Class 7 Exam > Class 7 Videos > Mathematics (Maths) Class 7 > Properties of Multiplication of Integers(Closure, Distributive Property)
Properties of Multiplication of Integers(Closure, Distributive Property) Video Lecture | Mathematics (Maths) Class 7
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FAQs on Properties of Multiplication of Integers(Closure, Distributive Property) Video Lecture - Mathematics (Maths) Class 7
| 1. What is closure in the context of multiplication of integers? |  |
Closure refers to the property that states that when two integers are multiplied, the result is always an integer. In other words, the product of any two integers is always an integer. For example, when multiplying -2 and 3, the result is -6, which is also an integer.
| 2. How does the distributive property apply to the multiplication of integers? | |
The distributive property states that when multiplying a number by the sum of two other numbers, it is equivalent to multiplying the number separately by each of the two numbers and then adding the products together. This property applies to the multiplication of integers as well. For example, when multiplying -3 by the sum of 4 and 5, we can distribute the multiplication as (-3 * 4) + (-3 * 5), which simplifies to -12 + (-15), resulting in -27.
| 3. Is closure applicable to all operations involving integers? | |
No, closure is not applicable to all operations involving integers. While closure holds true for the multiplication of integers, it does not hold true for division. When dividing two integers, the result may not always be an integer. For example, dividing 5 by 2 results in 2.5, which is not an integer.
| 4. Can the distributive property be used with any two integers? | |
Yes, the distributive property can be used with any two integers. It is a fundamental property of multiplication and addition that holds true for all integers. Whether the integers are positive, negative, or a combination of both, the distributive property can be applied to simplify expressions.
| 5. How does the distributive property help in simplifying multiplication of integers? | |
The distributive property allows us to break down a multiplication expression into simpler parts, making it easier to calculate the result. By distributing the multiplication over addition or subtraction, we can simplify the expression by multiplying each term separately and then performing the necessary addition or subtraction. This property is particularly useful when dealing with complex expressions or algebraic equations involving multiplication of integers.
Text Transcript from Video
about properties of multiplication for
integers property one let us multiply
any two integers and see whether their
product is an integer
for example minus 3 into minus 2 is
equal to 6 which is an integer thus we
see that the product of any two integers
is an integer hence if a and B are any
two integers then a into B is also an
integer this is called closure property
of multiplication of integers property -
let us multiply any two integers in
different orders and see whether their
products are same for example 8 into
minus 4 is equal to minus 32 and minus 4
into 8 is equal to minus 32 thus we see
that the product of any two integers
remains same whatever be the order of
multiplication hence if a and B are any
two integers then a into B is equal to B
into a this is called commutative
property of multiplication of integers
property 3 let us multiply any three
integers by taking them in different
groups and see whether the product in
each case is the same for example minus
8 into minus 10 into 9 is equal to minus
8 into minus 90 is equal to 720 and
minus 8 into minus 10 into 9 is equal to
80 into 9 is equal to 720 therefore
minus 8 into minus 10 into 9 is equal to
minus 8 into minus 10 into 9
thus given three integers they need not
be multiplied in the order in which they
are given we can group them in easy
combinations and find their product
hence if a B and C are any three
integers then a into B into C is equal
to a into B into C this is called
associative property of multiplication
of integers property for let us examine
the product of two integers one of which
is one for example minus 5 into 1 is
equal to minus 5 thus we find that the
product of any integer and one is always
that integer hence if a is any integer
then a into 1 is equal to 1 into a is
equal to a 1 is the identity element of
multiplication for integers
property 5 let us multiply an integer by
zero for example - 4 into 0 is equal to
0 thus the product of any integer by 0
is 0 hence if a is any integer then a
into 0 is equal to 0 into a is equal to
zero property 6 let us multiply an
integer by -1 for example 5 into minus 1
is equal to minus 5 hence if a is any
integer then a into minus 1 is equal to
minus 1 into a is equal to minus a
property 7 distributive property /
addition we can compute minus 5 into 6
plus -3 in two different ways first
minus 5 into 6 plus -3 is equal to minus
5 into plus 3 is equal to minus 15
second minus 5 into 6 plus minus 5 into
minus 3 is equal to minus 30 plus 15 is
equal to minus 15 thus we see that minus
5 into 6 plus minus 3 is equal to minus
5 into 6 plus minus 5 into minus 3 hence
if a B and C are any three integers then
a into B plus C is equal to a into B
plus a into C this is called
distributive property of multiplication
of integers over addition let us solve
an example in 8 in 2 minus Phi
plus X is equal to 8 into minus 5 plus 8
into 10 find X this gives us minus 40
plus 8x is equal to minus 40 plus 80
this implies 2 8x is equal to minus 40
plus 80 plus 40 this gives us 8x is
equal to 80 hence X is equal to 10
integers property one let us multiply
any two integers and see whether their
product is an integer
for example minus 3 into minus 2 is
equal to 6 which is an integer thus we
see that the product of any two integers
is an integer hence if a and B are any
two integers then a into B is also an
integer this is called closure property
of multiplication of integers property -
let us multiply any two integers in
different orders and see whether their
products are same for example 8 into
minus 4 is equal to minus 32 and minus 4
into 8 is equal to minus 32 thus we see
that the product of any two integers
remains same whatever be the order of
multiplication hence if a and B are any
two integers then a into B is equal to B
into a this is called commutative
property of multiplication of integers
property 3 let us multiply any three
integers by taking them in different
groups and see whether the product in
each case is the same for example minus
8 into minus 10 into 9 is equal to minus
8 into minus 90 is equal to 720 and
minus 8 into minus 10 into 9 is equal to
80 into 9 is equal to 720 therefore
minus 8 into minus 10 into 9 is equal to
minus 8 into minus 10 into 9
thus given three integers they need not
be multiplied in the order in which they
are given we can group them in easy
combinations and find their product
hence if a B and C are any three
integers then a into B into C is equal
to a into B into C this is called
associative property of multiplication
of integers property for let us examine
the product of two integers one of which
is one for example minus 5 into 1 is
equal to minus 5 thus we find that the
product of any integer and one is always
that integer hence if a is any integer
then a into 1 is equal to 1 into a is
equal to a 1 is the identity element of
multiplication for integers
property 5 let us multiply an integer by
zero for example - 4 into 0 is equal to
0 thus the product of any integer by 0
is 0 hence if a is any integer then a
into 0 is equal to 0 into a is equal to
zero property 6 let us multiply an
integer by -1 for example 5 into minus 1
is equal to minus 5 hence if a is any
integer then a into minus 1 is equal to
minus 1 into a is equal to minus a
property 7 distributive property /
addition we can compute minus 5 into 6
plus -3 in two different ways first
minus 5 into 6 plus -3 is equal to minus
5 into plus 3 is equal to minus 15
second minus 5 into 6 plus minus 5 into
minus 3 is equal to minus 30 plus 15 is
equal to minus 15 thus we see that minus
5 into 6 plus minus 3 is equal to minus
5 into 6 plus minus 5 into minus 3 hence
if a B and C are any three integers then
a into B plus C is equal to a into B
plus a into C this is called
distributive property of multiplication
of integers over addition let us solve
an example in 8 in 2 minus Phi
plus X is equal to 8 into minus 5 plus 8
into 10 find X this gives us minus 40
plus 8x is equal to minus 40 plus 80
this implies 2 8x is equal to minus 40
plus 80 plus 40 this gives us 8x is
equal to 80 hence X is equal to 10
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