➕ Class 7 · Number system

Integers for Class 7: notes, worked examples and practice

Integers are the whole numbers and their negatives. The rules for signs look like a lot to remember, but they all come from the number line.

Updated 21 October 2026. Every worked example and answer on this page is checked by automated tests.

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Notes

Integers: what you need to know

Chapter names and order differ by board and textbook edition, so follow your own textbook for the order.

Integers on the number line

Integers are ..., −3, −2, −1, 0, 1, 2, 3, ... Numbers to the right are greater. −2 is greater than −5 because it is further to the right.

Adding integers

Same signs: add the numbers and keep the sign, so −3 + (−4) = −7. Different signs: subtract the smaller from the larger and keep the sign of the larger, so −7 + 12 = 5.

Subtracting integers

Subtracting a number is the same as adding its opposite: 5 − (−8) = 5 + 8 = 13.

Multiplying and dividing

Same signs give a positive answer and different signs give a negative answer. (−6) × (−4) = 24 and (−48) ÷ 8 = −6.

Properties

Addition and multiplication are commutative and associative, and multiplying by 1 or adding 0 leaves a number unchanged. Division by zero is not defined.

Formulas and rules to remember

a − b = a + (−b)
(+) × (+) = +, (−) × (−) = +
(+) × (−) = −, (−) × (+) = −
The same sign rules apply to division

Solved examples

Example 1

Find −7 + 12.

The signs are different, so subtract: 12 − 7 = 5.
12 is bigger, so the answer is positive.

Answer: 5

Example 2

Find 5 − (−8).

Subtracting −8 is the same as adding 8.
5 + 8 = 13.

Answer: 13

Example 3

Find (−6) × (−4).

Both signs are negative, so the product is positive.
6 × 4 = 24.

Answer: 24

Example 4

Find (−48) ÷ 8.

The signs are different, so the quotient is negative.
48 ÷ 8 = 6.

Answer: −6

Avoid these

Common mistakes

Sign slips when subtracting a negative

5 − (−8) is 13, not −3. Change the subtraction to addition of the opposite.

Confusing −5 − 3 with −5 + 3

−5 − 3 = −8, because you move 3 more to the left of −5.

Squaring with a negative

(−3)² = 9, but −3² means −(3²) = −9.

10 practice questions with answers

Try each question on paper first, then tap it to check your answer. The questions are generated by code and each answer is checked.

−3 + 9 =
Answer: 6
−8 + 8 =
Answer: 0
7 − 1 =
Answer: 6
1 − 1 =
Answer: 0
−2 − 2 =
Answer: -4
7 × (−3) =
Answer: -21
9 × 10 =
Answer: 90
12 × (−7) =
Answer: -84
3 × 7 =
Answer: 21
8 × 12 =
Answer: 96

More practice

Printable worksheets (PDF with answers)

Adding and subtracting negative numbers (Grade 6)
Multiplying and dividing integers (Grade 7)

Games and lessons

Maths dictionary

FAQ

Integers Class 7: questions students ask

What are integers?

Integers are the set of whole numbers and their negatives, including zero: ..., −2, −1, 0, 1, 2, ...

Why is a negative times a negative positive?

Multiplying by −1 flips a number to its opposite, and doing it twice gets you back to where you started.

What is the rule for subtracting integers?

Add the opposite: a − b = a + (−b).

Is zero positive or negative?

Neither. Zero is an integer that is neither positive nor negative.

Which board is this integers page for?

It covers the ideas taught in CBSE, ICSE and state-board maths. Chapter names and order differ by board and textbook edition, so follow your own textbook for the exact order.

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