Q1.
Suppose you are using the number system that uses sticks to represent numbers, as in Method 1. Without using either the number names or the numerals of the Hindu number system, give a method for adding, subtracting, multiplying and dividing two numbers or two collections of sticks.
Answer
Every one of the four operations can be done by moving sticks about. Call the two collections A and B.
| Operation | What to do with the sticks | What the answer is |
|---|---|---|
| A + B | Push the two heaps together into one heap. | The combined heap |
| A − B | Pair each stick of B with a stick of A and take both away. Stop when B is exhausted. | The sticks of A still unpaired |
| A × B | For every single stick of B, lay out one fresh copy of the whole heap A. Then pool all those copies together. | The pooled heap |
| A ÷ B | From A, keep pulling out bunches, each bunch matched one-to-one with B. Beside each completed bunch place one marker stick. | The markers are the quotient; the sticks left in A that cannot fill a bunch are the remainder |
Why it happens: each rule is the meaning of the operation, stripped of names. Addition is putting collections together; subtraction is removing a matched part; multiplication is repeated addition of equal collections; division is repeated subtraction of equal collections, and the quotient is how many times you could do it — which is itself a number, so it too gets its own collection of markers. Nothing here needs the word “seven”.
Check it yourself: take A = 7 sticks and B = 3 sticks. Pull out bunches of 3: you get two bunches (two markers) and 1 stick left over. That is 7 ÷ 3 = 2 remainder 1 — obtained without saying a single number.