Class 7 Exam > Class 7 Videos > L9 : Comparing Rational Number - Rational Numbers , Maths, Class 7
L9 : Comparing Rational Number - Rational Numbers , Maths, Class 7 Video Lecture
FAQs on L9 : Comparing Rational Number - Rational Numbers , Maths, Class 7 Video Lecture
| 1. What are rational numbers? |  |
Ans. Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero. They include fractions, terminating decimals, and repeating decimals.
| 2. How can I compare rational numbers? | |
Ans. To compare rational numbers, we can convert them to the same form, either fractions or decimals, and then compare them. If they are already in the same form, we can compare their numerators or decimals directly.
| 3. Can rational numbers be negative? | |
Ans. Yes, rational numbers can be negative. They can be expressed as negative fractions or negative decimals. For example, -3/4 and -0.5 are both negative rational numbers.
| 4. What is the difference between a rational number and an irrational number? | |
Ans. The main difference between rational and irrational numbers is that rational numbers can be expressed as the ratio of two integers, while irrational numbers cannot be expressed as fractions or ratios. Irrational numbers include numbers like √2 and π.
| 5. How do I know if a decimal is a rational number? | |
Ans. A decimal is a rational number if it either terminates (ends) or repeats indefinitely. For example, 0.75 is a rational number because it terminates, while 0.333... (repeating 3s) is also a rational number because it repeats indefinitely.
Text Transcript from Video
hello friends this video on rational
numbers part 9 is brought to you by exam
fear calm no more fear from exam so now
that we know that okay rational numbers
are present on the number line it's time
to compare rational numbers how do we
know which number which rational number
is bigger and which one is smaller so
that that becomes a very interesting
question and many times now there exists
many types of rational numbers we have
positive rational numbers we have
negative rational numbers so let us deal
with them one by one so let us first
understand how do we compare two
positive rational numbers now any two
positive rational numbers can either
have same denominator or they can have
different denominators so you can have
these two different categories so one
option is that you might have numbers
like this 3 by 9 and 1 by 9 so these are
two different rational numbers both are
positive but both of them have the same
denominator
now when the denominators are same your
job becomes similar that's because when
the denominator is same you just need to
compare the numerator so in this case
the numerator here is 3 numerator here
is 4 so 3 is greater than 1 therefore 3
by 9 is greater than 1 by 9 so basically
when you have same denominators then you
just need to check the numerator
whichever has a greater numerator is a
greater rational number it is as simple
as that
now the question comes what happens if
we have different denominators so let us
take an example let's say you have two
rational numbers 1 by 2 and 3 by 5 now
here you do not have same denominator so
it is very difficult to understand which
is smaller and which is bigger so what
do we do so in this case what we do is
we are basically going to convert both
of these rational numbers into a form
such that both of them have the same
denominator so what do we do for that so
we find out the LCM of the denominators
so LCM of two and five so what is LCM
least common multiple so if we have
learned how to find the LCM in our
previous lessons in fact in class sixth
also you have learned how to find El
same in case you're forgotten please
refer to that particular video of
mathematics so LCM of two and five would
be ten right now what we will do you
consider the first rational number what
does that number which if you divide by
which you multiply by two you will get
ten in the denominator so five two into
five is ten so you divide both numerator
and denominator by five so what do you
get you get five by ten so basically one
by two and five by ten they are
equivalent because they refer to the
same value because you are multiplying
the same number to the numerator as well
as the denominator now we do a similar
thing for the second rational number
which is 3 by 5 we have to multiply the
numerator and the denominator in such a
way that in the result the denominator
is 10 so 5 into 2 is 10 so you multiply
the numerator also by 2 so this is 6 by
10 so now you have two rational numbers
5 by 10 and 6 by 10 where the
denominators are same now if you compare
5 by 10 and 6 by 10 which is bigger 6 is
bigger so 6 by 10 is bigger than 5 by 10
now what does 6 by 10 6 by 10 is
equivalent to 3 by 5 so 3 by 5 is less
than 5 by 10 which is equivalent to 1 by
2 so you can say that 1 by 2 is smaller
than 3 by 5 so this is how we compare
two rational numbers provided both of
them are positive rational numbers now
in a similar way let us see how do we
compare negative rational numbers
exactly same scenario now we will
imagine that if we are comparing
negative rational numbers now let's see
with same denominators you are given two
rational numbers minus 5
9 and minus 8 by 9 so which one is
bigger and which one is smaller now when
you see when you compare 8 with 5 you
would say that 8 is bigger than 5 so
should minus 8 also be greater than
minus 5 no it is just the opposite
minus 8 is less than minus 5 can you
tell me why for that you will have to
have a look at the number line so this
is how the number line is arranged right
and this side you have minus 1 - 2 - 3 -
4 - 5 and so on now what happens is as
you move towards the right hand side you
move towards positive numbers bigger
positive numbers so as you move towards
right on the number line the value
increases
now this remains true throughout the
number line so whether you are talking
about the right hand side of 0 and left
hand side of 0 as you move towards the
right the value increases that's because
it is something like this let's say you
have two chocolates now you're you ate
one so you are left with 1 you ate that
