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**Maths Ace Class 8 Solutions Chapter 1 Rational Numbers**

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Maths Ace Class 8 Math Book, Chapter 1, Rational Numbers. Here students can easily find step by step solutions of all the problems for Rational Numbers, Exercise 1.1, 1.2 and 1.3 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 1 solutions.

**Rational Numbers Exercise 1.1 Solution : **

**Question no – (1)**

**Solution : **

**(a)** Given number, 3/4

**(b)** Given number, 7/8

**(c)** Given number, -3/2

**(d)** Given number, 1/9

**Question no – (2) **

**Solution : **

**(a)** 1/5/17

= Lie between 0 and 1

**(b)** 12/5

= lie between 2 and 3

**(c)** -34/16

= lie between -3 and -2

**(d)** -12/70

= lie between -1 and 0

**Question no – (3) **

**Solution : **

**(a)** Absolute value of 8/3 is **8/3**

**(b)** Absolute value of -5/4 is **5/4**

**(c)** Absolute value of 3/-5 is **3/5**

**(d)** Absolute value of -6/-7 is **6/7**

**Question no – (4) **

**Solution : **

**(a) 3/4 and 5/6**

= 18 < 20

**∴** 3/4 < 5/6

**(b) 3/5 and 1/6**

= 18 > 5

**∴** 3/5 > 1/6

**(c) -3/2 and -6/8**

= – 24 < – 12

= – 3/2 < -6/8

**(d) 1/7 and 1/3**

= 3 < 7

= 1/7 < 1/3

**Question no – (5) **

**Solution : **

**(a) 3/6** = 3 × 2/6 × 2 = 6/12

4/3 = 16/12

-5/4 = -15/12

-3/2 = -18/12

Now in ascending order,

-3/2 < -5/4 < 3/6 < 4/3

**(b) LCM of 5, 7, 2, 8 **

3/5 = 3 × 56/5 × 56 = 168/280

1/7 = 40/280

-3/2 = -3 × 140/2 × 140 = -420/280

6/8 = 6 × 35/8 × 35 = 210/280

Now in ascending order,

**∴** -3/2 < 1/7 < 3/5 < 6/8

**(c)** **-3/2** = -3 × 30/2 × 30 = -90/60

8/5 = 8 × 12/5 × 12 = 96/60

7/4 = 7 × 15/4 × 15 = 105/60

– 2/3 = -2 × 20/3 × 20 = – 40/60

Now in ascending order,

**∴** -3/2 < -2/3 < 8/5 < 7/4

**(d)** **1/7** = 1 × 30/7 × 30 = 30/210

1/3 = 1 × 70/3 × 70 = 70/210

4/5 = 4 × 42/5 × 42 = 168/210

5/6 = 5 × 35/6 × 35 = 175/210

Now in ascending order,

**∴** 1/7 < 1/3 < 4/5 < 5/6

**Question no – (6) **

**Solution :**

**(a) 8/5** = 8 × 18/5 × 18 = 144/90

3/2 = 3 × 45/2 × 45 = 135/90

1/6 = 1 × 15/6 × 15 = 15/90

-5/6 = – 5 × 15/6 × 15 = -75/90

Now, in descending order,

8/5 > 3/2 > 1/6 > -5/6

**(b) 4/5** = 4 × 28/5 × 28 = 112/140

1/7 = 20/7 × 20 = 20/140

7/4 = 7 × 35/4 × 35 = 245/140

-2/5 = -2 × 28/5 × 28 = – 56/140

Now, in descending order,

**∴** 7/4 > 4/5 > 1/7 > – 2/5

**(c) -2/3 **= – 2 × 280/3 × 280 = -560/840

5/8 = 5 × 105/8 × 105 = 525/840

4/7 = 4 × 120/7 × 120 = 480/840

-4/5 = – 4 × 168/5 × 168 = – 672/840

Now, in descending order,

**∴** 5/8 > 4/7 > – 2/3 > – 4/5

**(d) 1/5 **= 1 × 168/5 × 168 = 168/840

2/3 = 2 × 280/3 × 280 = 560/840

3/8 = 3 × 105/8 × 105 = 315/840

5/7 = 5 × 120/7 × 120 = 600/840

Now, in descending order,

**∴** 5/7 > 2/3 > 3/8 > 1/5

**Rational Numbers Exercise 1.2 Solution : **

**Question no – (1) **

**Solution : **

**(a) 3/5 + 8/6**

= 18 + 40/30

= 58/30

= 29/15

= 1 14/15…(Solved)

**(b) 6/9 + 3/4 + 2/5**

= 120 + 13.5 + 72/180

= 327/180

= 1 49/60…(Solved)

**(c) 3/5 -6/7**

= 21 -30/35

= -9/35…(Solved)

