Year 7 - Integers - Free practice

Year 7 Integers Worksheets & Practice Tests

Adding and subtracting positive and negative numbers, the easy way.

Quick answer

How do you add and subtract integers?

Integers are whole numbers that can be positive, negative or zero. To add a negative integer, move left on the number line; to add a positive, move right. Subtracting a negative is the same as adding a positive: for example, 3 − (−2) = 3 + 2 = 5. Order integers by their position on the number line.

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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 7 integers: 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 integers with opposite signs
Calculate $-8 + 3$ .
Show worked solution
Key idea: When adding integers with opposite signs, find the difference between their absolute values and keep the sign of the integer with the larger absolute value.
1. Find the absolute values: $\lvert -8 \rvert = 8$ and $\lvert 3 \rvert = 3$ .
2. Subtract the smaller from the larger: $8 - 3 = 5$ .
3. Keep the sign of the integer with the larger absolute value (negative, since $\lvert -8 \rvert > \lvert 3 \rvert$ ): the answer is $-5$ .
Answer: $-8 + 3 = -5$
Example 2 · Subtracting a negative integer
Calculate $-4 - (-9)$ .
Show worked solution
Key idea: Subtracting a negative is the same as adding the positive: $a - (-b) = a + b$ .
1. Rewrite the subtraction of a negative as addition: $-4 - (-9) = -4 + 9$ .
2. The two integers now have opposite signs. Find the difference of the absolute values: $\lvert 9 \rvert - \lvert -4 \rvert = 9 - 4 = 5$ .
3. Keep the sign of the integer with the larger absolute value (positive, since $\lvert 9 \rvert > \lvert -4 \rvert$ ): the answer is $5$ .
Answer: $-4 - (-9) = 5$
Example 3 · Multi-step temperature problem
At midnight, the temperature in Canberra was $-3^\circ\text{C}$ . By 6 am it had dropped a further $5^\circ\text{C}$ , and by noon it had risen $12^\circ\text{C}$ from the 6 am temperature. What was the temperature at noon?
Show worked solution
Key idea: A drop is subtraction and a rise is addition. Work through each change in order, keeping track of the running temperature.
1. Write the starting temperature: $-3^\circ\text{C}$ .
2. Apply the drop of $5^\circ\text{C}$ by 6 am:
  $-3 - 5 = -8^\circ\text{C}$
3. Apply the rise of $12^\circ\text{C}$ from the 6 am temperature:
  $-8 + 12 = 4^\circ\text{C}$
4. The temperature at noon was $4^\circ\text{C}$ .
Answer: $4^\circ\text{C}$

Common mistakes

Where students usually lose marks

Confusing the sign of the answer when adding opposite signs

Student writes $-8 + 3 = 5$ (positive) instead of $-5$ .

Look at which integer has the larger absolute value. The answer takes that integer's sign. Here $\lvert -8 \rvert > \lvert 3 \rvert$ , so the answer must be negative.

Treating "minus a minus" as "minus a plus"

Student writes $-4 - (-9) = -4 - 9 = -13$ instead of $-4 + 9 = 5$ .

Two negatives next to each other (a subtraction sign and a negative sign) always combine to make a positive. Rewrite $-(-9)$ as $+9$ before doing anything else.

Adding absolute values instead of subtracting them

Student writes $-3 + 7 = -10$ by adding $3 + 7$ and keeping the negative sign.

Only add the absolute values when both integers have the same sign. When the signs are different, subtract the smaller absolute value from the larger one, then apply the sign of the larger.

Mixing up the direction of change in word problems

Student writes $-3 + 5$ for "the temperature dropped $5^\circ\text{C}$ " and gets $2^\circ\text{C}$ .

A drop or decrease means subtract; a rise or increase means add. Underline the key word in the problem and decide the direction before writing the calculation.

Try one yourself

Your turn

The temperature in Canberra was $-3^\circ\text{C}$ at midnight. By noon it had risen by $11^\circ\text{C}$ . What was the temperature at noon, in $^\circ\text{C}$ ?

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About this worksheet

Why we built it

Negative numbers are where a lot of Year 7 students stall - especially when subtraction and negatives collide. These worksheets give your student the repetition they need to make the sign rules automatic, with worked solutions that show each step.

What's covered

Sub-skills your student will practise

✓Comparing and ordering integers on a number line
✓Adding integers with the same and opposite signs
✓Subtracting integers (and why "minus a minus is plus")
✓Word problems involving temperature, debt, depth
✓Mixed-sign multi-step problems

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Parents on the practice questions.

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Frequently asked

Questions parents ask about integers

Why are negative numbers so tricky in Year 7?

Students have spent six years working with only positive numbers, so the sign rules feel arbitrary - especially 'subtract a negative becomes plus'. The fix is repetition until the rules become automatic rather than something students try to reason through each time.

What's the difference between -3 - 5 and -3 - (-5)?

-3 - 5 means starting at -3 and going down 5, landing at -8. -3 - (-5) means starting at -3 and subtracting a negative, which is the same as adding 5, landing at +2. The double-negative is where most students slip.

Do students need to know integer multiplication in Year 7?

Year 7 focuses on addition and subtraction of integers. Multiplication and division of integers are formally introduced in Year 8, though many teachers preview them once addition and subtraction are solid.

What's a quick check students can use on integer answers?

If the question involves more negatives than positives in the calculation, the answer should usually be negative - and vice versa. A quick sign-check catches about half of all integer errors before they leave the page.

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