What zero does
Brahmagupta's rules for zero
Zero in sums
Zero is a number now. Brahmagupta wrote down what zero does when you add it, take it away or multiply by it.
What do you think 6 × 0 is?
What this lesson covers
The idea
Adding zero to a number or subtracting zero from it leaves the number unchanged (a + 0 = a, a – 0 = a), and any number multiplied by zero gives zero (a × 0 = 0).
Zero in sums
Zero is a number now. Brahmagupta wrote down what zero does when you add it, take it away or multiply by it.
What do you think 6 × 0 is?
- 6
- 0
- 60
Three things to try
Do all three. Add an empty bag. Take away nothing. Then remove the bags of apples one by one.
Three rules
Brahmagupta's rules for zero: a + 0 = a, a − 0 = a, and a × 0 = 0.
Adding nothing or taking away nothing changes nothing. Zero bags of a apples is no apples.
Notes
a + 0 = a, a − 0 = a, a × 0 = 0.
Check yourself
What is 365 + 0?
Answer: 365
365 + 0 = 365. Adding zero leaves the number unchanged.
What is 48 × 0?
Answer: 0
48 × 0 = 0. Any number multiplied by zero gives zero.
One of these rules is false. Which one?
A shop sold 0 packets with 12 biscuits in each packet. How many biscuits did it sell?
- a × 0 = a — correct. This is the false one. a × 0 = 0, because 0 groups of a make nothing.
- a + 0 = a. This rule is true. Adding 0 leaves a unchanged.
- a − 0 = a. This rule is true. Taking away 0 leaves a unchanged.
- 0 — correct. Yes. 12 × 0 = 0.
- 12. One packet would be 12 biscuits. There were 0 packets.
- 120. There is no 10 here. 0 packets sell 0 biscuits.