How to Order Integers and Numbers

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To order integers and other real numbers, compare their positions on the number line. Numbers farther left are smaller; numbers farther right are larger.

Ordering integers

For positive integers, the number with the larger absolute value is larger. For negative integers, the number with the larger absolute value is smaller because it lies farther left. For example, \(-12< -5\).

Ordering mixed number types

Decimals, fractions, and percents are easiest to compare after converting them to the same form. For example, \(\frac{3}{4}=0.75\), so \(0.7<\frac{3}{4}\).

ACT tip

Circle the requested direction before sorting. Many wrong answers contain the right numbers in the wrong order.

Ordering Integers and Numbers

Think of this lesson as more than a rule to memorize. Ordering Integers and Numbers 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 Ordering Integers and Numbers

1) Order from least to greatest: \(-4,\ 7,\ 0,\ -9,\ 3\)

2) Order from least to greatest: \(12,\ -15,\ 6,\ -2,\ 0\)

3) Order from greatest to least: \(-8,\ -1,\ -12,\ 5,\ 2\)

4) Order from least to greatest: \(-3.5,\ -3,\ 2,\ 1.5,\ -4\)

5) Order from least to greatest: \(\frac{1}{2},\ -1,\ 0.25,\ -\frac{3}{4},\ 2\)

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

7) Order from least to greatest: \(-18,\ -20,\ -5,\ 4,\ 11\)

8) Order from least to greatest: \(0.6,\ \frac{2}{3},\ -0.4,\ -\frac{1}{2},\ 1\)

9) Order from greatest to least: \(-25,\ 14,\ -7,\ 0,\ 21\)

10) Order from least to greatest: \(-2.1,\ -2.01,\ -2.2,\ 2.02,\ 0\)

11) Order from least to greatest: \(\frac{5}{4},\ 1.2,\ -1.3,\ -\frac{6}{5},\ 0\)

12) Order from greatest to least: \(-\frac{3}{2},\ -1.25,\ 0.5,\ \frac{2}{3},\ -2\)

13) Order from least to greatest: \(-45,\ 18,\ -18,\ 45,\ -5,\ 5\)

14) Order from least to greatest: \(75\%,\ 0.8,\ \frac{7}{10},\ -0.2,\ -\frac{1}{4}\)

15) Order from greatest to least: \(-3.75,\ -3\frac{1}{2},\ -4,\ -3.6,\ 0\)

16) Order from least to greatest: \(-\frac{9}{4},\ -2.3,\ -2.05,\ 2.1,\ \frac{11}{5}\)

17) Order from greatest to least: \(\frac{5}{6},\ 0.82,\ -0.83,\ -\frac{4}{5},\ 1\)

18) Order from least to greatest: \(-100,\ -99.5,\ -100.5,\ 0,\ 99\)

19) Order from greatest to least: \(-\frac{7}{8},\ -0.9,\ -0.875,\ 0.1,\ \frac{1}{9}\)

20) Order from least to greatest: \(1.01,\ \frac{101}{100},\ -1.001,\ -\frac{11}{10},\ 0.99\)

Answers

1) \(-4,\ 7,\ 0,\ -9,\ 3=\color{red}{\text{-9, -4, 0, 3, 7}}\)

Solution
Least to greatest means left to right.
The order is \(-9,-4,0,3,7\).

2) \(12,\ -15,\ 6,\ -2,\ 0=\color{red}{\text{-15, -2, 0, 6, 12}}\)

Solution
List negatives first: \(-15,-2\).
Then list \(0,6,12\).

3) \(-8,\ -1,\ -12,\ 5,\ 2=\color{red}{\text{5, 2, -1, -8, -12}}\)

Solution
Greatest values are farthest right.
The order is \(5,2,-1,-8,-12\).

4) \(-3.5,\ -3,\ 2,\ 1.5,\ -4=\color{red}{\text{-4, -3.5, -3, 1.5, 2}}\)

Solution
Among negatives, more negative is smaller.
Then place positives: \(1.5,2\).

5) \(\frac{1}{2},\ -1,\ 0.25,\ -\frac{3}{4},\ 2=\color{red}{\text{-1, -\frac{3}{4}, 0.25, \frac{1}{2}, 2}}\)

Solution
Convert: \(\frac{1}{2}=0.5\), \(-\frac{3}{4}=-0.75\).
Order the decimals: \(-1,-0.75,0.25,0.5,2\).

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

Solution
Greatest to least starts with positives.
For negatives, \(-6>-10\).

7) \(-18,\ -20,\ -5,\ 4,\ 11=\color{red}{\text{-20, -18, -5, 4, 11}}\)

Solution
Least is farthest left.
\(-20<-18<-5<4<11\).

