Negative Numbers
Recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane.
Read this first
Numbers do not stop at zero. They keep going the other way. Those numbers are real: cold days, money you owe, floors below the ground.
Zero sits in the middle. and are the same distance from zero, just in opposite directions. The further left you go, the smaller the number.
Words you need
- Integer
- Any whole number, positive, negative or zero. , and are all integers. is not.
- Negative
- Less than zero. We write a minus sign in front: .
- Opposite
- The same distance from zero, on the other side. The opposite of is .
Worked example
e.g. Which is colder: C or C?
- You might say is bigger, because 7 is bigger than 2. Careful.
- Put both on a number line. sits further left than .
- Further left always means smaller. So is less than .
- Now check it in real life. C is colder. That matches.
Picture the number line. Left is smaller. Right is bigger. That rule never breaks.
Practice
The pictures fade as you go. By the last few you are on your own.
1Which number is greater: or ?with a picture
Answer is greater. It sits further right on the number line. Even though 4 looks like a bigger digit, is further from zero on the negative side, so it is smaller.
2The temperature is C and rises by . What is it now?with a picture
AnswerC. Rising means moving right along the number line. Start at , move 5 places right: .
3Put these in order from smallest to largest: , , , , with a hint
Need a hint?
Sketch a number line and mark each one. Then just read them off left to right.
Answer, , , , . Reading a number line left to right always gives you smallest to largest.
4Ravi's bank account is at . He deposits . What is his balance?with a hint
Need a hint?
A negative balance means he owes money. A deposit moves him towards zero.
Answer. He still owes . Moving 25 to the right from lands on .
5What is the opposite of ?on your own
Answer. Opposites are the same distance from zero on the other side.
6A lift starts on floor and goes up 6 floors. Where does it stop?on your own
AnswerFloor 4. Start at , move 6 to the right.
7Which is further from zero: or ?on your own
Answer. Distance from zero ignores the sign — is 9 away, is only 6 away. Note this is a different question from asking which is greater: is greater, but is further from zero.
Think about it
1
Jem says every negative number is smaller than every positive number. Is she right?
One good answerYes. Every negative sits left of zero and every positive sits right of zero, so any negative is always further left, and further left always means smaller.
2
Why does being further from zero than not make it the bigger number?
One good answerDistance from zero and size are different questions. Distance ignores direction; size does not. On the number line is a long way left, which makes it very small, even though the journey from zero is long.
3
Can you think of three real situations where negative numbers are genuinely useful?
One good answerFor example: temperature below freezing, money owed or an overdrawn account, floors below ground level, height below sea level, a golf score under par.
Common mistakes
Thinking is bigger than because 8 is bigger than 3.
With negatives, the bigger the digit, the smaller the number. is further left, so it is less than . Sketch the line whenever you are unsure.
Mixing up 'greater' with 'further from zero'.
These are different questions. is further from zero than , but is the greater number. Read the question carefully.
Forgetting which way to move when adding or subtracting.
Adding always moves right, subtracting always moves left — even when the numbers are negative. That rule does not change.