Maths Library

Operations with Integers: Year 8 maths

This topic develops fluency in adding, subtracting, multiplying, and dividing directed numbers. The sheet focuses on mastering sign rules and multi-step calculations with bracketed integers.

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What this covers

Operations with Integers is taught in Year 8 (age 12 to 13, KS3) as a topic to introduce. It sits in the Number strand.

Worked example

Calculate (-4) × (-3) - 15.

  1. Multiply negative by negative: (-4) × (-3) = 12
  2. Subtract 15 from 12: 12 - 15
  3. Calculate the final value: -3

Answer: -3

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Addition and subtraction of single digits involving one negative number
  2. Multiplication and division of two directed integers up to 12
  3. Subtracting a negative number and expressions with mixed addition/subtraction
  4. Multi-step expressions using BIDMAS/PEMDAS with negative values
  5. Complex nested brackets and powers of negative integers

Common mistakes

  • Applying the rule 'two negatives make a positive' incorrectly to addition (e.g. -4 - 3 = +7)
  • Misidentifying the sign when dividing a negative by a positive

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Calculate with positive and negative integers using formal written and mental methods.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Operations with Integers

Year 8 maths

Qs
6
Marks
18
NameDateScore / 18
1.
4 − (−2) =
[3]
2.
18 × 6 =
[3]
3.
−72 ÷ 9 =
[3]
4.
10 + 8 =
[3]
5.
9 × (−5) =
[3]
6.
−15 − (−18) =
[3]

Answer key

  1. 6Subtracting (−2) is the same as adding 2; 4 − (−2) = 6
  2. 108Different signs give a negative; the same signs give a positive; 18 × 6 = 108
  3. −8(−8) × 9 = −72, so the answer is −8
  4. 18Adding 8 moves right on the number line; 10 + 8 = 18
  5. −45Different signs give a negative; the same signs give a positive; 9 × (−5) = −45
  6. 3Subtracting (−18) is the same as adding 18; −15 − (−18) = 3