one also you're left with 0 now you
borrowed one more chocolate from your
frame so you have minus 1 because you
need to return that chocolate to him
later
now you borrowed one more chocolate from
your brother so your the balance is
minus 2 so basically what has happened
in your balance is gradually decreasing
from 2 to 1 to 0 to minus 1 to minus 2
and so on so basically in any number 9
as you move towards the right the values
increases as you move towards the left
the values decreases now when you
compare -5 + -8 - 5 comes before and -
aid comes somewhere here right so from
minus 5 to minus 8 you still go further
left that means your value is decreasing
that is why minus 8 is less than minus 5
so one simple it to remember this is
whenever you are
very rational numbers with negative sign
just do the reverse of what you would
have done with positive sign for example
if you compare 8 and 5 positive sign so
8 will be greater than 5 since both of
them carry a negative sign you choose to
reverse your sign that means in this
case minus 8 will be less than minus 5
so that is what you need to do perfect
so now in this case can you tell me
which will be bigger minus 5 by 9 or
minus 8 by 9 definitely minus 5 by 9
will be greater that's because minus 5
is greater than -8 okay now let's see
how do we handle the different
denominator scenario so the concept will
remain the same as we did in the
previous slide let's say you have minus
1 by 2 and you have minus 8 by 3 so we
will find out the LCM of both the
denominators that is LCM of 2 & 3 which
is 6 now let's consider the first
rational number we are going to divide
the numerator and the denominator with
the same number such that the result in
the denominator is 6 so 2 into 3 is 6 so
we multiply it by 3 so this is minus 3
by 6 now we consider the second rational
number which is minus 8 into 3 here also
we multiply the numerator and the
denominator by the same number such that
the denominator in the result is 6 3
into 2 is 6 so we multiply the numerator
also by 2 so this is minus 16 by 6 now
what do you have so you have two
rational numbers minus 3 by 6 then minus
16 by 6 such that the denominators are
same so let's compare the numerators
forget about the sign which is greater 3
or 16 16 is greater but you have a
negative sign with both of them so that
means 16 is smaller so minus 3 license
is greater than minus 16 by 6 so minus
3y 6 is actually minus 1 by 2 minus 16
by 6 is nothing but minus 8 by 3 so you
can say that minus 1 by 2 is greater
than minus 8 by 3 now let us compare
positive rational numbers with negative
rational numbers let's say that one
rational
is positive and the other rational
number is negative now in this case this
is the simplest scenario because in this
case a positive rational number will
always be greater than a negative one
and this will hold true all these
doesn't matter what the value of the
rational number is if it has a positive
sign and the other one has a negative
sign when the positive number will
always be greater than the negative one
so do you want to know why
well that's because whenever you look at
the number line you would see that any
negative number will always be located
towards the left hand side and we have
seen that as we go towards the left the
value decreases it doesn't matter
whichever negative number you are
talking about all the negative numbers
are located towards the left of the
positive numbers therefore all of them
are smaller than the positive numbers
thank you please visit example.com for
free quality education you can learn
with a simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
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on physics chemistry mathematics and
biology along with practical videos so
please subscribe to our channel for
daily updates thank you
numbers part 9 is brought to you by exam
fear calm no more fear from exam so now
that we know that okay rational numbers
are present on the number line it's time
to compare rational numbers how do we
know which number which rational number
is bigger and which one is smaller so
that that becomes a very interesting
question and many times now there exists
many types of rational numbers we have
positive rational numbers we have
negative rational numbers so let us deal
with them one by one so let us first
understand how do we compare two
positive rational numbers now any two
positive rational numbers can either
have same denominator or they can have
different denominators so you can have
these two different categories so one
option is that you might have numbers
like this 3 by 9 and 1 by 9 so these are
two different rational numbers both are
positive but both of them have the same
denominator
now when the denominators are same your
job becomes similar that's because when
the denominator is same you just need to
compare the numerator so in this case
the numerator here is 3 numerator here
is 4 so 3 is greater than 1 therefore 3
by 9 is greater than 1 by 9 so basically
when you have same denominators then you
just need to check the numerator
whichever has a greater numerator is a
greater rational number it is as simple
as that
now the question comes what happens if
we have different denominators so let us
take an example let's say you have two
rational numbers 1 by 2 and 3 by 5 now
here you do not have same denominator so
it is very difficult to understand which
is smaller and which is bigger so what
do we do so in this case what we do is
we are basically going to convert both
of these rational numbers into a form
such that both of them have the same
denominator so what do we do for that so
we find out the LCM of the denominators
so LCM of two and five so what is LCM
least common multiple so if we have
learned how to find the LCM in our
previous lessons in fact in class sixth
also you have learned how to find El
same in case you're forgotten please
refer to that particular video of
mathematics so LCM of two and five would
be ten right now what we will do you
consider the first rational number what
does that number which if you divide by
which you multiply by two you will get
ten in the denominator so five two into