**(d) 7/9 – (- 4/5)**

= 7/9 + 4/5

= 35 + 36/45

= 71/45

= 1 26/45…(Solved)

**(e) -11/10 – (-19/15)**

= -11/10 + 19/15

= -33 + 38/30

= 5/30

= 1/6…(Solved)

**(f) 4/5 × (3/9 + 2/3)**

= 4/5 × (3 + 6/9)

= 4/5 × 9/9

= 4/5…(Solved)

**(g) (6/9 × 3/4) + (6/9 × 5/7)**

= 3/6 + 30/63

= 189 + 180/378

= 369/378

= 41/42…(Solved)

**(h) 85/17 ÷ 64/16**

= 85/17 × 16/64

= 5/4…(Solved)

**Question no – (2) **

**Solution : **

To prove commutative property,

**1st,** (7/8 + 4/6)

= 21 + 16/24

= 37/24

**2nd,** (4/6 + 7/8)

= 16 + 21/24

= 37/24

**∴** 1st = 2nd

Therefore, Commutative property holds.

**Question no – (3) **

**Solution : **

To prove associative property,

**1st,** (7/8 + 2/5) + 8/3

= (35 + 16/40) + 8/3

= 51/40 + 8/3

= 153 + 320/120

= 473/120

**2nd,** 7/8 + (2/5 + 8/3)

= 7/8 + (6 + 40/15)

= 7/8 + 46/15

= 105 + 368/120

= 473/120

**∴** 1st = 2nd

Therefore, Associative property holds.

**Question no – (4) **

**Solution : **

To prove Commutative property,

**1st,** 7/11 – 6/5

= 35 – 66/55

= – 31/55

**2nd,** 6/5 – 7/11

= 66 – 35/55

= 31/55

**∴** 31/55 ≠ – 31/55

Therefore, Commutative property not hold.

**Question no – (5) **

**Solution : **

To prove Associative property,

**1st,** 8/9 – (9/10 – 2/5)

= 8/9 – (9 – 4/10)

= 8/9 – 5/10

= 80 – 45/90

= 35/90

= 7/18

**2nd,** (8/9 – 9/10) – 2/5

= 80 – 81/90 – 2/5

= – 1/90 – 2/5

= – 1/90 – 2/5

= – 1 – 36/90

= – 37/90

**∴** 7/18 ≠ – 37/90

Therefore, Associative property does not hold.

**Question no – (6) **

**Solution : **

**(a)** **L.H.S,** (5/125 × 36/6) × 100/24

= (6/25 × 100/24)

= 1

**R.H.S,** 5/125 × (36/6 × 100/24)

= 1/25 × (6 × 100/24)

= 1/25 × 25

= 1

**∴** L.H.S = R.H.S

**(b) L.H.S,** 5/4 × (54/48 + 105/75)

= 5/4 × (9/8 + 21/15)

= 5/4 × (9/8 + 7/5)

= 5/4 × (45 + 56/40)

= 5/4 × (101/40)

= 101/32

**R.H.S,** (5/4 × 54/48) + (5/4 × 105/75)

= 45/32 + 35/20

= 225 + 280/160

= 505/160

= 101/32

**∴** L.H.S = R.H.S

**∴** Distribution property.

**Question no – (7)**

**Solution : **

Given, 4/5 × (125/64 + 75/48) × 5/4 × (64/125 + 48/75)

= 4/5 × (375 + 300/192) × 5/4 × (192 + 240/375)

= 4/5 × 675/192 × 5/4 × 432/375

= 9 × 432/192 × 5

= 81/20

= 4 1/20…(Simplified)

**Rational Numbers Exercise 1.3 Solution : **

**Question no – (1) **

**Solution : **

Required buckets,

= 65 1/2 ÷ 5 3/4

= 131/2 ÷ 23/4

= 131/2 × 4/23

= 262/23

= 11 9/23

Therefore, 11 9/23 bucket’s of paint will required in all.

**Question no – (2) **

**Solution : **

Invest amount = 5 3/5 Lakhs

= 5L + 3/5 × 10,0000

= 5,60,00 Rs

Profit = 7000 + 1/4 × 1000

= 7250 Rs

**∴** Capital Expenditure

= (5,60,000 + 7250) Rs

= 567250 Rs

Therefore, Rs 567250 will available for expenditure.

**Question no – (3) **

**Solution : **

Speed = 255km/1 1/2h

= 255/3/2

= 255 × 2/3

= 170 km/h

**∴** Distance cover = (170 × 3 4/5) km

= (170 × 19/5)

= 646 km

Therefore, the speed of the train will be 170 km/h and distance cover in 3 hours will be 646 km.

**Next Chapter Solution : **

👉 Chapter 2 👈