Greater than means that one number is bigger than another, and its symbol is >. The statement 7 > 3 reads “seven is greater than three”. The open side of the symbol faces the bigger number and the point aims at the smaller one. On a number line, the greater number is always farther to the right.
In Spanish
mayor que
Also called
greater than sign, greater than symbol, more than, larger than, >
The open side of > faces the bigger number. On a number line the bigger number is the one farther right, which is why −2 > −6.
Formal definition and notation
For real numbersa and b, a > b means that a − b is positive. Equivalently, a lies to the right of b on a number line that increases to the right. The relation is strict: a > a is false. a > b says the same thing as b < a.
Words that mean >: more than, exceeds, above, over, bigger than.
Try it: which is greater?
Interactive
Drag the two points, or select one and use the arrow keys. The readout writes the comparison with the smaller number first; flip it to read the greater-than statement. Try two negative numbers.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Greater Than examples, step by step
Example 1: Compare two numbers
Warm-up
Put >, < or = between 386 and 368.
Hundreds: both have 3, so look at the next place.
Tens: 8 tens is more than 6 tens.
So 386 is the bigger number, and the open side faces it.
Answer:386 > 368
Example 2: Negative numbers and decimals
Core
Which is true: −4.5 > −4.2 or −4.2 > −4.5?
Both numbers are between −5 and −4.
−4.2 is 0.2 left of −4; −4.5 is 0.5 left of −4.
−4.2 is closer to 0, so it is farther right and greater.
Answer:−4.2 > −4.5 is true.
Example 3: Which numbers make it true?
Test-style
Which of the numbers 3, 5, 8, 10 make 2x − 1 > 9 true?
Solve like an equation: add 1 to both sides, 2x > 10.
Divide both sides by 2: x > 5.
5 itself is not greater than 5, so it does not count. Of the list, only 8 and 10 are greater than 5.
Answer: 8 and 10 make the inequality true; 5 does not, because 2(5) − 1 = 9, which equals 9 instead of being greater.
Common mistakes
✗ Mistake−8 > −3 because 8 is bigger than 3.
✓ Instead−3 > −8: −3 is farther right on the number line.
For negative numbers, the one closer to 0 is greater. Being 8 below zero is colder than being 3 below.
✗ MistakeWriting 4 > 9 to say “4 is less than 9”.
✓ Instead4 < 9, or 9 > 4.
The open side faces the bigger number. Read the symbol from left to right: the left number is the one being described.
✗ Mistake0.3 > 0.25 is false because 25 is bigger than 3.
✓ Instead0.3 > 0.25 is true: 0.30 is more than 0.25.
Line up decimal places before comparing. Add a zero, 0.30, and compare 30 hundredths to 25 hundredths.
< points the other way. 3 < 7 and 7 > 3 are the same fact, read from different ends.
Quick check: 3 questions
Question 1 of 3
Which statement is true?
Show answer and explanation
Answer: C.−1 is right of −5 on the number line, so −1 > −5. The first choice reverses it, and 0 and −3 are both less than the positive numbers they are compared with.
Question 2 of 3
Which symbol belongs in the blank: 0.7 ___ 0.65?
Show answer and explanation
Answer: A. 0.7 is 0.70, which is 70 hundredths, and that is more than 65 hundredths. So 0.7 > 0.65. Choosing < comes from comparing 7 with 65 as whole numbers.
Question 3 of 3
Which value of x does not make x > 12 true?
Show answer and explanation
Answer: D.x > 12 needs numbers bigger than 12. 12 is equal to 12, not greater, so it fails. 12.5, 13 and 100 are all greater than 12.
Greater Than: frequently asked questions
Which way does the greater than sign go?
The open, wide side faces the bigger number and the point faces the smaller one: 8 > 5. Read it left to right as “8 is greater than 5”. If the bigger number is on the right, you need the less than sign instead: 5 < 8. Both statements say the same thing.
Is 0 greater than a negative number?
Yes. 0 is greater than every negative number, because every negative number is to the left of 0 on the number line. So 0 > −1, 0 > −100 and 0 > −0.001. Likewise, every positive number is greater than 0, so any positive number is greater than any negative number.
What is the difference between > and ≥?
> means strictly greater: 5 > 5 is false. ≥ means greater than or equal to: 5 ≥ 5 is true. In word problems, “more than” means > while “at least” means ≥. On a number line graph, > uses an open circle at the boundary and ≥ a closed dot.
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