Comparing With Symbols
You have 8 stickers and your friend has 3 —
who has more? Sharing out sweets, comparing scores in a game, checking who's taller: all the time
we need a quick way to say one number is bigger than another. Mathematicians have a neat shorthand
for exactly that.
Once we know which number is
bigger or smaller,
we can write it down with three little signs:
> \quad < \quad =
- > means greater than — the left number is bigger.
- < means less than — the left number is smaller.
- = means equal to — the two numbers are exactly the same.
The pointed signs > and < have a
wide open end and a tiny pointy end. That is the whole secret to
getting them right, as the next card explains.
The hungry-mouth trick
Imagine the sign is a hungry mouth. The mouth is greedy, so it always opens wide
toward the bigger number — it wants to eat the bigger pile! The little
pointy end is left facing the smaller number. So:
8 > 3 \qquad 3 < 8
In both lines the wide mouth faces the 8 (the bigger number) and
the point faces the 3 (the smaller number). The fact is the same;
only the order of writing changed.
A hungry shark always swims at the bigger pile of fish. Its open jaws
are exactly the shape of > or <:
the wide mouth faces the bigger number, the closed snout faces the smaller one.
<
2 < 5 — the shark's open mouth faces the pile of five.
The equals sign = is two perfectly level lines — like a pair of
scales that balance. Put the same amount on each side and neither tips
down: they are equal.
3 = 3 — three coins each side, so the scales balance.
Two traps to remember every time:
- The open end (the wide mouth) always faces the BIGGER number.
- The small point always faces the smaller number.
- If you can't decide which way it goes, just point the open mouth at the bigger pile —
it never lies.
Reading the symbol out loud
The real skill is reading the symbol, left to right, like a sentence. We read
7 > 3 as "seven is greater than three", and
we read 3 < 7 as "three is less than seven".
Notice these say the same fact two ways — seven really is the bigger number either way.
When the two numbers are the same we use =:
5 = 5 reads "five is equal to five".
Worked examples
- 9 \;\square\; 4: nine is bigger, so the mouth opens toward the
9: 9 > 4, read "nine is greater than four".
- 2 \;\square\; 6: two is smaller, so the point faces the
2 and the mouth opens toward the 6:
2 < 6, read "two is less than six".
- 8 \;\square\; 8: both the same, so they balance:
8 = 8, read "eight is equal to eight".
See it: which way does the mouth face?
Here are two piles of counters with the correct symbol already in the middle. Check it
yourself: the open mouth faces the bigger pile. Press Refresh for a brand-new pair.
Press play. Two numbers appear, the correct symbol grows between them with its mouth
turning toward the larger number, and we read the whole sentence aloud. Replay it: each
time the numbers change, so the symbol may flip — and sometimes they are equal.
Khan Academy explains the greater-than and less-than symbols here: