Mathematics from zero
Comparing numbers
Two friends count their coins. One has 7, the other has 4. Who has more? You already know the answer — now let us make it exact, and learn the two signs that write it down.
After this lesson you can decide which of two numbers is bigger, smaller, or equal, and write the result with the three signs: greater than, less than, and equal.
Comparing is asking “which is more”. In the lesson on counting you learned that every number has a spot on the number line, growing to the right. That is the whole secret of comparing: the number further to the right is the bigger one. 7 sits to the right of 4, so 7 is the bigger number.
There are exactly three answers. When you compare two numbers, one of three things is true: the first is greater than the second, the first is less than the second, or they are equal (the same number, the same spot on the line). Nothing else can happen.
Each answer has a sign. Greater than is written >. Less than is written <.
Equal is written =. So “7 is greater than 4” becomes 7 > 4, and “4 is less than
7” becomes 4 < 7. Both sentences say the same thing — just from the other number’s
point of view.
Compare 4 and 9. Which sign goes between them?
Find both on the number line. 9 sits further to the right than 4, so 9 is the bigger
number. Reading left to right, “4 ? 9”: 4 is the smaller one, so 4 is less than 9.
The answer is 4 < 9. The same fact written the other way round is 9 > 4.
Common mistake
The most common mistake is mixing up < and >. Use this trick: the sign is like an
open mouth, and the wide-open side always faces the bigger number. The narrow
point touches the smaller number. In 4 < 9 the point touches 4 (smaller), the open
side faces 9 (bigger). Check every comparison this way and you can never flip it.
Which is greater, 6 or 9? Type the bigger number.
Which is less, 7 or 3? Type the smaller number.
Type the greater of 12 and 8.
On the number line, which sits further right: 4 or 10? Type it.
Fill the gap so it is true: 5 < ? — type a number bigger than 5.
In the true sentence 3 < 8, what does the wide-open side of the sign face?
Comparing two numbers means asking which is further right on the number line — that
one is bigger. There are exactly three results: greater than (>), less than (<),
and equal (=). The open side of < or > always faces the bigger number, the
point touches the smaller one.