Subjects arithmetic

Multiplication Sums 7D37D6

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Multiplication Sums 7D37D6


1. The problem is to find the sums of multiplication tables from 12 to 19. 2. The multiplication table for a number $n$ is the set of products $n \times 1, n \times 2, \ldots, n \times 10$. 3. To find the sum of the multiplication table for a number $n$, we use the formula for the sum of the first 10 natural numbers multiplied by $n$: $$\text{Sum} = n \times (1 + 2 + \cdots + 10)$$ 4. The sum of the first 10 natural numbers is: $$1 + 2 + \cdots + 10 = \frac{10 \times (10 + 1)}{2} = 55$$ 5. Therefore, the sum of the multiplication table for $n$ is: $$\text{Sum} = n \times 55$$ 6. Now, calculate the sums for $n = 12$ to $19$: - For $12$: $12 \times 55 = 660$ - For $13$: $13 \times 55 = 715$ - For $14$: $14 \times 55 = 770$ - For $15$: $15 \times 55 = 825$ - For $16$: $16 \times 55 = 880$ - For $17$: $17 \times 55 = 935$ - For $18$: $18 \times 55 = 990$ - For $19$: $19 \times 55 = 1045$ These are the sums of the multiplication tables from 12 to 19.