Topics
3. Integers & Exponents
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United States of AmericaVirginia
Grade 6

3.02 Compare and order integers

Lesson
Practice

Compare and order integers

We can use the following symbols to compare integers:

\gt means "is greater than", such as 7 \gt 2

\lt means "is less than", such as -2 \lt 4

= means "is equal to", such as -6 = -6

The number that is furthest right on the number line is always greater than the numbers on its left.

-8-7-6-5-4-3-2-1012345678

-4 is the furthest to the left, therefore it is the smallest integer plotted on this number line.

8 is the furthest to the right, therefore it is the largest integer plotted on this number line.

Writing the numbers from smallest to largest is called ascending order: -4,0,3,8.

Writing the numbers from largest to smallest is called descending order : 8,3,0,-4.

Exploration

Use the following applet to compare two integers.

Move the points of the integers on the number line and check the the boxes to compare the integers.

Loading interactive...

Put the red dot on 3 and the blue dot on -1.

Now put the red dot on -1 and the blue dot on 3.

Repeat with some other pairs of integers.

  1. What happens to the inequality symbol when the order of the integers is swapped?

Examples

Example 1

Which is the largest number marked on the number line?

-10-5051015
Worked Solution
Create a strategy

Recall that the further an integer is to the right on a number line, the larger the integer is.

Apply the idea

The integer farthest to the right on the number line is 13. So the largest number is 13.

Example 2

Consider the numbers -3 and -9.

a

Graph -3 and -9 on the number line.

Worked Solution
Create a strategy

We can see that -3 and -9 are both negative and so will be to the left of 0.

Apply the idea

To plot the point -3, start at 0 and count left 3 places. To plot the point -9, we can start at -5 and jump left a further 4 places.

-10-50510
b

Insert either \lt or \gt to make a true statement.

-3 \, \, ⬚ -9

Worked Solution
Create a strategy

If we are comparing two negative numbers, the number closer to zero will be the larger number.

Apply the idea

We can see from the previous number line that -3 is closer to 0 which means it is larger than -9. So, -3 \,\gt\, -9.

Example 3

Arrange the following numbers in ascending order:

11, \, -25, 19, \, -15, \, 28

Worked Solution
Create a strategy

Ascending means ordering from smallest to largest. We can do this by going from left to right on the number line.

Apply the idea

Plot the points on the number line:

-30-25-20-15-10-5051015202530

Arrange the list from least to greatest -25,\, -15,\, 11, \,19, \,28

Example 4

The melting point of krypton is -157°\text{C}. The melting point of radon is -71° \text{C}.

Write an inequality comparing the two melting points.

Worked Solution
Create a strategy

A negative integer with a smaller number has a greater value than a negative integer with a larger number. It is further to the left of 0 on a number line.

Apply the idea

-71 is a negative integer with a smaller number which means it has a greater value than -157.

-157\, \degree\text{C} \lt -71\, \degree\text{C}

Idea summary

The sizes of integers can be compared using inequality symbols.

The symbol \lt represents the phrase is less than.

The symbol \gt represents the phrase is greater than.

The symbol = represents the phrase is equal to.

Outcomes

6.NS.2

The student will reason and use multiple strategies to represent, compare, and order integers.

6.NS.2b

Compare and order integers using a number line.

6.NS.2c

Compare integers, using mathematical symbols (<, >, =).

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