Answer:
Which is greater in each of the following:
(i) 2/3, 5/2
(ii) −5/6, −4/3
(iii) −3/4, 2/(−3)
(iv) −1/4, 1/4
(v) −
3
2
7
, −
4
5
Solution:
To solve this question we will take the L.C.M of the denominator of the rational numbers or convert them into like fractions.
After converting them into like fractions, arrangement can easily be done by comparing the numerators.
L.C.M of 3 and 2 is 6
2/3 = (2 × 2)/(3 × 2) = 4/6
5/2 = (5 × 3)/(2 × 3) = 15/6
Since, 4/6 < 15/6
So, 2/3 < 5/2
(ii) −5/6 , −4/3
L.C.M of 6 and 3 is 6
- 5/6 = (−5 × 1)/(6 × 1) = −5/6
- 4/3 = (−4 × 2)/(3 × 2) = −8/6
Since,−5/6 > −8/6
So,−5/6 > −4/3
(iii) −3/4 , 2/−3
L.C.M of 4 and 3 is 12
−3/4 = (−3 × 3)/(4× 3) = −9/12
2/(−3) = (2 × 4)/(−3 × 4) = −8/12
Since, −9/12 < −8/12
So, −3/4 < 2/(−3)
(iv) −1/4 , 1/4
−1/4 < 1/4
(Negative number is always smaller than the positive number)
−
= −23/7 and −
= −19/5
L.C.M of 7 and 5 is 35
−23/7 = (−23 × 5)/(7 × 5) = −115/35
−19/7 = (−19 × 7)/(7 × 5) = −133/35
Since, −115/35 > −133/35
So, −
> −
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Answers & Comments
Answer:
Which is greater in each of the following:
(i) 2/3, 5/2
(ii) −5/6, −4/3
(iii) −3/4, 2/(−3)
(iv) −1/4, 1/4
(v) −
3
2
7
, −
3
4
5
Solution:
To solve this question we will take the L.C.M of the denominator of the rational numbers or convert them into like fractions.
After converting them into like fractions, arrangement can easily be done by comparing the numerators.
(i) 2/3, 5/2
L.C.M of 3 and 2 is 6
2/3 = (2 × 2)/(3 × 2) = 4/6
5/2 = (5 × 3)/(2 × 3) = 15/6
Since, 4/6 < 15/6
So, 2/3 < 5/2
(ii) −5/6 , −4/3
L.C.M of 6 and 3 is 6
- 5/6 = (−5 × 1)/(6 × 1) = −5/6
- 4/3 = (−4 × 2)/(3 × 2) = −8/6
Since,−5/6 > −8/6
So,−5/6 > −4/3
(iii) −3/4 , 2/−3
L.C.M of 4 and 3 is 12
−3/4 = (−3 × 3)/(4× 3) = −9/12
2/(−3) = (2 × 4)/(−3 × 4) = −8/12
Since, −9/12 < −8/12
So, −3/4 < 2/(−3)
(iv) −1/4 , 1/4
−1/4 < 1/4
(Negative number is always smaller than the positive number)
(v) −
3
2
7
, −
3
4
5
−
3
2
7
= −23/7 and −
3
4
5
= −19/5
L.C.M of 7 and 5 is 35
−23/7 = (−23 × 5)/(7 × 5) = −115/35
−19/7 = (−19 × 7)/(7 × 5) = −133/35
Since, −115/35 > −133/35
So, −
3
2
7
> −
3
4
5