WorksheetsAbout this worksheet
Sums with negative numbers, written with brackets as in school books: (−7) + 5. Every sum has at least one negative number.
What this skill is
Integers are the whole numbers together with their negatives: ... −3, −2, −1, 0, 1, 2, 3 ... They are needed for temperatures below zero, depths below sea level, floors below the ground and money owed. On a number line, negative numbers lie to the left of zero, and a number further left is always smaller, so −7 is less than −3.
A worked example
(−7) − (−3)
- Subtracting a number is the same as adding its opposite. The opposite of −3 is 3.
- So the sum becomes (−7) + 3.
- Start at −7 on the number line and move 3 steps to the right: −6, −5, −4.
The answer is −4.
Multiplying and dividing: (−6) × (−4) = 24, because the signs are the same. 20 ÷ (−5) = −4, because the signs are different.
Tips for parents and teachers
- Use a number line for adding and subtracting. Adding a negative number moves left; subtracting a negative number moves right.
- Subtracting a number is the same as adding its opposite: 3 − (−4) = 3 + 4.
- For multiplying and dividing: same signs give a positive answer, different signs give a negative answer.
How to use this sheet at home and in class
- At home: draw a number line from −10 to 10 on a strip of paper and keep it beside the sheet for the first week. Let the child move a finger or a coin along it.
- In class: teach "Add and subtract" fully before "Multiply and divide". The sign rules of the two are different, and children mix them when both are new.
- Use stories: the temperature was −7 degrees and rose by 3; a diver at −20 metres comes up 5 metres.
Mistakes to watch for
- Using the multiplication rule for addition: saying (−7) + (−3) is 10 because "two minuses make a plus". It is −10.
- Reading 3 − (−4) as 3 − 4. The two signs together turn into a plus: 3 + 4 = 7.
- Thinking −7 is bigger than −3 because 7 is bigger than 3.
What to try next
- BODMAS worksheets: order of operations.
- Simple equations worksheets: equations whose answers may need these rules.
- Comparing numbers worksheets: if the number line idea is shaky.