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1. Raj was playing around with multiplying odd and even numbers. Here's what he wrote on his paper:

3*5= 15 4*7 = 28 8*5 = 40 6 *4= 24 9*9= 81

Raj conjectured that an even number times an even or odd number will always be even.

Can you give a convincing argument to support his conjecture?​

Respuesta :

olayemiolakunle65

Raj's conjecture is valid i.e an even number times an even or odd number will always be even.

Even numbers are number that can be divided by 2 without leaving a remainder. Examples are: 4, 6, 8, 20, 50 etc. While odd numbers can not be divided evenly by 2. Examples are: 7, 11, 17, etc

Thus, the conjecture can be proved as follows:

i. Even number times an even number

  • 4 x 12 = 48
  • 6 x 8 = 48
  • 2 x 10 = 20
  • 12 x 16 = 192

Thus, an even number multiplied by an even number would give an even number.

ii. Even number times an odd number

  • 4 x 11 = 44
  • 6 x 5 = 30
  • 2 x 7 = 14
  • 8 x 17 = 136
  • Thus, an even number multiplied by an odd number would always give an even number.

Therefore, Raj's conjecture is valid.

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