Consider any 2 by 2 square of numbers in a calendar, as shown in the figure. Find products of numbers Class 8
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Consider any 2 by 2 square of numbers in a calendar, as shown in the figure. Find products of numbers Class 8
Question 1.
Consider any 2 by 2 square of numbers in a calendar, as shown in the figure. Class 8
Find products of numbers lying along each diagonal - 4 × 12 = 48, 5 × 11 = 55. Do this for the other 2 by 2 squares. What do you observe about the diagonal products? Explain why this happens.
Hint : Label the numbers in each 2 by square as
| a | (a + 1) |
| a + 7 | (a + 8) |
Solution:
Difference of the two products is always 7.
Because (a + 7) (a + 1) - a (a + 8)
= a² + 7a + a + 7 - a² - 8a
= a² + 8a + 7 - a² - 8a = 7.