Integers & Negative Numbers — Year 7 Revision Notes
These notes cover everything you need on integers and negative numbers for Year 7 (Stage 7) of Cambridge Lower Secondary Maths: ordering them, the four operations, and the all-important sign rules.
Ordering integers on a number line
A number line places integers in order, with negative numbers to the left of zero and positive numbers to the right. As you move right the numbers get larger, so −5 < −2 < 0 < 3. Remember that with negative numbers the digit that looks bigger is actually smaller: −9 is less than −1.
Tips
- Sketch a quick number line whenever you are comparing negative numbers.
- Read < as 'is less than' and > as 'is greater than'.
Adding and subtracting integers
Adding a negative is the same as subtracting, and subtracting a negative is the same as adding. So 4 + (−3) = 1 and 4 − (−3) = 7. A number line helps: to add you move right, to subtract you move left.
Key Facts & Formulas
- a − (−b) = a + b
- a + (−b) = a − b
Tips
- Rewrite double signs first: − (−) becomes +, and + (−) becomes −.
- Always check whether your answer should be positive or negative before writing it down.
Multiplying and dividing integers
When multiplying or dividing two integers, a same-sign pair gives a positive answer and a different-sign pair gives a negative answer. So (−6) × (−2) = 12 but (−6) × 2 = −12.
Key Facts & Formulas
- (+)(+) = +
- (−)(−) = +
- (+)(−) = −
- (−)(+) = −
Tips
- Work out the sign of the answer first, then multiply the digits.
- The sign rules are the same for division as for multiplication.
Revision Checklist
- I can order positive and negative integers using a number line
- I can add and subtract integers, including double signs
- I can multiply and divide integers using the sign rules
- I can use negative numbers in context, such as temperature
Frequently Asked Questions
Does two minuses always make a plus?
Only for multiplication, division and double signs. When you add two negative numbers the answer is still negative: (−3) + (−4) = −7.
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