Rational Numbers

In Text Questions:

Example 1: Is the number 2/3 rational? Think about it.

Answer: Yes, because this number is in the form of p/q where q≠0.

Example 2: List ten rational numbers.

Answer: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10


Example 3: Fill in the boxes:

(a) `5/4=(( ))/(16)``=(25)/(( ))=(15)/(( ))`

Answer: `5/4=(20)/(16)``=(25)/(20)=(15)/(12)`

(b) `3/7=(( ))/(14)``=(9)/(( ))=(6)/(( ))`

Answer: `3/7=(6)/(14)``=(9)/(21)=(6)/(14)`

Example 4: Is 5 a positive rational number?
Answer: Yes

Example 5: List five more positive rational numbers.
Answer: 6, 7, 8, 9 and 10

Example 6: Is – 8 a negative rational number?
Answer: Yes

Example 7: List five more negative rational numbers.
Answer: - 7, -6, -5, -4, -3

Example 8: Find the standard form of (i) `(18)/(45)` and (ii) `(12)/(18)`.

Answer: `(18)/(45)=(9xx2)/(9xx5)=2/5`

`(12)/(18)=(6xx2)/(6xx3)=2/3`

Example 9: Find five rational numbers between `5/7` and `3/8`.

Answer: LCM of 7 and 8 is 56. So, let us convert these numbers with 56 as denominator.

`5/7=(40)/(56)` and `3/8=(21)/(56)`

So, required numbers are as follows:

`(22)/(56)`, `(23)/(56)`, `(24)/(56)`, `(25)/(56)`, `(26)/(56)`


Example 10: Try these:

(a) `3/7+2/3`

Answer: `3/7+2/3`

`=(9+14)/(21)=(23)/(21)`

(b) `-5/6+(-3)/(11)`

Answer: `-5/6+(-3)/(11)`

`=(-55-18)/(66)=-(73)/(66)`

Exmaple 11: What will be the additive inverse of: `-3/9`, `(-9)/(11)`, `5/7`?

Answer: `3/9`, `(9)/(11)` and `-5/7`?

Example 12: Try these:

(a) `7/9-2/5`

Answer: `7/9-2/5`

`=(35-18)/(45)=(17)/(45)`

(b) `2\1/5-1/3`

Answer: `2\1/5-1/3=(11)/(5)-1/3`

`=(33-5)/(15)=(28)/(15)`


Example: 13: What will be:

(a) `-3/5xx7=?`

Answer: `-3/5xx7=(-21)/(5)`

(b) `-6/5xx(-2)=?`

Answer: `-6/5xx(-2)=(12)/(5)`

Example 14: Find the value of following:

(a) `3/4xx1/7`

Answer: `3/4xx1/7=(3)/(28)`

(b) `2/3xx5/9`

Answer: `2/3xx5/9=(10)/(27)`

Example 15: What will be the reciprocal of `-(6)/(11)` and `-(8)/(15)`?

Answer: `-(11)/(6)` and `-(15)/(8)`

Example 16: Find the following:

(a) `2/3÷7/8`

Answer: `2/3÷7/8``=2/3xx8/7=(16)/(21)`

(b) `-6/7÷5/7`

Answer: `-6/7÷5/7``=-6/7xx7/5=-6/5`



Copyright © excellup 2014