line

Which of the following is true regarding numbers A and B?

  1. A < 0
  2. 0 > B
  3. B < A
EXPLANATION

Let's analyze each statement in turn.

  • Statement I is true. The number A is to the left of zero. Therefore, A is smaller than 0, which we write as A < 0.

  • Statement II is true. The number B is to the left of zero. Therefore, B is smaller than 0, which we write as B < 0. This is the same as saying that 0 is greater than B, which we write as 0 > B.

  • Statement III is false. The number A is to the left of A. Therefore, A is smaller than B, which we write as A < B.

Therefore, the correct answer is "I and II only."

FLAG
Practice: Comparing Two Points on a Number Line

Which of the following is true regarding numbers $A$ and $B?$

  1. $0 < A$
  2. $B < 0$
  3. $A < B$
a
 II and III only
b
 I only
c
 II only
d
 III only
e
 I and II only
Practice: Comparing Two Points on a Number Line

Which of the following is true regarding numbers $A$ and $B?$

  1. $A < 0$
  2. $B < 0$
  3. $A < B$
a
 I and III only
b
 II only
c
 III only
d
 I, II and III
e
 I and II only
Practice: Comparing Two Points on a Number Line

Which of the following is true regarding numbers $A$ and $B?$

  1. $0 > A$
  2. $B > 0$
  3. $B > A$
a
 I only
b
 III only
c
 II only
d
 II and III only
e
 I and III only
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