five is ten so you divide both numerator
and denominator by five so what do you
get you get five by ten so basically one
by two and five by ten they are
equivalent because they refer to the
same value because you are multiplying
the same number to the numerator as well
as the denominator now we do a similar
thing for the second rational number
which is 3 by 5 we have to multiply the
numerator and the denominator in such a
way that in the result the denominator
is 10 so 5 into 2 is 10 so you multiply
the numerator also by 2 so this is 6 by
10 so now you have two rational numbers
5 by 10 and 6 by 10 where the
denominators are same now if you compare
5 by 10 and 6 by 10 which is bigger 6 is
bigger so 6 by 10 is bigger than 5 by 10
now what does 6 by 10 6 by 10 is
equivalent to 3 by 5 so 3 by 5 is less
than 5 by 10 which is equivalent to 1 by
2 so you can say that 1 by 2 is smaller
than 3 by 5 so this is how we compare
two rational numbers provided both of
them are positive rational numbers now
in a similar way let us see how do we
compare negative rational numbers
exactly same scenario now we will
imagine that if we are comparing
negative rational numbers now let's see
with same denominators you are given two
rational numbers minus 5
9 and minus 8 by 9 so which one is
bigger and which one is smaller now when
you see when you compare 8 with 5 you
would say that 8 is bigger than 5 so
should minus 8 also be greater than
minus 5 no it is just the opposite
minus 8 is less than minus 5 can you
tell me why for that you will have to
have a look at the number line so this
is how the number line is arranged right
and this side you have minus 1 - 2 - 3 -
4 - 5 and so on now what happens is as
you move towards the right hand side you
move towards positive numbers bigger
positive numbers so as you move towards
right on the number line the value
increases
now this remains true throughout the
number line so whether you are talking
about the right hand side of 0 and left
hand side of 0 as you move towards the
right the value increases that's because
it is something like this let's say you
have two chocolates now you're you ate
one so you are left with 1 you ate that
one also you're left with 0 now you
borrowed one more chocolate from your
frame so you have minus 1 because you
need to return that chocolate to him
later
now you borrowed one more chocolate from
your brother so your the balance is
minus 2 so basically what has happened
in your balance is gradually decreasing
from 2 to 1 to 0 to minus 1 to minus 2
and so on so basically in any number 9
as you move towards the right the values
increases as you move towards the left
the values decreases now when you
compare -5 + -8 - 5 comes before and -
aid comes somewhere here right so from
minus 5 to minus 8 you still go further
left that means your value is decreasing
that is why minus 8 is less than minus 5
so one simple it to remember this is
whenever you are
very rational numbers with negative sign
just do the reverse of what you would
have done with positive sign for example
if you compare 8 and 5 positive sign so
8 will be greater than 5 since both of
them carry a negative sign you choose to
reverse your sign that means in this
case minus 8 will be less than minus 5
so that is what you need to do perfect
so now in this case can you tell me
which will be bigger minus 5 by 9 or
minus 8 by 9 definitely minus 5 by 9
will be greater that's because minus 5
is greater than -8 okay now let's see
how do we handle the different
denominator scenario so the concept will
remain the same as we did in the
previous slide let's say you have minus
1 by 2 and you have minus 8 by 3 so we
will find out the LCM of both the
denominators that is LCM of 2 & 3 which
is 6 now let's consider the first
rational number we are going to divide
the numerator and the denominator with
the same number such that the result in
the denominator is 6 so 2 into 3 is 6 so
we multiply it by 3 so this is minus 3
by 6 now we consider the second rational
number which is minus 8 into 3 here also
we multiply the numerator and the
denominator by the same number such that
the denominator in the result is 6 3
into 2 is 6 so we multiply the numerator
also by 2 so this is minus 16 by 6 now
what do you have so you have two
rational numbers minus 3 by 6 then minus
16 by 6 such that the denominators are
same so let's compare the numerators
forget about the sign which is greater 3
or 16 16 is greater but you have a
negative sign with both of them so that
means 16 is smaller so minus 3 license
is greater than minus 16 by 6 so minus
3y 6 is actually minus 1 by 2 minus 16
by 6 is nothing but minus 8 by 3 so you
can say that minus 1 by 2 is greater
than minus 8 by 3 now let us compare
positive rational numbers with negative
rational numbers let's say that one
rational
is positive and the other rational
number is negative now in this case this
is the simplest scenario because in this
case a positive rational number will
always be greater than a negative one
and this will hold true all these
doesn't matter what the value of the
rational number is if it has a positive
sign and the other one has a negative
sign when the positive number will
always be greater than the negative one
so do you want to know why
well that's because whenever you look at
the number line you would see that any
negative number will always be located
towards the left hand side and we have
seen that as we go towards the left the
value decreases it doesn't matter
whichever negative number you are
talking about all the negative numbers
are located towards the left of the
positive numbers therefore all of them
are smaller than the positive numbers
thank you please visit example.com for
free quality education you can learn
with a simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
test we have content for class 6 to 12
on physics chemistry mathematics and
biology along with practical videos so
please subscribe to our channel for
daily updates thank you
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Dec 21, 2024 Last updated |
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