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Integer Sense and Number Lines

A free Pre-Algebra lesson from the “Number Foundations” unit, with a worked example and practice problems including step-by-step solutions.

Integers include whole numbers, their opposites, and zero. On a number line, values farther right are greater. Absolute value measures distance from zero, so it is always zero or positive.

What you'll learn

Why it matters: Bank balances, temperatures above and below zero, elevations above and below sea level, and golf scores all use signed numbers. Comparing them is the same as ordering them on a number line.

Worked example

Problem. Order -4, 2, -9, and 0 from least to greatest.

  1. Least means farthest left on the number line.
  2. -9 is left of -4, and both are left of 0.
  3. 2 is to the right of 0, so the order is -9, -4, 0, 2.

Answer: -9, -4, 0, 2

Practice problems

1. Which number is greatest?

Choices: -12 · -3 · 0 · -1

Show solution
  1. Warm-up: First identify exactly what the question is asking: Which number is greatest?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. The greatest number is farthest right on the number line.
  4. 0 is to the right of every negative option.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 0

2. Which number is least?

Choices: -8 · -2 · 1 · 4

Show solution
  1. Warm-up: First identify exactly what the question is asking: Which number is least?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. The least number is farthest left.
  4. -8 is left of -2, 1, and 4.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: -8

3. What is the absolute value of -11?

Show solution
  1. Warm-up: First identify exactly what the question is asking: What is the absolute value of -11?
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Absolute value means distance from zero.
  4. -11 is 11 units from zero.
  5. Check the result by substituting or estimating: the response should match 11 and make sense in the original problem.

Answer: 11

4. Which comparison is true?

Choices: -6 > -2 · -3 < -10 · 5 > -1 · 0 < -7

Show solution
  1. Core Practice: First identify exactly what the question is asking: Which comparison is true?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Positive numbers are greater than negative numbers.
  4. 5 is to the right of -1.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 5 > -1

5. How many units apart are -7 and 2 on a number line?

Show solution
  1. Core Practice: First identify exactly what the question is asking: How many units apart are -7 and 2 on a number line?
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Count the distance from -7 to 0, then 0 to 2.
  4. 7 + 2 = 9.
  5. Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.

Answer: 9

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