Year 8 - Integer operations - Free practice

Year 8 Integer Operations Worksheets & Practice

Add, subtract, multiply and divide integers with clear working, free worksheets included.

Quick answer

How do you add, subtract, multiply and divide integers?

Integers are whole numbers including negatives and zero. Add and subtract by moving along the number line, noting that subtracting a negative means adding. For multiplication and division, same signs give a positive result and different signs give a negative result. For example, −3 × −4 = 12 and −12 ÷ 3 = −4.

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 8 integer operations: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Adding and subtracting integers
Evaluate $-14 + 9 - (-5)$ .
Show worked solution
Key idea: Subtracting a negative is the same as adding its positive. Then work left to right.
1. Rewrite the subtraction of a negative: $-14 + 9 - (-5) = -14 + 9 + 5$
2. Add the positive integers first as a mental strategy: $9 + 5 = 14$ , so $-14 + 14$
3. Evaluate: $-14 + 14 = 0$
Answer: $0$
Example 2 · Order of operations with negative numbers
Evaluate $3 - (-2)^3 \div 4 \times (-1)$ .
Show worked solution
Key idea: Follow BODMAS: evaluate the power first, then division and multiplication left to right, then subtraction.
1. Evaluate the power: $(-2)^3 = -8$ , so the expression becomes $3 - (-8) \div 4 \times (-1)$
2. Division (left to right): $(-8) \div 4 = -2$ , giving $3 - (-2) \times (-1)$
3. Multiplication: $(-2) \times (-1) = 2$ , giving $3 - 2$
4. Subtract: $3 - 2 = 1$
Answer: $1$
Example 3 · Real-life problem: temperature change
At midnight the temperature in a town was $-6{°}$ C. By noon it had risen by $11{°}$ C, then during the afternoon it fell by $3{°}$ C for each of the next $4$ hours. What was the temperature at the end of those $4$ hours?
Show worked solution
Key idea: Rise means add, fall means subtract. A repeated fall can be written as multiplication.
1. Temperature at noon after the rise: $-6 + 11 = 5 \text{ °C}$
2. Total drop over 4 hours: $3 \times 4 = 12 \text{ °C}$
3. Temperature after the fall: $5 - 12 = -7 \text{ °C}$
Answer: $-7{°}$ C

Common mistakes

Where students usually lose marks

Confusing (-2)² with -2²

Student writes $(-2)^2 = -4$ (treats it the same as $-2^2$ ).

The brackets matter. $(-2)^2 = (-2) \times (-2) = 4$ , whereas $-2^2 = -(2 \times 2) = -4$ . Always apply the exponent to everything inside the brackets.

Subtracting a negative gives a negative

Student writes $7 - (-3) = 4$ instead of $10$ .

Subtracting a negative flips the sign, making it an addition: $7 - (-3) = 7 + 3 = 10$ . Think of it as removing a debt, which makes you richer.

Ignoring sign rules in multiplication and division

Student writes $(-4) \times (-5) = -20$ (keeps the negative).

When two integers with the same sign are multiplied or divided, the result is always positive. When the signs differ, the result is negative. Check: negative $\times$ negative $=$ positive, so $(-4) \times (-5) = 20$ .

Applying BODMAS incorrectly with negatives

Student evaluates $10 - 3 \times (-2)$ as $10 - 3 = 7$ , then $7 \times (-2) = -14$ .

Multiplication must be done before subtraction. First find $3 \times (-2) = -6$ , then $10 - (-6) = 10 + 6 = 16$ . Write out each step to avoid rushing into left-to-right working.

Try one yourself

Your turn

Calculate $(-5) \times (-3) + (-8) \div 2$ .

Got a different integer operations question wrong? Upload it to Tuterly and get the worked solution and a fresh one to practise, free.

About this worksheet

Why we built it

Integer operations extend Year 8 students beyond whole numbers to include negative values across all four operations. These worksheets build fluency with adding, subtracting, multiplying and dividing integers, covering the sign rules that trip up so many students, with fully worked solutions on every question so your child can see exactly where their reasoning should go.

What's covered

Sub-skills your student will practise

✓Adding and subtracting positive and negative integers
✓Multiplying integers using sign rules (positive × negative, etc.)
✓Dividing integers and determining the correct sign
✓Order of operations with negative numbers
✓Efficient mental strategies for integer calculations
✓Mixed four-operation problems with integers

From our families

Parents on the practice questions.

“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”

Rebecca M.

Year 8 · Maths

“My daughter used to leave revision until the night before. Having a platform she can dip into for fifteen minutes after dinner has completely changed that. She's calmer going into assessments, and honestly, so am I.”

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Year 9 · Maths

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Ella, student

Year 10 · Maths

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Frequently asked

Questions parents ask about integer operations

Why do two negatives make a positive when multiplying?

It comes down to the sign rules for multiplication. A negative times a negative gives a positive because each negative reverses the direction on the number line, and two reversals bring you back to positive. Students often confuse this with addition, where two negatives simply give a larger negative.

What is the most common mistake Year 8 students make with integer operations?

Mixing up the rules for addition and multiplication is very common. For example, treating negative × negative as negative instead of positive. Working through the sign rules step by step, rather than trying to remember shortcuts, helps students avoid this error consistently.

How does this topic connect to the rest of Year 8 maths?

Integer operations underpin nearly everything in Year 8, including algebra, substitution into formulas and working with rational numbers. A solid understanding here makes topics like linear equations and graphing on the Cartesian plane much more manageable.

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