TOPICS

Unit-1(Examples)

Rational Numbers

**Example-1 :-** Find 3/7 + (-6/11) + (-8/21) + 5/22 .

3/7 + (-6/11) + (-8/21) + 5/22 L.C.M of 7, 11, 21, 22 is 462 Then, (198 - 252 - 176 + 105 )/462 = (303 - 428)/462 = -125/462

**Example-2 :-** Find -4/5 x 3/7 x 15/16 x (-14/9)

-4/5 x 3/7 x 15/16 x (-14/9) = [(-4/5) x 3/7] x [15/16 x (-14/9)] = (-12/35) x (-35/24) = -12/24 = -1/2

**Example-3 :-** Write the additive inverse of the following:

(i) -7/19 (ii) 21/112

(i) -7/19 Here, 7/19 is the additive inverse of -7/19 because -7/19 + 7/19 = 0 (ii) 21/112 Here, -21/112 is the additive inverse of 21/112 because -21/112 + 21/112 = 0

**Example-4 :-** Verify that – (– x) is the same as x for

(i) x = 13/17 (ii) x = -21/31

(i) x = 13/17 The additive inverse of x = 13/17 is -x = -13/17 Then -13/17 + 13/17 = 0 Now, - (- x) = - (- 13/17) = 13/17 (i) x = -21/31 The additive inverse of x = -21/31 is -x = 21/31 Then -21/31 + 21/31 = 0 Now, - (- x) = - [- (-21/31] = -21/31

**Example-5 :-** Find 2/5 x (-3/7) - 1/14 - 3/7 x 3/5 .

2/5 x (-3/7) - 1/14 - 3/7 x 3/5 = 2/5 x (-3/7) - 3/7 x 3/5 - 1/14 [by commutativity] = 2/5 x (-3/7) + (-3/7) x 3/5 - 1/14 = (-3/7)[2/5 + 3/5] - 1/14 [by distributivity] = -3/7 x 1 - 1/14 = -3/7 - 1/14 = (-6 - 1)/14 = -7/14 = -1/2

**Example-6 :-** Write any 3 rational numbers between –2 and 0.

In these numbers, we can multiply and divide by 10 in -2 and 0. Then, -2 x 10/10 = -20/10 and 0 x 10/10 = 0 /10 Since, the numbers in between -20/10 and 0/10 are -19/10, -18/10, -17/10,.....-1/10. So, we can take any 3 rational numbers in between them numbers.

**Example-7 :-** : Find any ten rational numbers between -5/6 and 5/8 .

Firstly, we convert same denominator of the both values. Then, In -5/6 multiply and divide by 4. I will get (-5 x 4)/(6 x 4) = -20/24. Also, In 5/8 multiply and divide by 3. I will get (5 x 3)/(8 x 3) = 15/24. So, we can find that ten rational number in -20/24, -19/24, -18/24,......15/24.

**Example-8 :-** Find a rational number between 1/4 and 1/2.

Firstly, We find the mean of the given rational numbers. i.e., (a + b)/2 since, a = 1/4 and b = 1/2 (1/4 + 1/2)/2 = (1 + 2)/8 = 3/8 So, 3/8 lies in between 1/4 and 1/2.

**Example-9 :-** Find three rational numbers between 1/4 and 1/2.

Firstly, We find the mean of the given rational numbers. i.e., (a + b)/2 since, a = 1/4 and b = 1/2 (1/4 + 1/2)/2 = (1 + 2)/8 = 3/8 So, 3/8 lies in between 1/4 and 1/2. i.e., 1/4 < 3/8 < 1/2 Secondly, we again find the mean in between 1/4 and 3/8. since, a = 1/4 and b = 3/8 (1/4 + 3/8)/2 = (2 + 3)/16 = 5/16 So, 5/16 lies in between 1/4 and 3/8. Finally, we again find the mean in between 3/8 and 1/2 (3/8 + 1/2)/2 = (3 + 4)/16 = 7/16 So, 7/16 lies in between 3/8 and 1/2. Now, 5/16, 3/8, 7/16 are be three rational numbers in between 1/4 and 1/2.

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