The Other Side of Zero | Mathematics Grade 6 CBSE

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The six ideas of integers

Once we allow numbers below zero, counting works both ways. Tap each term to see what it means with a quick example.

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The three big ideas

Some quantities have a natural "below zero" side: a temperature of 5° below freezing is −5, a basement two floors down is −2, ₹100 owed is −100.
A number written with a minus sign, like −5, is a negative number; the everyday counting numbers 1, 2, 3, … are positive and may be written +1, +2, +3.
The whole numbers, their negatives, and zero together make up the integers: …, −3, −2, −1, 0, +1, +2, +3, …
Zero is special: it is neither positive nor negative — it is the dividing point between the two sides.

Worked example. In Leh one winter morning the temperature was 4° below zero. Write this as an integer, and write the integer for a hill station that was 4° above zero.

Below zero takes a minus sign: 4° below zero = −4.

Above zero is positive: 4° above zero = +4. The two are opposites, the same distance from 0.

Common mistake: thinking −4 and 4 are the same because both "have a 4". They are opposites — one is below zero, the other above.

Extend the number line to the left of zero for the negatives: …, −3, −2, −1, 0, 1, 2, 3, …
The rule of order: a number is larger if it lies further to the right, and smaller if it lies further to the left.
So every positive number is greater than zero, and every negative number is less than zero. Also, any positive > any negative.
Among negatives, the one closer to zero is the larger: −2 > −7, because −2 sits to the right of −7. The opposite of a number is its mirror across zero (the opposite of +8 is −8).

Worked example. Arrange these temperatures from coldest to warmest: −2°C, 3°C, −6°C, 0°C.

Place them on the number line. From left (smallest) to right (largest): −6, −2, 0, 3.

Coldest to warmest: −6°C, −2°C, 0°C, 3°C.

Common mistake: reading −6 as bigger than −2 "because 6 > 2". For negatives it is the reverse — the larger the digit, the smaller (more negative) the number.

Think of the number line: adding a positive moves right, adding a negative moves left.
Same signs: add the values and keep the common sign. (−6) + (−4) = −10; (+6) + (+4) = +10.
Different signs: subtract the smaller value from the larger and keep the sign of the larger value. (−9) + (+5) = −4; (+9) + (−5) = +4.
Subtracting is adding the opposite: a − b = a + (opposite of b). So 4 − (−6) = 4 + 6 = 10, and 3 − 8 = 3 + (−8) = −5.
A number plus its opposite always gives zero: 7 + (−7) = 0.

Worked example. A lift starts at the ground floor (0), goes down 3 floors, then up 5 floors. On which floor does it stop?

Down 3 is +(−3); up 5 is +(+5). Final position = 0 + (−3) + (+5).

(−3) + (+5): different signs, 5 − 3 = 2, sign of the larger (+5) is positive → +2. The lift stops on the 2nd floor.

Common mistake: reading two minus signs as still negative. Subtracting a negative, like 4 − (−6), turns into adding: 4 + 6 = 10.

Where you'll meet it

Integers at work

Temperature

Weather reports for Shimla or Leh in winter show readings like −4°C. Negative numbers let us record and compare how far below freezing it is.

Lifts & basements

In a mall, lift buttons read B2, B1, G, 1, 2 … Treating the ground floor as 0 and basements as −1, −2 makes "go down then up" a simple integer sum.

Money in and out

A shopkeeper records money received as positive and money spent or owed as negative. Adding the day's entries shows whether the balance is above or below zero.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

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