Rational Numbers
Class 8th Mathematics CBSE Solution
- Using appropriate properties find.(i) (ii)
- Write the additive inverse of each of the following. (i) (ii) (iii) (iv) (v)…
- Find the multiplicative inverse of the following. (i) -13 (ii) -13/19 (iii) 1/5…
- Name the property under multiplication used in each of the following. (i) -4/5 x…
- Multiply 6/13 by the reciprocal of -7/16
- Tell what property allows you to compute as
- Is 0.3 the multiplicative inverse of 3 1/3 ? Why or why not?
- Write. (i) The rational number that does not have a reciprocal. (ii) The…
- Fill in the blanks. (i) Zero has ________ reciprocal. (ii) The numbers ________…
- Represent these numbers on the number line. (i) 7/4 (ii) -5/6
- Represent -2/11 , -5/11 , -9/11 on the number line.
- Write five rational numbers which are smaller than 2.
- Find ten rational numbers between -2/5 and 1/2
- Find five rational numbers between. (i) 2/3 4/5 (ii) -3/2 5/3 (iii) 1/4 1/2…
- Write five rational numbers greater than -2.
- Find ten rational numbers between 3/5 and 3/4
Exercises 1.1
Question 1.Using appropriate properties find.
(i) 
(ii) 
Answer:
(i)
Using Commutative property we write,
Now taking 
common we get,
Taking LCM, we have
= 2
(ii) 
Using commutative property we get,
Take 
common to get,
Question 2.
Write the additive inverse of each of the following.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
Answer:
(i) The additive inverse of “a” is given as “-a”
Therefore,
(ii) The additive inverse of “a” is given as “-a”
Therefore,
(iii) The additive inverse of “a” is given as “-a”
Therefore,
(iv) The additive inverse of “a” is given as “-a”
Therefore,
(v) The additive inverse of “a” is given as “-a”
Therefore,
Question 3.
Find the multiplicative inverse of the following.
(i) -13
(ii) 
(iii) 
(iv) 
(v) 
(vi) -1
Answer:
(i) The multiplicative inverse of “a” is given as “
”
Therefore,
(ii) The multiplicative inverse of “a” is given as “”
Therefore,
(iii) The multiplicative inverse of “a” is given as “”
Therefore,
(iv) The multiplicative inverse of “a” is given as “”
Therefore,
(v) The multiplicative inverse of “a” is given as “”
Therefore,
(vi) The multiplicative inverse of “a” is given as “”
Therefore,
Multiplicative inverse of -1 is 
Question 4.
Name the property under multiplication used in each of the following.
(i) 
(ii) 
(iii) 
Answer:
(i) Multiplicative identity is applied in 
As, 1 × m = m × 1, where m is any rational number.
(ii) Commutative property is applied in 
where m and n are rational numbers
(iii) Multiplicative inverse property is applied here in 
Multiplication of any rational number to its inverse gives identity of multiplication that is 1
Question 5.
Multiply 
by the reciprocal of 
Answer:
The reciprocal of 
Now, 
Question 6.
Tell what property allows you to compute 
as 
Answer:
Associative Property: a x (b x c) = (a x b) x c
According to this property, the way we group during multiplication does not matter. As shown above multiplying the L.H.S is same as the multiplication of R.H.S
The associative property allows us to write
as 
Question 7.
Is 0.3 the multiplicative inverse of 
Why or why not?
Answer:
0.3 can be written as, 
Yes
Question 8.
Write.
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Answer:
(i) Zero is one such number that does not have a reciprocal.
(ii) 1 and -1 are the rational numbers that are equal to their reciprocals.
(iii) Zero is the only rational number that is equal to its negative.
Question 9.
Fill in the blanks.
(i) Zero has ________ reciprocal.
(ii) The numbers ________ and ________ are their own reciprocals.
(iii) The reciprocal of – 5 is ________.
(iv) Reciprocal of 
where 
is ________.
(v) The product of two rational numbers is always a _______.
(vi) The reciprocal of a positive rational number is ________.
Answer:
(i) Zero has No reciprocal
(ii) The numbers 1 and -1 are their own reciprocals.
(iii) The reciprocal of – 5 is 
(iv) Reciprocal of 
where 
is x.
(v) The product of two rational numbers is always a rational number.
(vi) The reciprocal of a positive rational number is a positive rational number.
Exercises 1.2
Question 1.Represent these numbers on the number line.
(i) 
(ii) 
Answer:
(i) 
is equivalent to 1.75
So, we will plot this on number line with making divisions of 4 between any two numbers as shown in the figure below
Therefore,
(ii) 
is equivalent to -0.83
-5/6 = -1 + 1/6 = - 0.833
Question 2.
Represent 
on the number line.
Answer:
In a rational number, the number below the bar i.e. the denominator tells the number of equal parts into which the first unit has been divided. The numerator tells ‘how many’ of these parts are considered.
We will divide the distance between -1 and 0 in 11 equal parts.
Here, 
means 2, 5 and 9 markings of 
each on the left of zero and starting from 0 respectively.
Question 3.
Write five rational numbers which are smaller than 2.
Answer:
Let us multiply and divide 2 by any number greater than 1, let it be 2 for instance.
Then,
We have to find rational numbers less than 2.
Now, we can write rational numbers less that 
Therefore, the rational numbers less than 2 are 
Now it need not be that the number you multiply or divide by has to be 2, Let the number be 3 for instance.
then,
Now, the rational number less than 2, will be less than 
Therefore, the rational numbers less than 2 are 
Try yourself forming other rational numbers less than 2.
Question 4.
Find ten rational numbers between
and 
Answer: We have to find 10 rational numbers between -2/5 and 1/2.
Now we can do that by multiplying numerator and denominator of both the rational numbers with the same number so that the denominator of both the rational numbers become same.
For that let's take L.C.M of 5 and 2. And it is 10. So we have to make denominator of both the rational numbers as 10 or any multiple of 10
Question 5.
Find five rational numbers between.
(i) 
(ii) 
(iii) 
Answer:
(i) 
can be written as
Five rational numbers between are 
(ii) 
can be written as
Five rational numbers between are 
(iii) 
can be written as 
Five rational numbers between 
are 
Question 6.
Write five rational numbers greater than –2.
Answer:
Any number which lies after -2 are greater than -2. Example, 
Then, rational numbers are, 
Or we can see that, 1, 2, 3, 4, 5, ... are all greater than -2 and are rational number.
Question 7.
Find ten rational numbers between 
and 
Answer:
For finding rational numbers between two rational numbers 3/5 and 5/4.
Take L.C.M of the denominators of the numbers.
We have 4 and 5 as the denominators. L.C.M of 4 and 5 = 20
Now we have to make the denominators of each rational numbers 20 by multiplying and dividing.
But this way we will have only three rational numbers in between, so multiply numerator and denominator by any number greater than 1, Let us multiply by 4
we get
Now keeps on increasing the numerator by one and start getting the Numbers between the Rational numbers
We will have 