What are negative numbers?
Answer in short
Negative numbers are numbers less than zero, written with a ‘−’ sign in front, like −1, −2 and −3. In Bela's Building of Fun, floors below the ground floor (Floor 0) have negative numbers and floors above it have positive numbers. Zero is neither positive nor negative. A number and its inverse, like +3 and −3, add up to zero.
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Can there be less than zero?
First we learnt the counting numbers 1, 2, 3, … Then came 0, which means nothing, and fractions in between. The number line we have used starts at 0 and goes only to the right. But can there be numbers less than 0? Think of a lift going below the ground floor, a temperature colder than freezing, or owing someone money. All of these are ways of having ‘less than zero’.
Bela’s Building of Fun
Bela turned a multi-storeyed building into a Building of Fun for children, with some floors below the ground. A lift moves between the floors. It has two buttons: ‘+’ to go up and ‘−’ to go down.
- Pressing ‘+’ twice is written + + or +2 (two floors up).
- Pressing ‘−’ three times is written − − − or −3 (three floors down).
Numbering the floors
The entry, the Welcome Hall, is on the ground floor. To reach the Food Court from there you press +1, so the Food Court is on Floor +1; the Art Centre is on Floor +2. To reach the Toy Store you press −1, so it is on Floor −1; the Video Games shop is on Floor −2. The ground floor is Floor 0, because you need no button press to reach it from there.
| Floors above ground | Ground | Floors below ground |
|---|---|---|
| +1 Food Court, +2 Art Centre, +3 Books, +4 Ice Cream, +5 Sports, +6 Space | 0 Welcome Hall | −1 Toys, −2 Video Games, −3 Cinema, −4 Ghost House, −5 Dinosaur |
Notice that +3 is both the floor number of the book store and the number of floors you move when you press +3.
Positive, negative and zero
- A number with a ‘+’ sign in front is a positive number. Floors above the ground have positive numbers.
- A number with a ‘−’ sign in front is a negative number. Floors below the ground have negative numbers.
- Zero is neither positive nor negative, so we put no sign in front of it.
Back to zero: inverses
Basant, in a hurry on the ground floor, presses +3 by mistake. To stay on the ground floor, he can cancel it by pressing −3: (+3) + (−3) = 0. We call −3 the inverse of +3, and +3 the inverse of −3. A number and its inverse always add up to zero, which is why the inverse is also called the additive inverse. The inverse of +4 is −4, of −1 is +1, and of 0 is 0.
Comparing with floors
A lower floor has a smaller number. Floor +3 is below Floor +4, so +3 < +4. Floor −4 is below Floor −3, so −4 < −3. Every negative floor is below Floor 0, so every negative number is less than 0, and every positive number is greater than 0.
Negative numbers around us
Negative numbers appear in many places. Temperatures below 0°C, the freezing point of water, are negative; heights below sea level are negative; and in a bank account, money taken out (a debit) is counted as negative. To see where all these numbers sit, read integers on the number line.
Practice
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In the Building of Fun, the Toy Store is one floor below the ground floor. Its floor number is:
Show answer
Answer: (c) −1
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Which button presses take you three floors down?
Show answer
Answer: (b) − − −
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The inverse of +9 is:
Show answer
Answer: (b) −9
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Give two real-life situations where we use negative numbers.
Show answer
Answer: Temperatures below 0°C, like −4°C in Leh on a winter night, and heights below sea level. Debits in a bank account and floors below the ground are other examples.
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From Floor +2, you press −3. Where do you reach? Write the expression.
Show answer
Answer: Floor −1, the Toy Store: (+2) + (−3) = −1.
Questions students ask
What is a negative number?
A number less than zero. It is written with a ‘−’ sign in front, such as −3, and lies to the left of 0 on the number line.
Is zero positive or negative?
Neither. Zero is the reference point between the positive and the negative numbers, so we put no sign in front of it.
What is the inverse of a number?
The number that gives zero when added to it. The inverse of +3 is −3, and the inverse of −3 is +3. The inverse of 0 is 0.
Where do we see negative numbers in daily life?
In temperatures below 0°C, in heights below sea level, in basement floors, and in bank accounts, where debits (money taken out) are negative.
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