8) \(0.6,\ \frac{2}{3},\ -0.4,\ -\frac{1}{2},\ 1=\color{red}{\text{-\frac{1}{2}, -0.4, 0.6, \frac{2}{3}, 1}}\)

Solution
Convert \(\frac{2}{3}\approx0.667\) and \(-\frac{1}{2}=-0.5\).
Order: \(-0.5,-0.4,0.6,0.667,1\).

9) \(-25,\ 14,\ -7,\ 0,\ 21=\color{red}{\text{21, 14, 0, -7, -25}}\)

Solution
Start with positives \(21,14\), then zero.
For negatives, \(-7>-25\).

10) \(-2.1,\ -2.01,\ -2.2,\ 2.02,\ 0=\color{red}{\text{-2.2, -2.1, -2.01, 0, 2.02}}\)

Solution
For negative decimals, the more negative value is smaller.
Then place \(0\) before the positive value.

11) \(\frac{5}{4},\ 1.2,\ -1.3,\ -\frac{6}{5},\ 0=\color{red}{\text{-1.3, -\frac{6}{5}, 0, 1.2, \frac{5}{4}}}\)

Solution
Convert \(\frac{5}{4}=1.25\), \(-\frac{6}{5}=-1.2\).
Order: \(-1.3,-1.2,0,1.2,1.25\).

12) \(-\frac{3}{2},\ -1.25,\ 0.5,\ \frac{2}{3},\ -2=\color{red}{\text{\frac{2}{3}, 0.5, -1.25, -\frac{3}{2}, -2}}\)

Solution
Convert \(-\frac{3}{2}=-1.5\), \(\frac{2}{3}\approx0.667\).
Greatest to least is \(0.667,0.5,-1.25,-1.5,-2\).

13) \(-45,\ 18,\ -18,\ 45,\ -5,\ 5=\color{red}{\text{-45, -18, -5, 5, 18, 45}}\)

Solution
List negatives from farthest left to closest to zero.
Then positives from smallest to largest.

14) \(75\%,\ 0.8,\ \frac{7}{10},\ -0.2,\ -\frac{1}{4}=\color{red}{\text{-\frac{1}{4}, -0.2, \frac{7}{10}, 75\%, 0.8}}\)

Solution
Convert \(75\%=0.75\), \(\frac{7}{10}=0.7\), \(-\frac{1}{4}=-0.25\).
Order: \(-0.25,-0.2,0.7,0.75,0.8\).

15) \(-3.75,\ -3\frac{1}{2},\ -4,\ -3.6,\ 0=\color{red}{\text{0, -3\frac{1}{2}, -3.6, -3.75, -4}}\)

Solution
Convert \(-3\frac{1}{2}=-3.5\).
Greatest to least is \(0,-3.5,-3.6,-3.75,-4\).

16) \(-\frac{9}{4},\ -2.3,\ -2.05,\ 2.1,\ \frac{11}{5}=\color{red}{\text{-2.3, -\frac{9}{4}, -2.05, 2.1, \frac{11}{5}}}\)

Solution
Convert \(-\frac{9}{4}=-2.25\), \(\frac{11}{5}=2.2\).
Order: \(-2.3,-2.25,-2.05,2.1,2.2\).

17) \(\frac{5}{6},\ 0.82,\ -0.83,\ -\frac{4}{5},\ 1=\color{red}{\text{1, \frac{5}{6}, 0.82, -\frac{4}{5}, -0.83}}\)

Solution
Convert \(\frac{5}{6}\approx0.833\), \(-\frac{4}{5}=-0.8\).
Greatest to least is \(1,0.833,0.82,-0.8,-0.83\).

18) \(-100,\ -99.5,\ -100.5,\ 0,\ 99=\color{red}{\text{-100.5, -100, -99.5, 0, 99}}\)

Solution
For negatives near \(-100\), the more negative value is smaller.
Then place \(0\) and \(99\).

19) \(-\frac{7}{8},\ -0.9,\ -0.875,\ 0.1,\ \frac{1}{9}=\color{red}{\text{\frac{1}{9}, 0.1, -\frac{7}{8}, -0.875, -0.9}}\)

Solution
Convert \(-\frac{7}{8}=-0.875\), \(\frac{1}{9}\approx0.111\).
Greatest to least is \(0.111,0.1,-0.875,-0.875,-0.9\).

20) \(1.01,\ \frac{101}{100},\ -1.001,\ -\frac{11}{10},\ 0.99=\color{red}{\text{-\frac{11}{10}, -1.001, 0.99, 1.01, \frac{101}{100}}}\)

Solution
Convert \(\frac{101}{100}=1.01\), \(-\frac{11}{10}=-1.1\).
Order: \(-1.1,-1.001,0.99,1.01,1.01\).

How to Order Integers and Numbers