Page 32 - Revised Maths Wisdom Class - 6

30 MATHS

5. Subtract the sum of –1150 and –198 from 6234.

6. The sum of two integers is 1308. If one of the integers is –198, find the other.
7. What should be subtracted from –2000 to get 1901?

8. Fill in the blanks.
(a) The predecessor of –980 is __________ . (b) The successor of –199 is __________ .

9. At sunrise, the outside temperature is 3° below zero. By lunch time, the temperature rose by 15° and then fell
by 5° by night. What was the temperature at the end of the day?

10. A hike starts at an elevation 60 m below sea level and ends at a point 8000 m higher than the starting point.
How high would the person be at the end of the hike above sea level?

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 (i) 5 - 2 - 4 (ii) 8 - 3 - 5

A Hollow Integer Grid - 3 10 - 6 - 4
- 3 9 - 7 - 2 - 7 9

There is something special about the numbers in these two grids.
Top row : 5 + (- 2) + (- 4) = - 1 Top row : 8 + (- 3) + (- 5) = 0

Bottom row : (- 3) + 9 + (- 7) = - 1 Bottom row : (- 2) + (- 7) + 9 = 0
Left column : 5 + (- 3) + (- 3) = - 1 Left column : 8 + (- 6) + (- 2) = 0
Right column : (- 4) + 10 + (- 7) = - 1 Right column : (- 5) + (- 4) + 9 = 0