Ordering and Comparing Integers

Integers are compared almost in the same way as whole numbers, but with addition of some rules.

Steps for comparing integers:

If we compare numbers with different signs, then negative number is less than positive.
If numbers are both positive then this is the case when we compare whole numbers.
If numbers are both negative then we compare numbers without signs. The bigger positive number, the smaller negative. For example, if we compare -3 and -5, then we compare 3 and 5 (numbers without signs). Since ${3}<{5}$ then $-{3}>-{5}$ .

Example 1. Compare 4567 and -12345.

Numbers are with different signs. Negative number is always less than positive. Therefore, ${4567}>-{12345}$ .

Next example.

Example 2. Compare -300 and 0.

0 is always bigger than any negative number, so $-{300}<{0}$ .

Next example.

Example 3. Compare -12 and -234.

Compare numbers without signs: 12 and 234.

Since ${12}<{234}$ then $-{12}>-{234}$ .

Next example.

Example 4. Compare -234 and -123.

Compare numbers without signs: 234 and 123.

Since ${234}>{123}$ then $-{234}<-{123}$ .

Last example.

Example 5. Compare -2345 and -2346.

Compare numbers without signs: 2345 and 2346.

Since ${2345}<{2346}$ then $-{2345}>-{2346}$ .

Now, practice a bit.

Exercise 1. Compare -456 and 12.

Answer: $-{456}<{12}$ . Hint: numbers are with different signs.

Next exercise.

Exercise 2. Compare 0 and 12.

Answer: ${12}>{0}$ . Hint: positive number is greater than 0.

Next exercise.

Exercise 3. Compare -45673 and -234.

Answer: $-{45673}<-{234}$ .

Next exercise.

Exercise 4. Compare -3456 and -3500.

Answer: $-{3456}>-{3500}$ .

Last exercise.

Exercise 5. Compare -86743 and -86743.

Answer: Numbers are equal, i.e. $-{86743}=-{86743}$ .