Negative Numbers and Integers
Complete interactive solutions for Exercise 4(A), Exercise 4(B), Multiple Choice Questions, Statement Questions, and Assertion-Reason Questions.
Quick Rules to Remember
These four ideas explain almost every solution in the chapter.
Opposite integers
Opposite integers are equally far from zero but lie on opposite sides. The opposite of -8 is 8.
Comparison
The integer farther right is greater. Among negative integers, the number closer to zero is greater.
Addition
Move right when adding a positive integer and move left when adding a negative integer.
Subtraction
Change subtraction into addition of the opposite. For example, 4 - (-2) = 4 + 2 = 6.
Exercise 4(A)
Opposites, comparison, ascending order, descending order, and number-line reasoning.
- 20. The negative or opposite of -20 is -(-20) = 20.
- 0. Zero is its own opposite, so -(0) = 0.
- -8. The negative of 8 is -(8) = -8.
- A loss of Rs. 10. A negative amount represents the opposite of a gain.
- Positive. North is opposite to South.
- -5 > -7. When the signs of both sides are changed, the inequality reverses.
- Right side. Since 3 > -2, 3 lies to the right of -2.
- Left side. Since -8 < -6, -8 lies to the left of -6.
Integers increase from left to right on a number line. Therefore, ascending order is obtained by reading from left to right.
- -14 < -9 < -5 < 0 < 4 < 8 < 12
- -9 < -6 < 0 < 5 < 7 < 9
Integers decrease when a number line is read from right to left. Therefore, descending order is obtained by reading from right to left.
- 12 > 11 > 5 > 3 > 0 > -1 > -4 > -10
- 6 > 3 > -4 > -7 > -8 > -12
- An integer is greater than every number on its left.
- An integer is greater than every number to its left.
- 2 is to the right of -4.
- -3 is less than 2, and 3 is greater than -2.
- -4 is greater than -8, and 4 is less than 8.
- 5 is greater than 2, and -5 is less than -2.
- -6 is less than 3, and the opposite of -6 is greater than the opposite of 3.
- 8 is greater than -5, and -8 is less than 5.
- -15 is greater than -23 because -15 is closer to zero.
- 15 is greater than -12 because every positive integer is greater than every negative integer.
- 8 is greater than 0.
- 0 is greater than -3.
- -6 is smaller than 0.
- -3 is smaller than 2.
- -51 is smaller than 15.
- 0 is smaller than 13.
- 3 > 0
- 0 > -8
- -9 < -3
- -3 < 3
- 5 > -1
- -13 < 0
- -8 > -18
- -8, -5, -1, 0, 4, 5
- -7, -6, -3, 0, 2, 3, 4
- 15, 8, 0, -2, -3, -5
- 23, 12, 7, 6, 0, -11
- False. There is no smallest integer because negative integers continue indefinitely.
- True. The opposite of -17 is 17.
- True. The opposite of zero is zero.
- True. Every negative integer is smaller than 0.
- False. Every positive integer is greater than 0.
- False. Zero is included in the set of integers.
Exercise 4(B)
Addition and subtraction of integers using number lines.
- (+7) + (+4) = +11. Start at 7 and move 4 units right.
- 0 + (+6) = +6. Start at 0 and move 6 units right.
- (+5) + 0 = +5. Adding zero causes no movement.
- (-4) + (+5) = +1. Start at -4 and move 5 units right.
- 0 + (-2) = -2. Start at 0 and move 2 units left.
- (-1) + (+4) = +3. Start at -1 and move 4 units right.
- (+4) + (-2) = +2. Move 2 units left from 4.
- (+3) + (-6) = -3. Move 6 units left from 3.
- 3 + (-7) = -4. Move 7 units left from 3.
- (-1) + (-2) = -3.
- (-3) + (-4) = -7.
- (-2) + (-5) = -7.
- (+10) - (+2) = +8.
- (+8) - (-5) = +13.
- (-6) - (+2) = -8.
- (-7) - (+5) = -12.
- (+4) - (-2) = +6.
- (-8) - (-4) = -4.
- 3 more than -1 is -1 + 3 = 2.
- 5 less than 2 is 2 - 5 = -3.
- 5 more than -9 is -9 + 5 = -4.
- 4 less than -4 is -4 - 4 = -8.
- 7 more than 0 is 0 + 7 = 7.
- 7 less than -8 is -8 - 7 = -15.
- 13 + 15 = 28.
- -13 + 15 = 2.
- 13 + (-15) = -2.
- -13 + (-15) = -28.
- 8 - 5 = 3.
- 8 - (-5) = 13.
- -7 - 4 = -11.
- -2 - (-8) = 6.
- 12 - (-3) = 15.
- -3 - (-6) = 3.
Multiple Choice and Reasoning Questions
Choose an option to receive instant feedback and then read the explanation.
A is 5 units to the right of zero. B is 3 units to the left of zero, so B = -3.
If m > n, then m - n > 0. If m = n, then m - n = 0. In both cases, m - n is greater than or equal to 0.
Every integer P has an opposite -P, and P + (-P) = 0. This works for positive and negative values of P.
Starting at 3 and moving 5 units left ends at -2. This movement represents 3 - 5.
Starting at -1 and moving 3 units right ends at 2. This movement represents -1 + 3.
Starting at 4 and moving 5 units left ends at -1. This movement represents 4 - 5.
The integers are 6, 7, 8, 9, 10, 11, 12, 13 and 14. Their number is 9.
Zero is neither positive nor negative. Therefore it represents neither gain nor loss.
Statement 1: If m lies on the left side of n on a number line, then m < n.
Statement 2: The integer on the left of another integer is smaller.
Both statements express the same correct number-line rule.
Assertion: -8 < -5, 8 > -5, -8 < 5 and 8 > 5. After changing both signs and reversing each inequality, the new comparisons are also true.
Reason: When the signs on both sides of an inequality are changed, the inequality sign reverses.
Both the Assertion and Reason are true, and the Reason explains the Assertion.
Interactive Integer Practice Laboratory
Enter your own integers and receive an instant answer.
Find the opposite
Enter any integer.
Compare two integers
Enter two integers.
Add or subtract
Ascending order checker
Enter comma-separated integers.
Frequently Asked Questions
What is an integer?
An integer is a whole number that may be negative, positive, or zero. Examples include -4, 0, and 9.
Is zero positive or negative?
Zero is an integer, but it is neither positive nor negative.
Which of two negative integers is greater?
The negative integer closer to zero is greater. For example, -3 is greater than -8.
How are integers added on a number line?
Start at the first integer. Move right for a positive second integer and left for a negative second integer.
How is subtraction of integers simplified?
Replace subtraction with addition of the opposite. For example, 6 - (-4) becomes 6 + 4, which equals 10.