Negative Numbers
Negative Numbers is a key number topic at GCSE Maths. This Foundation worksheet gives you exam-style questions on calculating with negative numbers, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. Two negatives multiplied give a positive; subtracting a negative is adding.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
Stretch yourself beyond the basics.
Topic overview
Negative numbers are values below zero, used for temperatures, bank balances, depths and directions. On a number line they extend leftwards, so \(-5\) sits further left, and therefore lower, than \(-2\).
Ordering catches people out. With negatives, the larger the digit the smaller the number, so \(-7\) is less than \(-3\). Picturing the number line removes the confusion.
The rules for multiplying and dividing are short: two signs the same give a positive, two signs different give a negative. For adding and subtracting, thinking in terms of movement along a number line is more reliable than memorising rules.
Revision notes
Ordering and the number line
Numbers increase from left to right. Negative numbers sit to the left of zero, so \(-8 < -3 < 0 < 2\).
A common error is treating \(-8\) as larger than \(-3\) because \(8 > 3\). On the line, \(-8\) is further from zero in the negative direction, so it is smaller.
Adding and subtracting
Adding moves right and subtracting moves left. Two adjacent signs combine: \(+\ -\) or \(-\ +\) becomes subtract, while \(-\ -\) becomes add.
So \(5 - (-3) = 5 + 3 = 8\), and \(-4 + (-2) = -4 - 2 = -6\).
Multiplying and dividing
Same signs give a positive answer, different signs give a negative one.
So \(-6 \times -3 = 18\) but \(-6 \times 3 = -18\). The same rule applies to division: \(-20 \div -4 = 5\).
Key points
- Negative numbers lie to the left of zero.
- The larger the digit, the smaller a negative number is.
- Adding moves right; subtracting moves left.
- Two minus signs together become a plus.
- Same signs multiply or divide to a positive.
- Different signs multiply or divide to a negative.
Worked examples
Example 1
Work out \(-7 + 12\).
Working
Example 2
Work out \(3 - (-8)\).
Working
Example 3
Work out \(-4 \times -5\).
Working
Common mistakes
Thinking \(-8\) is greater than \(-3\).
On the number line −8 is further left, so it is smaller. The digit size is misleading.
Mishandling two adjacent signs.
5 − (−3) is 5 + 3 = 8. Two minuses make a plus.
Applying the sign rules to addition.
The same-sign rule is for multiplying and dividing. For adding and subtracting, think about movement along the line.
Losing the sign in the final answer.
A negative answer must keep its minus sign, especially in temperature or balance questions.
Exam tips
- Sketch a number line whenever the signs are confusing.
- Rewrite double signs as a single sign before calculating.
- State clearly whether an answer is positive or negative.
- Check the answer makes sense in context, such as a temperature drop giving a lower value.
Key terms
- Negative number
- A value less than zero.
- Number line
- A line showing numbers in order, increasing to the right.
- Integer
- A whole number, which may be positive, negative or zero.
- Difference
- The gap between two numbers, always given as a positive amount.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.