Less than Symbol in Math - Use Less Than Sign in Homework
The less than sign (<) shows the value on the left is smaller than the value on the right: 3 < 5 reads "3 is less than 5." The open side faces the larger number. On a number line, a < b means a sits left of b. When the two values can also be equal, use ≤ instead of <.
What the less than sign means
We write this symbol between two values whenever the left one is the smaller of the pair. It belongs to the inequality signs, the same group as >, ≤, and ≥. Compare 3 and 5 and you write 3 < 5, then say it aloud as "three is less than five."
A number line makes the rule visible: on it, the number on the left is always the smaller one. Take any two numbers a and b. Then a < b means the point for a lands to the left of the point for b. Walk the line from left to right and the values rise, so anything behind you on the left is smaller.
The < and > shapes have been printed since the 1600s; credit for introducing them in 1631 is usually given to Thomas Harriot's posthumous work. The history is worth a glance, but what you actually use in homework is the number-line reading.
How to remember which way < points
Everyone flips < and > at first. One rule settles it: the open side of the sign faces the larger number, and the point faces the smaller one. Picture an alligator mouth that always opens toward the bigger pile of food. In 3 < 5 the wide opening turns toward 5, which marks 5 as the larger value.
Now read your own work out loud, left to right. When the sentence is true, the sign is facing the right way. 3 < 5 says "3 is less than 5," which holds. Swap it to 5 < 3 and you are saying "5 is less than 3," which does not. That read-back catches most direction mistakes on its own.
Less than vs greater than
The pair are mirror images. < points left at the smaller number; > points right at the larger one. Flip a statement and swap the sign, and you keep the same meaning.
Statement | Reads as | Is true when |
3 < 5 | 3 is less than 5 | the left value is smaller |
5 > 3 | 5 is greater than 3 | the left value is larger |
a < b | a is less than b | a sits left of b on the number line |
b > a | b is greater than a | b sits right of a on the number line |
Reading <, >, and the equals and not-equals signs together rests on the same number-line logic used in Math is Fun. The quick test on any line: the pointed end should touch the smaller number.
Less than (<) vs less than or equal to (≤)
These two look alike, and the difference is one small bar. Plain < is strict: the left value has to be strictly smaller, so equality is off the table. Add the bar and you get ≤, "less than or equal to," which lets the two sides match.
- 3 < 5 holds, but 5 < 5 does not, because 5 is not strictly smaller than itself.
- 5 ≤ 5 holds, since equality is allowed, and 3 ≤ 5 holds as well.
Reach for < when the values cannot be equal; reach for ≤ when they can. A speed cap of "at most 60" takes ≤, while "strictly below 60" takes <.
Common mistakes
The sign itself is tiny, and small slips are where points get lost. Run through this list whenever an answer feels wrong.
- Writing "less then." The comparison is "than," as in "less than." "Then" belongs to sequence ("then we add"). Real searches already type it "less then," so it pays to catch it now.
- Pointing the wrong way. Read the statement aloud. If it is false, the sign is flipped.
- Using < when equality counts. If the two values may be equal, < is the wrong mark; pick ≤.
- Comparing across zero. Negatives sit on the left of the line, so -2 < 1 is true even though "2" looks bigger than "1."
For the formal definition and the historical note, Wikipedia gives a compact reference.
What to do next
Reading the sign is only the setup; the point is to use it. The very < you just read is the symbol behind Algebra 1's Linear Inequalities unit, where you write and solve statements like x < 4.
Open that Linear Inequalities unit when you want guided examples. You can also type a topic such as "comparing numbers" together with your level to build a short, interactive practice set.
Once inequalities click, the next move replaces the comparison with an equals sign and solves for the value: How to Solve a Linear Equation walks through that step.
Sources and review
- Wikipedia: Less-than sign, accessed September 30, 2026.
- Math is Fun: Equal, Less and Greater Than, accessed September 30, 2026.