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?

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

Example 6: Is – 8 a negative rational number?

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