Page 11 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\01_Chapter\01_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-6 Reader’s Sign _______________________ Date __________

Ordering Integers

For any two integers on the number line, an integer to the right is always greater than the integer
to its left.

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

Remember Think and Answer
• 0 is less than every positive integer.
• 0 is greater than every negative integer. 1. What is the smallest
• Every positive integer is greater than every negative integer. positive integer?
• The negative integer nearest to the 0 on the number line will be greater. 2. What is the greatest
negative integer?
Addition and Subtraction of Integers

Addition of Integers
Addition of Integers with the Same Sign

If two integers have the same sign, we add their absolute values and put the common sign before
the sum.
For example: (a) (+2) + (+4) = +6 (b) (–3) + (–7) = –10
Addition of Integers with Different Signs

If two integers have different signs, we find the difference of Quick Check
in their absolute values and put the sign of the integer having a Evaluate the following:
greater absolute value. (a) (–6) + (–7)
For example: (a) (–9) + (+3) = – (9 – 3) = –6 (b) (+13) – (–11)
(b) (–5) + (+7) = + (7 – 5) = +2 or 2 (c) (+5) + (–6)
(c) (+8) + (–5) = + (8 – 5) = +3 or 3 (d) (–7) – (–15)
Subtraction of Integers (e) (–9) + (–10) – (–19)

To subtract an integer from a given integer, we add the additive inverse of the integer to the given
integer.
For example: (a) 3 – 7 = 3 + additive inverse of 7 = 3 + (–7) = –4
(b) (–2) – (–7) = (–2) + additive inverse of (–7) = (–2) + (+7) = +5 or 5
(c) (–1) – (+4) = (–1) + additive inverse of (+4) = (–1) + (–4) = –5
Properties of Addition and Subtraction of Integers

Property Properties of Addition of Integers Properties of Subtraction of Integers
Closure Property The sum of any two integers is an The difference of any two integers is
integer. an integer.
If a and b are any two integers, then If a and b are any two integers, then
a + b is also an integer. a – b is also an integer.
E.g., 30 + 3 = 33, is an integer. E.g., 10 – 7 = 10 + (–7) = 3, is an integer.
Thus, integers are closed under
addition. Thus, integers are closed under
subtraction.

9 Integers