Page 32 - Maths Skill - 6

30 Maths

4. Simplify the following.

(i) – 15 + [(– 5) – (– 10)] (ii) [– 100 – (– 25)] + 75
(iii) 32 + [(– 20) – 40] – (– 10) (iv) 21 + [(– 7) – 35]
(v) [76 – (– 51)] + [(– 31) – 20] (vi) – 120 + [(– 89) – 92]

5. Write the predecessor of the following.
(i) 10 (ii) – 579 (iii) 688 (iv) – 453
6. Add – 55 to the difference of 100 and – 210.

7. The sum of two integers is – 20. If one of them is – 9, what is the other?
8. Find the value of: 4 – 7 + (– 5) – (– 3) + 5.

9. If * is an operation such that for any two integers a and b, a * b = a – (b + 1) + (– 2), find the value of:
(i) (– 3) * (– 5) (ii) 2 * (– 3) (iii) (– 5) * (– 3) (iv) (– 3) * 2 (v) Is a * b = b * a?

BRAHMAGUPTA’S RULES FOR ADDITION

(Brahma-sphuta-siddhanta 18.30, 628 CE)
1. A pair of positive integers added together is positive. (e.g., 6 + 3 = 9).
2. The addition of two negative integers is negative. To add two negatives, add the numbers (without the signs),
then apply a minus sign to get the result. (e.g., (- 6) + (- 3) = - 9).
3. To add a positive and a negative number, subtract the smaller number (without the sign) from the greater
number (without the sign), and then place the sign of the greater number to get the result.
(e.g., - 9 + 3 = - 6, 4 + (- 5) = - 1 and - 4 + 7 = 3).

4. The sum of a number with its inverse equals zero (e.g., (4 + ( - 4) = 0)).
5. The sum of any number and zero equals the same number. (e.g., - 3 + 0 = - 3 and 0 + 0 = 0).

BRAHMAGUPTA’S RULES FOR SUBTRACTION
(Brahma-sphuta-siddhanta 18.31-18.32):

1. Positive results are obtained when a greater positive is subtracted from a smaller positive. (e.g., 5 - 3 = 2).
2. Subtracting a greater positive from a smaller positive gives a negative value. (e.g., 3 - 5 = - 2).
3. Subtracting a negative number is the same as adding the corresponding positive number.
(e.g., 3 - (- 5) = 3 + 5 = 8).
4. Subtracting a number from itself produces zero. (e.g., 5 - 5 = 0 and - 5 – (- 5) = 0).
5. Zero is subtracted from a number to obtain the same number. (e.g., - 5 - 0 = - 5 and 0 - 0 = 0).
6. Subtracting a number from zero gives the number’s inverse (e.g., 0 - (- 5) = 5).

EXPLORATIONS WITH INTEGERS

A Hollow Integer Grid

5 - 2 - 4 8 - 3 - 5

- 3 10 - 6 - 4
- 3 9 - 7 - 2 - 7 9

(i) (ii)