The product of 89 and 234 is 20826, not 314.
How to infer the correctness of a product
The multiplication of two positive integers equals another positive integer. Each term of a multiplication can be rewritten as sums of multiples of 10, which can be simplified by algebra:
- [tex]89 \times 234[/tex] Given
- [tex](80 + 9) \times (200+30+4)[/tex] Definition of decimal numbers
- [tex](80 + 9)\times 200 + (80 + 9)\times 30 + (80+9)\times 4[/tex] Distributive property
- [tex]80\times 200 + 9\times 200 + 80\times 30 + 9\times 30 + 80 \times 4 + 9\times 4[/tex] Distributive property
- [tex]16000 + 1800 + 2400 + 270 + 320 +36[/tex] Definition of multiplication
- [tex]20826[/tex] Definition of addition/Result
Based on real algebra properties, we know that the product of 89 and 234 is 20826, not 314. [tex]\blacksquare[/tex]
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