Question

Find three rational numbers between
(i) -1 and -2 (ii) 0.1 and 0.11 (iii) 5/7 and 6/7 (iv) 1/4 and 1/5​

Answer 1

Answer:

Step-by-step explanation:

(1) Let y =-1 and x = -2

Here, x>y and we have to find three rational numbers, so n=3

d=(y−x)/(n+1)=(−1+2)/(3+1)=1/4

Since, the three, rational numbers x and y are x+ d, x+2d and x+ 3d

now , x=d=−2+1/4=(−8+1)/4=−7/4

x+2d=−2+2/4=(−8+2)/4=−6/4=−3/2

and x+3d=(2−3)/4=(−8+3)/4=−5/4

Hence, three rational numbers between -1 and -2 are −7/4,−3/2and−5/4

(2)let x= 0.1 and y= 0.11

Here, x<y and we have to find three rational numbers

using similar method used above in question (1),

Hence , three rational numbers between, 0.1 and 0.11 and 0.1025, 0.105, 0.1075

Also, without using above formula the three rational numbers between 0.1 and 0.11 are 0.101, 0.102, 0.103.

(3)Let , x=5/7andy=6/7

Here, x<y Here, we have to find three rational numbers.

consider,

n=3,

d=y−xn+1

d=67−574=174=128

Since, the three rational number between x and y are ( x+d ) , (x+2d) and (x+3d)

now, x+d=5/7+1/28=(20+1)/28=21/28

x+2d=5/7+2/28=(20+2)/28=22/28

x+3d=5/7=3/28=(20+3)/28=23/28

Hence, three rational numbers between 5/7and6/7are21/28,22/28,23/28

(4)Let x=1/4 and y=1/5

so, a rational number between x and y=(x+y)/2

A rational number between 1/4and1/5=(1/4+1/5)/2=([5+4]/20)/2

9/[2×20]=9/40

Again, a rational number between 1/4and9/40=[1/4+9/40]/2=[(10+9)/40]/2=19/(2×40)=19/80

Again , a rational number between 1/5and9/40=([1/5+9/40]/2)={(8+9)/40}/2=(17/40)/2=(17/[40×2])=17/80

Hence, three rational numbers between 1/4and1/5are,9/40,19/80,17/80.

Answer 2

yo there bro this is the answer ^^