How to Arrange, Order, and Compare Integers

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Comparing integers means deciding which value is greater, less, or equal. Arranging or ordering integers means placing several values in a requested order.

Comparison symbols

\(a>b\) means \(a\) is greater than \(b\).
\(a<b\) means \(a\) is less than \(b\).
\(a=b\) means the values are equal.

On a number line, the number to the right is greater. This is why \(4>-6\), but \(-9<-2\). Among negatives, the number closer to zero is greater.

ACT tip

If a problem mixes comparisons and ordering, compare pairs first, then arrange the full list. Keep the original values unchanged; do not drop negative signs while sorting.

Teacher-style explanation: Arrange, Order, and Comparing Integers

Think of this lesson as more than a rule to memorize. Arrange, Order, and Comparing Integers is about number-line meaning, signs, and distance from zero. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.

Integers are easiest when you picture direction on a number line. Positive numbers move right, negative numbers move left, and absolute value measures distance from zero.

Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.

Read what is given and what is being asked.
Choose the rule that connects them.
Substitute carefully and simplify in small steps.
Check the final answer against the original question.

A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.

Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.

When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.

On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.

Free printable Worksheets

Exercises for Arrange, Order, and Compare Integers

1) Insert \(<\), \(>\), or \(=\): \(-6\ \square\ 2\)

2) Insert \(<\), \(>\), or \(=\): \(-3\ \square\ -8\)

3) Insert \(<\), \(>\), or \(=\): \(0\ \square\ -1\)

4) Order from least to greatest: \(-2,\ 5,\ -7,\ 1\)

5) Order from greatest to least: \(-10,\ -4,\ 6,\ 0\)

6) Insert \(<\), \(>\), or \(=\): \(|-9|\ \square\ 8\)

7) Insert \(<\), \(>\), or \(=\): \(-12\ \square\ -15\)

8) Order from least to greatest: \(14,\ -9,\ 3,\ -14,\ 0\)

9) Which is greatest: \(-18,\ -21,\ -3,\ -11\)?

10) Which is least: \(24,\ -30,\ -24,\ 3\)?

11) Insert \(<\), \(>\), or \(=\): \(-4+7\ \square\ 2\)

12) Insert \(<\), \(>\), or \(=\): \(-5-6\ \square\ -10\)

13) Order from greatest to least: \(-16,\ 8,\ -2,\ 16,\ -8\)

14) Arrange from least to greatest: \(-1.5,\ -2,\ 0,\ 1,\ -1\)

15) Insert \(<\), \(>\), or \(=\): \(-3^2\ \square\ (-3)^2\)

16) Order from least to greatest: \(-\frac{5}{2},\ -2.4,\ 2,\ 0,\ -3\)

17) Which is greatest: \(-8+12,\ 6-9,\ -2(-3),\ -15\div3\)?

18) Insert \(<\), \(>\), or \(=\): \(-|7|\ \square\ |-7|\)

19) Order from greatest to least: \(\frac{3}{4},\ 0.8,\ -0.7,\ -\frac{4}{5},\ 0\)

20) Arrange from least to greatest: \(-20\div4,\ (-2)^3,\ -3^2,\ 7-15,\ |-6|\)

Answers

1) \(-6\ \square\ 2=\color{red}{<}\)

Solution
\(-6\) is left of \(2\).
Therefore \(-6<2\).

2) \(-3\ \square\ -8=\color{red}{>}\)

Solution
\(-3\) is closer to zero than \(-8\).
Therefore \(-3>-8\).

3) \(0\ \square\ -1=\color{red}{>}\)

Solution
Zero is to the right of every negative number.
So \(0>-1\).

4) \(-2,\ 5,\ -7,\ 1=\color{red}{\text{-7, -2, 1, 5}}\)

Solution
Least to greatest moves left to right.
The order is \(-7,-2,1,5\).

5) \(-10,\ -4,\ 6,\ 0=\color{red}{\text{6, 0, -4, -10}}\)

Solution
Greatest values are farthest right.
The order is \(6,0,-4,-10\).

6) \(|-9|\ \square\ 8=\color{red}{>}\)

Solution
\(|-9|=9\).
Since \(9>8\), use \(>\).

7) \(-12\ \square\ -15=\color{red}{>}\)

Solution
Both are negative.
\(-12\) is closer to zero, so \(-12>-15\).

8) \(14,\ -9,\ 3,\ -14,\ 0=\color{red}{\text{-14, -9, 0, 3, 14}}\)

Solution
Start with the most negative value.
Then move right: \(-14,-9,0,3,14\).

9) \(-18,\ -21,\ -3,\ -11=\color{red}{-3}\)

Solution
All values are negative.
The greatest is closest to zero: \(-3\).

10) \(24,\ -30,\ -24,\ 3=\color{red}{-30}\)

Solution
The least number is farthest left.
\(-30\) is less than the other values.

11) \(-4+7\ \square\ 2=\color{red}{>}\)

Solution
Simplify: \(-4+7=3\).
Because \(3>2\), use \(>\).

12) \(-5-6\ \square\ -10=\color{red}{<}\)

Solution
Simplify: \(-5-6=-11\).
Because \(-11<-10\), use \(<\).

13) \(-16,\ 8,\ -2,\ 16,\ -8=\color{red}{\text{16, 8, -2, -8, -16}}\)

Solution
List positives first: \(16,8\).
Then negatives from closest to zero to farthest left.

14) \(-1.5,\ -2,\ 0,\ 1,\ -1=\color{red}{\text{-2, -1.5, -1, 0, 1}}\)

Solution
Order negative values first: \(-2,-1.5,-1\).
Then \(0,1\).

15) \(-3^2\ \square\ (-3)^2=\color{red}{<}\)

Solution
\(-3^2=-(3^2)=-9\).
\((-3)^2=9\), and \(-9<9\).

16) \(-\frac{5}{2},\ -2.4,\ 2,\ 0,\ -3=\color{red}{\text{-3, -\frac{5}{2}, -2.4, 0, 2}}\)

Solution
Convert \(-\frac{5}{2}=-2.5\).
Then order: \(-3,-2.5,-2.4,0,2\).

17) \(-8+12,\ 6-9,\ -2(-3),\ -15\div3=\color{red}{6}\)

Solution
Evaluate: \(-8+12=4\), \(6-9=-3\), \(-2(-3)=6\), \(-15\div3=-5\).
The greatest value is \(6\).

18) \(-|7|\ \square\ |-7|=\color{red}{<}\)

Solution
\(-|7|=-7\) and \(|-7|=7\).
Because \(-7<7\), use \(<\).

19) \(\frac{3}{4},\ 0.8,\ -0.7,\ -\frac{4}{5},\ 0=\color{red}{\text{0.8, \frac{3}{4}, 0, -0.7, -\frac{4}{5}}}\)

Solution
Convert \(\frac{3}{4}=0.75\) and \(-\frac{4}{5}=-0.8\).
Greatest to least is \(0.8,0.75,0,-0.7,-0.8\).

20) \(-20\div4,\ (-2)^3,\ -3^2,\ 7-15,\ |-6|=\color{red}{\text{-9, -8, -8, -5, 6}}\)

Solution
Evaluate: \(-20\div4=-5\), \((-2)^3=-8\), \(-3^2=-9\), \(7-15=-8\), \(|-6|=6\).
Least to greatest is \(-9,-8,-8,-5,6\).

How to Arrange, Order, and Compare Integers