1. Represent these numbers on the number line.
(i) 7/4
Solution:
(ii) -5/6
Solution:
2. Represent -2/11, -5/11, -9/11 on a number line.
Solution:
3. Write five rational numbers which are smaller than 2.
Solution:
We can write 2 as 20/10
Hence, we can say that, the five rational numbers which are smaller than 2 are:
2/10, 5/10, 10/10, 15/10, 19/10
4. Find the rational numbers between -2/5 and ½.
Solution:
First make the denominators same,
Now,
-2/5 = (-2 × 10)/(5 × 10) = -20/50
½ = (1 × 25)/(2 × 25) = 25/50
So,
Ten rational numbers between -2/5 and ½ = ten rational numbers between -20/50 and 25/50
Hence, ten rational numbers between -20/50 and 25/50 = -18/50, -15/50, -5/50, -2/50, 4/50, 5/50, 8/50, 12/50, 15/50, 20/50
5. Find five rational numbers between.
(i) 2/3 and 4/5
Solution:
First make the denominators same,
Now,
2/3 = (2 × 20)/(3 × 20) = 40/60
4/5 = (4 × 12)/(5 × 12) = 48/60
So,
Five rational numbers between 2/3 and 4/5 = five rational numbers between 40/60 and 48/60
Hence, Five rational numbers between 40/60 and 48/60 = 41/60, 42/60, 43/60, 44/60, 45/60
(ii) -3/2 and 5/3
Solution:
First make the denominators same,
Now,
-3/2 = (-3 × 3)/(2× 3) = -9/6
5/3 = (5 × 2)/(3 × 2) = 10/6
So,
Five rational numbers between -3/2 and 5/3 = five rational numbers between -9/6 and 10/6
Hence, Five rational numbers between -9/6 and 10/6 = -8/6, -7/6, -5/6, 4/6, 5/6
(iii) ¼ and ½
Solution:
First make the denominators same,
Now,
¼ = (1 × 8)/(4 × 8) = 8/32
½ = (1 × 16)/(2 × 16) = 16/32
So,
Five rational numbers between ¼ and ½ = five rational numbers between 8/32 and 16/32
Hence, Five rational numbers between 8/32 and 16/32 = 9/32, 10/32, 11/32, 12/32, 13/32.
6. Write five rational numbers greater than -2.
Solution:
We can write -2 as (– 20/10)
Hence, the five rational numbers greater than -2 are
-10/10, -5/10, -1/10, 5/10, 7/10
7. Find ten rational numbers between 3/5 and ¾,
Solution:
First make the denominators same,
Now,
3/5 = (3 × 32)/(5× 32) = 96/160
3/4 = (3 × 40)/(4 × 40) = 120/160
So,
Ten rational numbers between 3/5 and ¾ = ten rational numbers between 96/160 and 120/160
Hence, ten rational numbers between 96/160 and 120/160 = 97/160, 98/160, 99/160, 100/160, 101/160, 102/160, 102/160, 104/160, 105/160, 106/160.
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