Math Inequalities: Less Than & Greater Than Signs

Hi there. This post is about comparison signs such as the less than sign (<), the greater than sign (>), the less than or equal to sign (≤) and the greater than or equal to sign (≥).

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Sections

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• The Less Than Sign & The Greater Than Sign
• Less Than Or Equal Signs & Greater Than Or Equal Signs
• Answers
• Notes

The Less Than Sign & The Greater Than Sign

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With the less than sign < and the greater than sign (>) we deal with quantities that are not equal. Here are some examples.

Examples

1. The inequality 7 < 9 means that 7 is less than 9 or 9 is greater than 7.

2. The number 20 is greater than 10 or 10 is less than 20. This is represented by 20 > 10 or 10 < 20.

3. Here is a case with negative numbers. Zero is greater than negative five. In math notation, this would 0 > -5 or -5 < 0.

4. Here is another example with negatives. We have -10 > - 20 or -20 < -10. The number that is more negative is the "smaller" number.

5. The signs can be extended past two numbers. We have 0 < 5 < 10 or 10 > 5 > 0.

You can look at these inequality symbols like arrows where the larger number "points" at the smaller number. Another way to look at it is that the symbols is like a mouth where the smaller number tries to eat the bigger number (see image below).

Visual Guide With Aligator Mouths

When dealing with numbers, remember that the negative number closest to zero is the larger number. A negative number that is more negative is father away from zero.

Number Line Visual Guide

Exercises

For questions 1 to 5, use the less than sign (<) or the greater than sign (>) when filling in the gray area.

Q1) 100 ____ 77

Q2) -2 ____ 1

Q3) 0 ____ 9

Q4) 42 ____ 45

Q5) 10 ____ 2 ____ -1

Less Than Or Equal To Signs & Greater Than Or Equal To Signs

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An extension of the above cases would be adding on an equal sign. The numbers can be equal on top of being either less than or greater than.

The symbol for the less than or equal to sign is ≤ and the greater than or equal sign to is indicated by ≥. (We read from left to right.)

Examples

1. In the previous section there was the inequality 7 < 9. This inequality is still true with the ≤ sign. It would be 7 ≤ 9 or 9 ≥ 7.

2. The number 0 is at least greater than or equal to -1. The math notation would be 0 ≥ -1 or -1 ≤ 0.

3. The number 20 is at least greater or equal to the number 20. This is represented as 20 ≥ 20 and not by 20 > 20.

4. Adding the numbers 7 and 11 gives 18 which is greater than or equal to 15. The math notation would be (7 + 11) ≥ 15 or 18 ≥ 15.

Exercises

For questions 1 to 5, use the less than sign (≤) or the greater than sign (≥) when filling in the blanks.

Q1) -1 ____ 1

Q2) 3 ____ 0

Q3) (7 + 5) ____ (20 - 8)

Q4) -1 ____ (-6 + 7)

Q5) (1 + 4) ____ 5 ____ (12 - 6)

Answers

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Set One

Q1) 100 > 77

Q2) -2 < 1

Q3) 0 < 9

Q4) 42 < 45

Q5) 10 > 2 > -1

Set Two

Q1) -1 ≤ 1

Q2) 3 ≥ 0

Q3) (7 + 5) ≤ (20 - 8) or (7 + 5) ≥ (20 - 8) or 12 ≤ 12

Q4) -1 ≤ (-6 + 7)

Q5) (1 + 4) ≤ 5 ≤ (12 - 6)

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Another Aligator Learning Aid For Inequalities

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Notes

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• For simplicity, the exercise problems deal with addition and subtraction.

• Natural extensions would include multiplication, division, fractions, exponents, square roots and more. Adding these with inequalities would definitely increase the difficulty levels.

• For cases like -1 ≤ 10 you do not necessarily need ≤ when < is enough.

• I did not include interval notation as I would need to include the concept of infinity. One could refer to this image.