Skill: Compare and order integers

Explanation and Free Practice Resources

Ordering integers means determining relative magnitude among positive integers, negative integers, and zero, using their positions on a number line and symbols such as <, >, and =; numbers farther right are greater, so every positive integer is greater than zero and every negative integer, while zero is greater than every negative integer. Comparison of negative integers requires recognizing that a smaller absolute value represents the greater number, rather than judging by magnitude alone. This understanding supports integer operations, inequalities, and coordinate reasoning; comparisons of rational, irrational, or other more advanced number sets are not included.

Detailed Explanation: Compare and order integers

To compare and order integers, use their positions on a number line:

  • Numbers farther to the right are greater.
  • Every positive integer is greater than 00.
  • 00 is greater than every negative integer.
  • For negative integers, the number with the smaller absolute value is greater. For example, −2>−5-2>-5 because −2-2 is farther right on the number line.

Example: Order −4, 2, −1, 0, 3-4,\ 2,\ -1,\ 0,\ 3 from least to greatest.

  1. Find the negative integers. Since −4-4 is farther left than −1-1,
−4<−1.-4<-1.
  1. Place 00 after all negative integers:
−4<−1<0.-4<-1<0.
  1. Place the positive integers in order. Since 22 is less than 33,
2<3.2<3.
  1. Combine the numbers:
−4<−1<0<2<3.\boxed{-4<-1<0<2<3}.

So, from least to greatest, the integers are −4, −1, 0, 2, 3-4,\ -1,\ 0,\ 2,\ 3.

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Number Sense - Ordering 4 Integers (both)


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