Less than means smaller in value, and its symbol is <. The statement 4 < 9 reads “4 is less than 9.” The pointed end of the symbol always faces the smaller number. On a number line, the smaller number is farther left, so −3 < 2 even though 3 is bigger than 2. Less than does not include equal.
In Spanish
menor que
Also called
less than sign, < symbol, smaller than, fewer than
Less means farther left on the number line. For an inequality like x < 3, the open circle shows that 3 itself is not included.
Formal definition and notation
For real numbers a and b, a < b means b − a is positive; equivalently, a lies to the left of b on a number line oriented left to right. The relation is strict: a < a is never true. It is the reverse of greater than (a < b exactly when b > a), and with “equal to” it forms a ≤ b. In algebra, x < c describes every number to the left of c, graphed with an open circle at c.
Greater than (>) is the reverse comparison: 4 < 9 and 9 > 4 say the same thing.
Less Thanvs."Less than" in word problems
“7 less than y” means y − 7. It names a number; it is not a comparison.
Quick check: 3 questions
Question 1 of 3
Which statement is true?
Show answer and explanation
Answer: C.−2 is to the left of 1, so −2 < 1. −7 is less than −5; 0.5 = 0.50 is more than 0.45; and 34 = 0.75 is more than 23 ≈ 0.67.
Question 2 of 3
How do you write “x is less than 6”?
Show answer and explanation
Answer: A. Write the words in order with the symbol pointing at x: x < 6. 6 < x and x > 6 say x is greater, and x ≤ 6 also allows 6.
Question 3 of 3
Which number makes x < −2 true?
Show answer and explanation
Answer: D.−2.5 is to the left of −2, so it is less. −2 is equal, not less, and 0 and 3 are greater.
Less Than: frequently asked questions
Which way does the less than sign go?
The pointed end faces the smaller number, and the open end faces the larger number. So “3 is less than 8” is 3 < 8: read from left to right, the small number comes first. A common memory trick is that the open mouth always faces the bigger amount, or that < looks like a slanted L, for Less.
What is the difference between < and ≤?
< means strictly less than, so equal values do not count: 6 < 6 is false. ≤ means less than or equal to, so 6 ≤ 6 is true. On a number line graph, x < 6 uses an open circle at 6 and x ≤ 6 uses a filled dot.
Is a negative number less than zero?
Yes. Every negative number is less than 0, and every negative number is less than every positive number. Among negatives, the one farther from zero is smaller: −10 < −1. On a number line, negative numbers sit to the left of 0, and left always means less.
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The opposite of a negative number is positive.Number System · Grade 6, Grade 7, Grade 8Greater Than or Equal ToGreater than or equal to means a value is either bigger than a number or exactly equal to it, and its symbol is ≥. The inequality x ≥ 3 is true for 3 and every number above it. It means “at least 3”. On a number line it is graphed with a filled dot, because the endpoint is included.Symbols and Notation · Grade 6, Grade 7, Algebra 1At Least and At MostAt least and at most are word-problem phrases for limits that include the boundary. “At least 3” means 3 or more, written x ≥ 3. “At most 3” means 3 or less, written x ≤ 3. In both cases the number 3 itself is allowed, so it gets a filled dot on a number line.Problem Solving · Grade 6, Grade 7, Algebra 1