The number line
Reading and marking integers on the line, from −10 to 10 and in steps of 2, 5 or 10, so negative numbers have a place before pupils calculate with them.
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Teaching guide: operations with integers
Integers are the whole numbers, zero and the negative numbers. In Grade 6 pupils place them on the number line and compare them; in Grades 7 and 8 they add, subtract, multiply and divide them with the sign rules. This free generator creates A4 worksheets for every step, from reading the number line to removing square brackets and working out powers with a negative base, with an answer key that shows the rule used.
Student worksheet 
Answer key < Compare and order
Opposites, absolute value and order: −8 < −3 because it is further left, even though 8 is greater than 3.
Adding and subtracting
Same signs, add; different signs, subtract. Subtracting is adding the opposite, and chains are solved by grouping positives and negatives.
Removing brackets
A − before a bracket changes the sign of every term inside it. With square brackets, start with the innermost brackets.
Multiplying, dividing and powers
The sign rules of multiplication and division, the sign of a product of three or four factors and the difference between (−2)⁴ and −2⁴.
Step-by-step answer key
Every answer with its step, such as −(8 − 5) = −3 or +(4 × 6) = 24, and the rule used beside it. Write (+5) or just 5, and choose × or ·.
Frequently asked questions about integer worksheets
How do you add two integers?
With the same sign, add their absolute values and keep the sign: (−4) + (−6) = −10. With different signs, subtract the smaller absolute value from the larger and take the sign of the number with the greater absolute value: (+5) + (−8) = −3.
How do you subtract integers?
Subtracting is adding the opposite: (−3) − (−5) = (−3) + (+5) = 2. That is why a − before a negative number gives a +: 7 − (−2) = 7 + 2 = 9.
What are the sign rules for multiplying and dividing integers?
Two equal signs give +, and two different signs give −: (−3) × (−4) = 12 and (−24) ÷ (+6) = −4. With more factors, the answer is negative when an odd number of factors are negative.
Why is (−2)⁴ not the same as −2⁴?
In (−2)⁴ the base is −2, and four negative factors give +16. In −2⁴ the exponent only applies to the 2: −2⁴ = −(2⁴) = −16. Level 3 of multiplying practises this difference.
Which grades are these worksheets for?
The number line, opposites, absolute value and the first additions are for Grade 6; the four operations and removing brackets for Grade 7; chains, square brackets, powers and missing terms for Grade 8. Once pupils are confident with single operations, they can move on to the order of operations with negative numbers.
How are the numbers written in the operations?
By default every number carries its sign in brackets: (+5) + (−3). Under More options you can choose the simplified form, 5 + (−3), where only negative numbers are in brackets, and the × or · sign for multiplying.
What other worksheets go well with integers?
The order of operations with negative numbers, linear equations, which use them at every step, and fraction operations. Find every resource under maths worksheets.
How do I print only the answer key?
Click Print and choose "Answer key", or "Worksheet and answer key" for both. Your browser's print dialog can also save it as a PDF.
Is any pupil data sent anywhere?
No. Worksheets are generated in your browser and templates are saved in your browser's memory.
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