Number System (Classes VI-VIII) • Topic 3 of 6

Integers & Their Operations

Integers extend the whole numbers to include negatives, and this is where children meet their first big conceptual jump: numbers that are 'less than nothing'. The misconceptions are predictable and CTET tests them directly. The biggest is negative magnitude confusion, where a child says -5 is greater than -2 because 5 is bigger than 2, forgetting that on the number line -5 sits further left and is therefore smaller. A close second is the rule muddle in operations: confusing 'add a negative' with 'multiply negatives'. A teacher should ground the SIGNS in a context (debt, temperature, floors below ground) and only then move to rules: for addition, same signs add and keep the sign while different signs subtract and take the bigger number's sign; for multiplication and division, two like signs give plus and two unlike signs give minus. The number line is the single best tool here, because it makes -5 < -2 visible rather than something to memorise. CTET often presents a child's wrong subtraction or comparison and asks you to name the misconception.

✅ Solved examples

1. Evaluate (-7) + 4.
Different signs, so subtract: 7 - 4 = 3, and take the sign of the larger magnitude (7 is negative). The answer is -3.
2. A child claims -8 is greater than -3. What is the misconception?
The child is comparing magnitudes (8 > 3) and ignoring the negative sign. On the number line -8 lies further left, so -8 is actually LESS than -3. The number line fixes this directly.
3. Evaluate (-6) x (-5).
Two negative (like) signs multiply to a positive. 6 x 5 = 30, so the answer is +30.
4. Subtract: 3 - (-4).
Subtracting a negative is the same as adding its opposite: 3 - (-4) = 3 + 4 = 7.

✏️ Practice — try these, take hints as needed

1. Evaluate (-9) + (-6).
Same signs add.
Keep the common sign.
-15
2. Arrange in ascending order: -3, 0, -7, 2, -1.
Furthest left on the number line is smallest.
All negatives come before 0.
-7, -3, -1, 0, 2
3. A child writes (-4) x 3 = 12. What rule has been forgotten?
Count the unlike signs.
One negative and one positive.
Unlike signs give a negative product, so the answer is -12, not 12.
4. Evaluate (-20) / (4).
Unlike signs in division.
20 / 4 = 5.
-5

📝 Topic test — 8 questions

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