2. Subtraction
1.
Addition:- The addition of two or more numbers is the total
amount of those values combined.
Addend:- Addend is the number
which is added to another.
2.
Subtraction:- Subtraction is an arithmetic operation that
represents the operation of removing objects from a collection.
Minuend:- The minuend is the number from which something is
taken. Minuend must be the large number.
Subtrahend:- The subtrahend is the number that is subtracted and
it must be the smaller number.
Difference:- The outcome after applying the operation of
subtraction is called the difference.
3.
Multiplication:- Multiplication is the process of calculating the
result when a number is taken be times.
Multiplicand:- The number to be multiplied is called the
multiplicand.
Multiplier:- The number with which we multiply a number is
called the multiplier.
Product or Factor:- The product is the result of multiplying , or an
expression that identifies factors to be multiplied.
4.
Division:- Division means separating a large group into
smaller groups of equal sizes. It is said that division is nothing but repeated
subtraction.
Divisor:- Divisor is the number by which another number is to
be divided.
Dividend:- The number which we divide is called the dividend.
Quotient:- The result obtained after the operation of division
is called the quotient.
Remainder:- The number left over in a division problem is
called the remainder.
Relation Between Dividend, Divisor, Quotient, and
Remainder
Dividend =
(Quotient × Divisor) + Remainder
The arithmetic operations and their parts have been illustrated below attractively.
Few examples of the arithmetic operations have been given in the video below.
Laws of operations:-
1.
Commutative
Law:- If the whole numbers
being added are interchanged, the result remains the same, i.e. 3 + 5 = 5 + 3
=8. This rule is called ‘Commutative law’. Multiplication also obeys this rule.
But subtraction and division do not obey this rule. e.g. 3 × 5 = 5 × 3 = 15,
but 3 – 5 ≠ 5 – 3 and 3 ÷ 5 ≠ 5 ÷ 3.
2.
Associative
law:- In addition the manner
of associating the whole numbers by using brackets does not change the answer.
This is called ‘Associative law of addition’, e.g. (4 + 5) + 2 = 4 + (5 + 2) =
11.
Multiplication
also obeys this rule but subtraction and division do not obey this rule
(4 × 5) × 2 =
4 × (5 × 2) = 40, but (4 – 5) – 2 ≠ 4 – (5 – 2) and (4 ÷ 5) ÷ 2 ≠ 4 ÷ (5 ÷ 2)
3.
Distributive
law:- It can be said that
multiplication is “distributive” over addition as here we actually distribute
multiplication over addition e.g.
5(4 + 3) = 5 × 4 + 5 × 3 = 35
4.
Law of
closure:- When we add the
natural numbers, we get a natural number again, e.g. (2 + 5) = 7. Thus, the set
of natural numbers is closed under addition.
The set of
natural numbers is closed for multiplication also but not for subtraction
(e.g. 2 – 6 =
-4 is not a natural number).
5. Identity
element:- Addition of zero does not change the identity of a number
(e.g. 6 + 0 = 6). Zero is called the ‘Identity element’. or ‘Additive Identity’.
Multiplication of any number by 1 does not change it (e.g. 40 × 1 = 40). 1 is called 'Identity Element' or ‘Multiplicative Identity’.
The chart below describes it shortly and properly.
The chart below describes it shortly and properly.
The laws of these operations have been described along with examples in the video below.
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