Rational Numbers

Exercise 9.2

Question 1: Find the sum:

(a) `5/4+(-11)/(4)`

Answer: `5/4+(-11)/(4)=4/5-(11)/4`

`=(5-11)/4=-6/4=-3/2`

(b) `5/3+3/5`

Answer: `5/3+3/5`

`=(25+9)/(15)=(34)/(15)`


(c) `(-9)/(10)+(22)/(15)`

Answer: `(-9)/(10)+(22)/(15)`

`=(-27+44)/(30)=(17)/(30)`

(d) `(-3)/(-11)+5/9`

Answer: `(-3)/(-11)+5/9`

`=(3)/(11)+5/9`

`=(27+55)/(99)=(82)/(99)`

(e) `(-8)/(19)+(-2)/(57)`

Answer: `(-8)/(19)+(-2)/(57)`

`=(-8)/(19)-(2)/(57)`

`=(-24-2)/(57)=(-26)/(57)`

(f) `-2/3+0`

Answer: When zero is added to any number, the value of number does not change.

`-2/3+0=-2/3`

(g) `-2\1/3+4\3/5`

Answer: `-2\1/3+4\3/5=-7/3+(23)/(5)`

`=(-35+69)/(15)=(34)/(15)`

Question 2: Find the value of following:

(a) `(7)/(24)-(17)/(36)`

Answer: `(7)/(24)-(17)/(36)`

`=(21-34)/(72)=-(13)/(72)`

(b) `(5)/(63)-621`

Answer: `(5)/(63)-621`

`=(5-39123)/(63)=-(39118)/(63)`

(c) `(-6)/(13)-715`

Answer: `(-6)/(13)-715`

`=(-6-9295)/(13)=(-9301)/(13)`

(d) `(-3)/(8)-(7)/(11)`

Answer: `(-3)/(8)-(7)/(11)`

`=(-33-56)/(88)=-(89)/(88)`

(e) `-2\1/9-6`

Answer: `-2\1/9-6=-(19)/(9)-6`

`=(-19-54)/(9)=-(73)/(9)`


Question 3: Find the product of following:

(a) `9/2xx(-7)/(4)`

Answer: `9/2xx(-7)/(4)=-(63)/(8)`

(b) `(3)/(10)xx-9`

Answer: `(3)/(10)xx-9=-(27)/(10)`

(c) `-6/5xx(9)/(11)`

Answer: `-6/5xx(9)/(11)=-(54)/(55)`

(d) `3/7xx(-2)/(5)`

Answer: `3/7xx(-2)/(5)=-(6)/(35)`

(e) `(3)/(11)xx2/5`

Answer: `(3)/(11)xx2/5=(6)/(55)`

(f) `(3)/(-5)xx(-5)/(3)`

Answer: `(3)/(-5)xx(-5)/(3)=1`


Question 4: Find the value of following:

(a) `-4÷2/3`

Answer: `-4÷2/3`

`=4xx3/2=-6`

(b) `-3/5÷2`

Answer: `-3/5÷2`

`=-3/5xx1/2=(-3)/(10)`

(c) `-4/5÷(-3)`

Answer: `-4/5÷(-3)`

`=-4/5xx(-1)/(3)=(4)/(15)`

(d) `-1/8÷3/4`

Answer: `-1/8÷3/4`

`=-1/8xx4/3=-1/6`

(e) `-(2)/(13)÷1/7`

Answer: `-(2)/(13)÷1/7`

`=-(2)/(13)xx7/1=-(14)/(13)`

(f) `-(7)/(12)÷(-2)/(13)`

Answer: `-(7)/(12)÷(-2)/(13)`

`=-(7)/(12)xx(-13)/(2)=(91)/(24)`

(g) `(3)/(13)÷(-4)/(65)`

Answer: `(3)/(13)÷(-4)/(65)`

`=(3)/(13)xx(-65)/(4)=-(15)/(4)`



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