Negatives order by depth below zero, so the bigger-looking number can be the smaller
Lower means smaller
Which is smaller, −2 or −7? On a thermometer, −2 is 2 steps below zero. −7 is 7 steps below zero, which is 5 steps further down than −2.
−7 is lower on the scale, so −7 is the smaller number, and −7° is the colder temperature. This is the comparison that catches people out: 7 is bigger than 2, but −7 is smaller than −2, because it is further below zero.
The level reads −2°, and −7° is marked 5 steps below it. The lower of the two is the smaller.
Left means smaller
The same rule holds on a number line laid flat. The further left a number is, the smaller it is. Reading from left to right gives the numbers in order from smallest to largest: −6, then −1, then 3.
Every negative number is smaller than 0, and every positive number is bigger than 0, so every negative number is smaller than every positive number.
−6 is furthest to the left, so it is the smallest. 3 is the only number right of zero, so it is the largest.
Writing it with < and >
The sign > means "is greater than", and < means "is less than". The open side of the sign always faces the larger number.
−2 is higher than −3, so −2 > −3. −7 is deeper below zero than −2, so −7 < −2. The higher of two numbers is the larger, however the digits look.
−7 lies to the left of −3, and −3 to the left of −2, so −7 < −3 < −2.
Putting a list in order
Five freezers are at 2 °C, −9 °C, −14 °C, −1 °C and −11 °C. To list them from coldest to warmest, start with the negative numbers. The one furthest below zero is the smallest, so −14 comes first, then −11, then −9, then −1. The only positive temperature, 2, comes last.
From coldest to warmest the order is −14, −11, −9, −1, 2.
Marked on one line, the five temperatures read from left to right in order, coldest first.
The usual mistakes
Ordering by how big the digits look. −1 is not smaller than −9 because 1 is smaller than 9. −9 is 9 steps below zero and −1 is only 1 step below, so −9 is the smaller.
Reading the list the wrong way round. Smallest first starts at the number furthest below zero, not at the number closest to it.
Your turn
1.Which is smallest: -1, 5 or -8?