Make a suitable project on Integers and fundamental operations of integers with example
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Step-by-step explanation:
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Answer:
We have four fundamental operations on integers. They are addition, subtraction, multiplication, and division.
Fundamental Operations on Integers 1
Step-by-step explanation:
Addition of integers having the same sign
1. The sum of two positive integers is the sum of their absolute values with a positive sign.
Example 1: Add (+ 6) + (+4).
Solution: On a number line, first draw an arrow from 0 to 6 and then go 4 steps ahead. The tip of the last arrow reaches +10. So, (+ 6) + (+ 4) = +10
Fundamental Operations on Integers 3
2. The sum of two negative integers is the sum of their absolute values with negative sign(-).
Example 2: Add (-3) + (-4).
Solution: On a number line, first we draw an arrow on the left side of zero from 0 to -3 and then further move to the left 4 steps. The tip of the last arrow is at -7. So, (-3) + (-4) = (-7)
Fundamental Operations on Integers 4
Addition of integers having opposite signs
The sum of two integers having opposite signs is the difference of their absolute values with the sign of integer of greater absolute value.
Example 3: Add(+6) + (-9).
Solution: On a number line, first we draw an arrow from 0 to 6 on the right and then go 9 steps to the left. The tip of the last arrow is at -3. So, (+6) + (-9) = (-3)
2. Subtraction of integers
In subtraction, we change the sign of the integer which is to be subtracted and then add to the first integer. In other words, if a and b are two integers, then a – b = a + (-b)
Example 4: Subtract 5 from 12.
Solution: (12) – (5) = (12) + (-5) = 7
Fundamental Operations on Integers 6
Example 5: Subtract -7 from -15.
Solution: (-15) – (-7) = (-15) + (7)= -8
Fundamental Operations on Integers 7
Example 6: Subtract 6 from -10.
Solution: (-10) -(6) = (-10) + (- 6)
Fundamental Operations on Integers 8
Example 7: Subtract (-5) from 4.
Solution: 4 – (-5) = 4 + (5) = 9
Fundamental Operations on Integers 9
To subtract (-5) from 4, we have to find a number which when added to (-5) gives us 4. So, on the number line we start from (-5) and move up to 4. Now find how many units we have moved. We have moved 9 units.
So, 4-(-5) =9
3. Multiplication of integers
Multiplication of integers having the same sign
When two integers have the same sign, their product is the product of their absolute values with positive sign.
Examples
(a) (+6) × (+7) = + 42 or 42
(b) (+5) × (+10) = + 50 or 50
(c) (-3) × (-5) = + 15 or 15
(d) (-20) × (-6) = 120
(e) (12) × (5) = 60
Multiplication of integers having opposite signs
The product of two integers having opposite signs is the product of their absolute values with negative sign.
Examples
(a) (-10) × (8) = (- 80)
(b) (- 5) × (7) = (-35)
(c) (12) × (-3) = (-36)
(d) (-6) × (3) = (-18)
(e) 5 × (-4) = (-20)
Note:
plus × minus = minus
minus × plus = minus
minus × minus = plus
plus × plus = plus
4. Division of integers
Division of integers having the same sign
Division of two integers having the same sign is the division of their absolute value with a positive sign. If both integers have the same sign, then the quotient will be positive.
Examples:
(a) (+9) ÷ (+3) = (3)
(b) (-9) ÷ (-3) = (3)
(c) (-24) ÷ (-12) = (2)
Division of integers having opposite signs
If both integers have different signs, the quotient will be negative.
Examples: (a) 12 ÷ (-3) = (-4)
(b) (-10) ÷ (5) = (-2)
(c) (-18) ÷ (3) = (-6)
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