Page 293 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\15_Chapter_10\Chapter_10
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Subtraction of Integers

Subtraction is the reverse of addition. Let us first learn how to subtract an integer from another
integer on the number line.

1. To subtract a positive integer, we move to the left on the number line.
For example: To subtract 5 from 3, start from 3 and move 5 steps backwards/left.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

Thus, 3 – 5 = –2.
2. To subtract a negative integer, we move to the right on the number line.

For example: To subtract –5 from –4, start from (–4) and move 5 steps to the right.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Thus, –4 – (–5) = 1.

Note: We assign ‘+’ sign for the movement towards right and ‘–’ sign for the movement towards left.

Rule for Subtraction Remember

For the subtraction of integers, change the sign of Subtracting an integer means adding its
integer to be subtracted (subtrahend) and add it to additive inverse.
the first integer (minuend). Let us see some examples (a) 75 – (–150) = 75 + (+150) = 225
to understand it.
additive inverse of –150
Example 9: Subtract the following: (b) 75 – (+150) = 75 + (–150) = –75

(a) 5 from 7 (b) –6 from 8

(c) 5 from –12 (d) –12 from –15 additive inverse of +150
Solution: (a) 7 – 5 = 7 + (–5) = 2 [Q Additive inverse of 5 is (–5)]

(b) 8 – (–6) = 8 + (6) = 14 [Q Additive inverse of (–6) is 6]
(c) (–12) – 5 = (–12) + (–5) = –17 [Q Additive inverse of 5 is (–5)]

(d) (–15) – (–12) = (–15) + 12 = –3 [Q Additive inverse of (–12) is 12]

Knowledge Desk
Brahmagupta’s Rules for Subtraction (Brahma-sphuta-siddhanta 18.31-18.32): Brahmagupta was
the first Indian mathematician who defined first set of rules for dealing with negative numbers.
1. If a smaller positive is subtracted from a larger positive, the result is positive.
2. If a larger positive is subtracted from a smaller positive, the result is negative.
3. Subtracting a negative number is the same as adding the corresponding positive number.
4. Subtracting a number from itself gives zero.
5. Subtracting zero from a number gives the same number. Subtracting a number from zero gives the
number’s inverse.

291 The Other Side of Zero