Rational Numbers NCERT Exercise 9.1
Part 2
Question 5: The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.
Answer: `P=2\1/3=7/3`
`Q=2\2/3=8/3`
`R=-1\1/3=-4/3`
`S=-1\2/3=-5/3`
Question 6: Which of the following pairs represent the same rational number?
(a) `-(7)/(21)` and `3/9`
Answer: Since one of the numbers is negative and another is positive, hence they cannot be same.
(b) `-(16)/(20)` and `(20)/(25)`
Answer: Since one of the numbers is negative and another is positive, they cannot be same.
(c) `(-2)/(-3)` and `2/3`
Answer: Both the numbers are positive and have same numerator and denominator, so they are same.
(d) `(-3)/(5)` and `(-12)/(20)`
Answer: Let us first convert the given numbers into standard form:
First number has co-prime numerator and denominator, so it is in standard form. Second number can be converted to standard form as follows:
`(-12)/(20)=(-3xx4)/(5xx4)=-3/5`
So, both numbers are same.
(e) `(8)/(-5)` and `(-24)/(15)`
Answer: First number has co-prime numerator and denominator.
Let us convert the second number into standard form:
`(-24)/(15)=(-8xx3)/(5xx3)=-8/5`
So, both numbers are same.
(f) `1/3` and `-1/9`
Answer: One of the numbers is negative and another is positive, so they cannot be same.
(g) `(-5)/(-9)` and `(5)/(-9)`
Answer: One of the numbers is negative and another is positive, so they cannot be same.
Question 7: Rewrite the following rational numbers in the simplest form:
(a) `(-8)/(6)`
Answer: `(-8)/(6)=(-2xx4)/(2xx3)=(-4)/(3)`
(b) `(25)/(45)`
Answer: `(25)/(45)=(5xx5)/(5xx9)=5/9`
(c) `(-44)/(72)`
Answer: `(-44)/(72)=(-4xx11)/(4xx18)=(-11)/(18)`
(d) `(-8)/(10)`
Answer: `(-8)/(10)=(-2xx4)/(2xx5)=-4/5`
Question 8: Fill in the boxes with the correct symbol out of >, < and =.
(a) `(-7)/(5)[ ]2/3`
Answer: In this case, the negative number is less than the positive number.
`(-7)/(5)<2/3`
(b) `(-4)/(5)[ ](-5)/(7)`
Answer: Let us first find the LCM of denominators and then convert the numbers with LCM as denominator. LCM of 5 and 7 is 35.
`(-4)/(5)=(-28)/(35)` and `(-5)/(7)=(-25)/(35)`
Hence, `(-4)/(5)<(-5)/(7)`
(c) `(-7)/(8)[ ](14)/(-16)`
Answer: LCM of 8 and 16 is 16.
`(-7)/(8)=(-14)/(16)`
Hence, `(-7)/(8)=(14)/(-16)`
(d) `(-8)/(5)[ ](-7)/(4)`
Answer: LCM of 5 and 4 is 20.
`(-8)/(5)=(-32)/(20)` and `(-7)/(4)=(-35)/(20)`
Hence, `(-8)/(5)>(-7)/(4)`
(e) `(1)/(-3)[ ](-1)/(4)`
Answer: LCM of 3 and 4 is 12.
`(-1)/(3)=(-4)/(12)` and `(-1)/(4)=(-3)/(12)`
Hence, `(1)/(-3)<(-1)/(4)`
(f) `(5)/(-11)[ ](-5)/(11)`
Answer: `(5)/(-11)=(-5)/(11)`
(g) `0[ ](-7)/(6)`
Answer: Any negative number is less than zero.
Hence, `0>(-7)/(6)`
Question 9:
(a) `2/3`, `5/2`
Answer: LCM of 3 and 2 is 6.
`2/3=4/6` and `5/2=(15)/(6)`
Hence, `5/2>2/3`
(b) `(-5)/(6)`, `(-4)/(3)`
Answer: LCM of 3 and 6 is 6.
`(-4)/(3)=(-8)/(6)`
Hence, `(-5)/(6)>(-4)/(3)`
(c) `(-3)/(4)`, `(2)/(-3)`
Answer: LCM of 4 and 3 is 12.
`(-3)/(4)=(-9)/(12)` and `(-2)/(3)=(-8)/(12)`
Hence, `(-2)/(3)>(-3)/(4)`
(d) `(-1)/(4)`, `1/4`
Answer: Any negative number is always less than any positive number.
Hence, `1/4> -1/4`
(e) `-3\2/7`, `-3\4/5`
Answer: LCM of 7 and 5 is 35.
`-3\2/7=(-22)/(7)` and `-3\4/5=(-19)/(5)`
Now, `(-22)/(7)=(-110)/(35)` and `(-19)/(5)=(-133)/(35)`
Hence, `-3\2/7> -3\4/5`
Question 10: Write the following rational numbers in ascending order:
(a) `-3/5`, `-2/5`, `-1/5`
Answer: In this case, denominator is same in all numbers:
Hence, `-3/5< -2/5< -1/5`
(b) `1/3`, `-2/9`, `-4/3`
Answer: LCM of 3 and 9 is 9. Let us convert these numbers with denominator as 9.
`1/3=3/9` and `-4/3=(-12)/(9)`
Hence, `-4/3< -2/9<1/3`
(c) `-3/7`, `-3/2`, `-3/4`
Answer: LCM of 2, 4 and 7 is 28. Let us convert these numbers with denominator as 28.
`-3/7=-(12)/(28)`, `-3/2=-(42)/(28)`, `-3/4=-(21)/(28)`
Hence, `-3/2< -3/4< -3/7`