Q1.
When do you think the product is greater than both the numbers multiplied, when is it in between the two numbers, and when is it smaller than both? [Hint: The relationship between the product and the numbers multiplied depends on whether they are between 0 and 1 or they are greater than 1.]
Answer
Everything depends on where each number sits compared with 1.
| Situation | Multiplication | Relationship |
|---|---|---|
| Both numbers greater than 1 | 4/3 × 4 = 16/3 | Product is greater than both |
| Both numbers between 0 and 1 | 3/4 × 2/5 = 3/10 | Product is less than both |
| One between 0 and 1, one greater than 1 | 3/4 × 5 = 15/4 | Product lies in between the two |
Check the middle row: 3/4 = 15/20 and 2/5 = 8/20
Product 3/10 = 6/20
6/20 < 8/20 < 15/20 ✔
Product 3/10 = 6/20
6/20 < 8/20 < 15/20 ✔
Why it happens: multiplying by a number smaller than 1 means taking only a part of the other number, so the answer shrinks. Multiplying by a number bigger than 1 means taking more than all of it, so the answer grows.