Special numbers
Ordering and comparing numbers
Numbers can be positive or negative. On a number line, numbers get bigger as you move to the right, so you can compare them and put them in order.
The number line
A number line has zero in the middle. • Positive numbers are to the right of zero. • Negative numbers, like -1 and -20, are to the left of zero. The further right a number is, the greater it is. So -3 is greater than -5, because -3 is nearer to zero. Negative numbers are used for cold temperatures and for depths below sea level.
Comparing with < and >
We compare two numbers using symbols: • < means 'is less than' • > means 'is greater than' The wide open end always faces the bigger number. For example: -30 < 0 and -50 > -60. A positive number is always greater than a negative number, so 10 > -15.
Ordering numbers
To order numbers, compare them and line them up. • Smallest to largest starts with the most negative number. • Largest to smallest starts with the number nearest to (or above) zero. For temperatures, the coldest temperature is the smallest number. So -5 °C is colder than -2 °C.
Worked examples
Comparing two negative numbers
- Compare -5 and -3.
- Mark them on a number line. -3 is further to the right, so it is greater.
Answer: -3 > -5.
Choosing < or >
- Compare -50 and -60.
- -50 is nearer to zero, so it is to the right of -60 and is greater.
Answer: -50 > -60.
Ordering temperatures from coldest
- Order -4 °C, -2 °C, 0 °C and 3 °C from coldest.
- The coldest is the smallest number, so read from left to right on the number line.
Answer: -4, -2, 0, 3.
Where you see this in real life
- Reading temperatures in a freezer, which are below 0 °C.
- Describing how deep a diver is below sea level.
- Comparing floors above and below the ground in a building.
Key words
- Negative number
- A number less than zero, written with a minus sign, such as -5.
- Positive number
- A number greater than zero, such as 5.
- Number line
- A line with numbers in order; they get bigger to the right.
- is less than, <
- The symbol < shows the first number is smaller.
- is greater than, >
- The symbol > shows the first number is bigger.
- Order
- To arrange numbers from smallest to largest or largest to smallest.