Year 7 · Directed number
Place positive and negative numbers on a number line
Learn how to place negative numbers on a number line and add, subtract, multiply and divide with them, on paper and on a calculator.
Definition
A negative number is a number below zero, such as a temperature of -6 degrees C or a bank balance that is overdrawn. On a number line the negative numbers run to the left of 0, mirroring the positive numbers on the right. Every number has a size and a sign: -8 and 8 are the same distance from 0 but on opposite sides. All the arithmetic you already know still works with negatives, once you keep track of direction as well as distance.
Why Do I Have to Learn This?
Negative numbers describe things below zero, like freezing temperatures or owing money. They let us measure in both directions.
Key Rules:
- 1. On a number line the negative numbers sit to the left of 0, and further left always means smaller: -7 is less than -2.
Remember:
- •Further left on the number line means smaller, like signs multiply to a positive, and subtracting a negative is adding.
Don’t Forget...
- •Thinking -7 is bigger than -2 because 7 is bigger than 2. The minus sign reverses the comparison: -7 sits further left on the number line, further below zero, so it is the smaller number.
- •Working out 5 - (-3) as 2 by ignoring the second minus sign. Subtracting a negative is the same as adding, so 5 - (-3) = 5 + 3 = 8; the two signs combine into one operation before any counting starts.
- •Expecting a calculator to give 9 for -3 squared typed without brackets. The calculator squares the 3 first and then applies the minus, returning -9; squaring the negative number itself needs brackets, as in (-3) squared.
Directed number
A number with a sign, so positive or negative.
−3 and +5 are directed numbers. On a number line, −3 sits three steps to the left of zero.
Worked Example:
The temperature in a freezer store is -6 degrees C. The door is left open and the temperature rises by 10 degrees. What is the temperature now?
Start at -6 on the number line; a rise of 10 degrees is a jump of 10 to the right.
Break the jump at 0: climbing from -6 up to 0 uses 6 of the 10 degrees.
That leaves 10 - 6 = 4 degrees to carry on past 0.
So -6 + 10 = 4.
Answer: 4 degrees C
Why It Works:
The sign of a number gives its direction from 0, so adding a negative moves left, which is exactly what subtracting a positive does. Zero pairs work because a number and its opposite sum to 0, and adding 0 changes nothing. Multiplying by a negative reverses direction on the number line, so reversing twice, as in -6 x -2, lands back on the positive side.
Another Example:
Work out (-8 + 3) x (-2) - 5 without a calculator.
Brackets first: -8 + 3 means starting at -8 and moving 3 to the right, which gives -5.
Next the multiplication: -5 x -2 has two like signs, so the answer is positive 10.
Finally subtract: 10 - 5 = 5.
Answer: 5
Animated Example:
Free Place positive and negative numbers on a number line Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Before this: Negative numbers (Year 5) · Next: Non-calculator methods (Year 10 Foundation)
Let’s Practise the Concept
Step 1 of 3
Put them in order
Tap the numbers from smallest to largest.
In order so far: nothing yet